The document provides a course calendar and summary score sheet for a differential equations class over two quarters. It lists the dates, topics to be covered from the textbook, assigned problem sets and projects, and spaces to record scores on quizzes, problem sets, and final grades. The course covers key topics in differential equations over 31 class days each quarter, including definitions, families of curves, exact and linear equations, integrating factors, undetermined coefficients, variation of parameters, and Laplace transforms. It assesses students with three long quizzes and records their ongoing and total scores on problem sets and projects.
MIT Math Syllabus 10-3 Lesson 5: Complex numbersLawrence De Vera
The document discusses complex numbers. It introduces the imaginary unit i, where i2 = -1. A complex number is defined as a number of the form a + bi, where a is the real part and b is the imaginary part. The key operations of addition, subtraction, multiplication and division are defined for complex numbers. It also discusses powers of i, noting that i4 = 1, so in powers of i, the remainder of dividing the exponent by 4 determines the value of in.
Indonesia has a population of over 241 million people as of 2011 according to BKKBN census data, with an expected growth rate of 3.5 million people annually. The majority religion in Indonesia is Islam, which is practiced by over 200 million Indonesians, though other religions such as Christianity, Buddhism, Hinduism and Confucianism are also recognized. Indonesia has over 17,000 islands and is the world's largest archipelago, spanning over 5.8 million square kilometers of water. Some of the largest cities in Indonesia include Jakarta, Surabaya, Bekasi, Depok and Bandung.
This document provides information about wood carving motifs and techniques in Indonesia, with a focus on Jepara. It begins with background on Indonesia's history, culture, and wood carving motifs from different regions. It then discusses simple, moderate, and complex motif designs. The document presents a case study on Jepara, describing its history and importance for wood carving. Specific techniques used in Jepara include carving teak wood boxes featuring lotus motifs. Teak wood and tools like chisels and hammers are the primary materials used for wood carving in Jepara.
Helmi, Komodo Dragon, National Park Indonesia, Presentation, Galapagos Equa...Helmi .
1) Komodo dragons still exist on 5 islands within Komodo National Park in Indonesia, including an estimated population of over 3,000 dragons spread across the islands.
2) The park contains diverse terrestrial and marine habitats that are home to over 1,000 fish species, 385 coral species, mangroves, and sea grass, and is a UNESCO World Heritage Site designated to protect biodiversity including the Komodo dragon.
3) Park management goals include ensuring the long-term survival of Komodo dragons, sustainable use of resources for tourism, education and research, and protecting fish and invertebrate stocks.
Ict, culture and future indonesia narendra wYudi Herdiana
Narenda Wicaksono discusses Microsoft's mobile strategy in Indonesia, including:
1. Promoting operator billing to increase access to mobile payments in Indonesia where credit card penetration is low.
2. Highlighting top-grossing apps in Indonesia that use operator billing and have achieved over 1 million downloads and $1 billion in revenue.
3. Announcing the DVLUP Olympiad competition for university students to develop apps using Microsoft's open innovation platforms and APIs for opportunities to win prizes.
Japan Asean Digital Content Developer ForumMarlin Sugama
This presentation was chosen to represent Indonesia in Japan ASEAN digital content developer forum- a meeting between Japan and ASEAN countries to discuss collaboration possibilits
This document provides information about poverty in Indonesia, including statistics and cultural factors. Some key points:
- 13.33% of Indonesia's population, or 31.02 million people, lived below the poverty line in 2010 according to government statistics. The provinces with the highest poverty rates were Papua, West Papua, and Maluku.
- Poverty is defined as the inability to meet basic food needs based on average per capita expenditures. Poverty indices show the extent individuals fall below the poverty line and inequality among the poor.
- Cultural characteristics like a sense of helplessness and not belonging are proposed to contribute to the cycle of poverty according to the "culture of poverty" concept. Developing
MIT Math Syllabus 10-3 Lesson 5: Complex numbersLawrence De Vera
The document discusses complex numbers. It introduces the imaginary unit i, where i2 = -1. A complex number is defined as a number of the form a + bi, where a is the real part and b is the imaginary part. The key operations of addition, subtraction, multiplication and division are defined for complex numbers. It also discusses powers of i, noting that i4 = 1, so in powers of i, the remainder of dividing the exponent by 4 determines the value of in.
Indonesia has a population of over 241 million people as of 2011 according to BKKBN census data, with an expected growth rate of 3.5 million people annually. The majority religion in Indonesia is Islam, which is practiced by over 200 million Indonesians, though other religions such as Christianity, Buddhism, Hinduism and Confucianism are also recognized. Indonesia has over 17,000 islands and is the world's largest archipelago, spanning over 5.8 million square kilometers of water. Some of the largest cities in Indonesia include Jakarta, Surabaya, Bekasi, Depok and Bandung.
This document provides information about wood carving motifs and techniques in Indonesia, with a focus on Jepara. It begins with background on Indonesia's history, culture, and wood carving motifs from different regions. It then discusses simple, moderate, and complex motif designs. The document presents a case study on Jepara, describing its history and importance for wood carving. Specific techniques used in Jepara include carving teak wood boxes featuring lotus motifs. Teak wood and tools like chisels and hammers are the primary materials used for wood carving in Jepara.
Helmi, Komodo Dragon, National Park Indonesia, Presentation, Galapagos Equa...Helmi .
1) Komodo dragons still exist on 5 islands within Komodo National Park in Indonesia, including an estimated population of over 3,000 dragons spread across the islands.
2) The park contains diverse terrestrial and marine habitats that are home to over 1,000 fish species, 385 coral species, mangroves, and sea grass, and is a UNESCO World Heritage Site designated to protect biodiversity including the Komodo dragon.
3) Park management goals include ensuring the long-term survival of Komodo dragons, sustainable use of resources for tourism, education and research, and protecting fish and invertebrate stocks.
Ict, culture and future indonesia narendra wYudi Herdiana
Narenda Wicaksono discusses Microsoft's mobile strategy in Indonesia, including:
1. Promoting operator billing to increase access to mobile payments in Indonesia where credit card penetration is low.
2. Highlighting top-grossing apps in Indonesia that use operator billing and have achieved over 1 million downloads and $1 billion in revenue.
3. Announcing the DVLUP Olympiad competition for university students to develop apps using Microsoft's open innovation platforms and APIs for opportunities to win prizes.
Japan Asean Digital Content Developer ForumMarlin Sugama
This presentation was chosen to represent Indonesia in Japan ASEAN digital content developer forum- a meeting between Japan and ASEAN countries to discuss collaboration possibilits
This document provides information about poverty in Indonesia, including statistics and cultural factors. Some key points:
- 13.33% of Indonesia's population, or 31.02 million people, lived below the poverty line in 2010 according to government statistics. The provinces with the highest poverty rates were Papua, West Papua, and Maluku.
- Poverty is defined as the inability to meet basic food needs based on average per capita expenditures. Poverty indices show the extent individuals fall below the poverty line and inequality among the poor.
- Cultural characteristics like a sense of helplessness and not belonging are proposed to contribute to the cycle of poverty according to the "culture of poverty" concept. Developing
This document provides an overview of Indonesia, including its location, flag, religions, festivals, culture, national costumes, population, and area. Some key details include Indonesia has a population of 249.9 million people as of 2016 and spans an area of 1,905,000 square kilometers. The religions practiced are Islam, Protestantism, Roman Catholicism, Hinduism, and Buddhism. Festivals celebrated include Ramadan, Id-al-Fitr, and Eid al-Fitr. Elements of Indonesian culture discussed are gamelan music, Balinese dances like barong and rangda and kecak, Balinese painting, and national costumes like batik, kebaya, and peci.
The document provides an overview of Indonesia's history, political structure, contemporary economic system, and key challenges for government and business. It outlines Indonesia's history from Japanese occupation to recent democratic transformations. It describes the current political system including the president, parties, and branches of government. It also details the key industries, trade partners, GDP, and exchange rates of Indonesia's economic system. Finally, it discusses challenges such as corruption, bureaucracy, and terrorism that the government and businesses face.
Indonesia has implemented several initiatives to expand ICT access across its thousands of islands. These include the Palapa Ring broadband fiber optic network to connect more regions, and mobile M-PLIK vehicles that provide affordable Internet access in rural areas. While these have increased connectivity, challenges remain in fully funding infrastructure and addressing issues like uneven resource distribution and software piracy. Lessons indicate that expanding broadband access can significantly increase economic growth, and that universal access is important for development.
Indonesia is an ethnically and culturally diverse country made up of over 17,000 islands. It has the world's largest Muslim population and has a history of being influenced by various religions and foreign powers. Some key aspects of managing cross-culturally in Indonesia include maintaining strict hierarchies, building trust and personal relationships over long periods of time, and avoiding direct confrontation, as decision making focuses on consensus building and maintaining harmony. Paternalistic leadership is common, and flexibility to changes requires a proven track record.
1) The document outlines the course outcomes for Calculus I with Analytic Geometry. It discusses fundamental concepts like analytic geometry, functions, limits, continuity, derivatives, and their applications.
2) The course aims to teach students to analyze and solve problems involving lines, circles, conics, transcendental functions, derivatives, tangents, normals, maxima/minima, and related rates.
3) The assessment tasks and grading criteria are also presented, including quizzes, classwork, and a final examination. Minimum averages for satisfactory performance are provided.
MIT Math Syllabus 10-3 Lesson 1: Sets and the real number systemLawrence De Vera
1) The document discusses sets and the real number system in algebra. It defines a set as a well-defined collection of distinct objects and describes important sets like the set of real numbers.
2) It explains different ways to describe sets using roster/listing and rule/set-builder notation with examples. It also covers set relationships like subsets, intersections, unions and uses Venn diagrams to illustrate these relationships.
3) The last part defines operations on sets such as union, intersection, complement, difference and Cartesian product with examples. It concludes by defining the real number system as the union of rational and irrational numbers.
Analisa Isu-Isu Strategis RPJMD Propinsi Maluku UtaraOswar Mungkasa
Dokumen tersebut membahas analisis isu-isu strategis yang menjadi dasar penyusunan Rencana Pembangunan Jangka Menengah Provinsi Maluku Utara periode 2014-2018. Isu-isu strategis yang diidentifikasi antara lain pembangunan infrastruktur seperti jalan dan jembatan serta upaya meningkatkan daya saing ekonomi provinsi.
This short document does not contain any meaningful information to summarize in 3 sentences or less. It only contains blank lines and the words "THANK YOU", which provides no context or details about any topic.
Indonesia is an archipelago located in Southeast Asia consisting of over 17,000 islands with a population of over 238 million people. It has a diverse cuisine that varies by region and has been influenced by Indian, Middle Eastern, Chinese, and European cuisines. Some popular Indonesian dishes include nasi goreng, gado-gado, sate, and soto, which are considered national dishes. Fast food prices range from approximately 5,000 to 100,000 rupiah while meal prices are slightly higher, ranging from 8,000 to 150,000 rupiah.
Indonesia is an archipelago located in Southeast Asia known for its beaches, volcanoes, and diverse cuisine including nasi goreng, batagor, and ayam goreng kuning. The country is also home to endangered wildlife like tigers, elephants, and komodo dragons, as well as orangutans. Indonesia has a tropical climate and uses rupiah as its currency, with a long history dating back to ancient Hindu-Buddhist kingdoms and the spread of Islam in later centuries.
A short talk about Indonesia.
Useful for Indonesian students to introduce their countries to foreigners. :)
Also, some travel itineraries suggestions to explore the heritages and precious gems in Indonesia.
The document provides information about resume formats and samples for civil engineers. It includes summaries and examples of 8 common resume types: chronological, functional, curriculum vitae (CV), combination, targeted, professional, new graduate, and executive resumes. It also lists additional resources on resume writing tips and interview questions and answers that may be useful for civil engineers.
Indonesia is an archipelago country made up of over 17,000 islands located in Southeast Asia. It has a population of over 240 million people and its capital and largest city is Jakarta. The national language is Indonesian but there are over 700 local languages spoken. Indonesia has a diverse landscape and climate with tropical rainforests, over 10% of the world's flowering plants, and 17% of bird species. It also has significant natural resources like oil, natural gas and minerals.
Pancasila is Indonesia's national philosophy based on five principles of belief in God, just and civilized humanity, the unity of Indonesia, democracy guided by wisdom of deliberations among representatives, and social justice for all people of Indonesia. It was established in 1945 as the foundational philosophy to unite Indonesia's diversity of over 17,000 islands and hundreds of ethnic and religious groups. Indonesia has over 400 volcanoes, making it prone to volcanic eruptions, and is located on the seismically active Ring of Fire. It has a rich variety of endemic flora and fauna as well as cultural traditions across its many islands.
UNICEF Digital Citizenship and Safety- Indonesia presentationAkshay Sinha
This document summarizes information about digital citizenship and safety in Indonesia. It provides an overview of Indonesia's population and economy. It then discusses characteristics of internet usage in Indonesia, including its growth, mobile usage, and digital divide. The document outlines common online activities of Indonesians like social networking, blogging, and streaming. It also examines safety risks such as piracy, sexual content, child exploitation, and terrorism online. The document concludes with recommendations for improving digital safety in Indonesia.
This Indonesia Power Point highlights these facts and much more including: 20 Points on General Information, 8 Points on Family Life, 20 Points on Food, 20 Points on Food Etiquette, 13 Points on Social Etiquette, 27 Points on Business Etiquette, and 14 Points on Trivia.
The document provides information on various types of reference materials like almanacs, atlases, brochures, dictionaries, directories, encyclopedias, experts, magazines, newspapers, and thesauruses. It also discusses different types of writing like narrative and informational. Additionally, it outlines how to use resources in a book including the table of contents, index, glossary, headings, subtitles, captions, footnotes, and taking notes.
The document defines sequences and their different types, including arithmetic and geometric sequences. It provides examples of finding the nth term or general term of sequences given initial terms. It also discusses how to find the common difference of arithmetic sequences and common ratio of geometric sequences. The document explains how to calculate arithmetic means, harmonic means, and geometric means of sequences. It provides information on finding the sums of finite and infinite arithmetic, harmonic, and geometric sequences.
The document discusses polynomial functions. It defines a polynomial function and distinguishes it from other function types. It lists the objectives of understanding degree, using theorems to determine factors and roots, and approximating graphs of polynomial functions. Key points are that every polynomial equation has at least one real or complex root based on the Fundamental Theorem of Algebra, and that a polynomial of degree n will have n roots.
This document provides an overview of Indonesia, including its location, flag, religions, festivals, culture, national costumes, population, and area. Some key details include Indonesia has a population of 249.9 million people as of 2016 and spans an area of 1,905,000 square kilometers. The religions practiced are Islam, Protestantism, Roman Catholicism, Hinduism, and Buddhism. Festivals celebrated include Ramadan, Id-al-Fitr, and Eid al-Fitr. Elements of Indonesian culture discussed are gamelan music, Balinese dances like barong and rangda and kecak, Balinese painting, and national costumes like batik, kebaya, and peci.
The document provides an overview of Indonesia's history, political structure, contemporary economic system, and key challenges for government and business. It outlines Indonesia's history from Japanese occupation to recent democratic transformations. It describes the current political system including the president, parties, and branches of government. It also details the key industries, trade partners, GDP, and exchange rates of Indonesia's economic system. Finally, it discusses challenges such as corruption, bureaucracy, and terrorism that the government and businesses face.
Indonesia has implemented several initiatives to expand ICT access across its thousands of islands. These include the Palapa Ring broadband fiber optic network to connect more regions, and mobile M-PLIK vehicles that provide affordable Internet access in rural areas. While these have increased connectivity, challenges remain in fully funding infrastructure and addressing issues like uneven resource distribution and software piracy. Lessons indicate that expanding broadband access can significantly increase economic growth, and that universal access is important for development.
Indonesia is an ethnically and culturally diverse country made up of over 17,000 islands. It has the world's largest Muslim population and has a history of being influenced by various religions and foreign powers. Some key aspects of managing cross-culturally in Indonesia include maintaining strict hierarchies, building trust and personal relationships over long periods of time, and avoiding direct confrontation, as decision making focuses on consensus building and maintaining harmony. Paternalistic leadership is common, and flexibility to changes requires a proven track record.
1) The document outlines the course outcomes for Calculus I with Analytic Geometry. It discusses fundamental concepts like analytic geometry, functions, limits, continuity, derivatives, and their applications.
2) The course aims to teach students to analyze and solve problems involving lines, circles, conics, transcendental functions, derivatives, tangents, normals, maxima/minima, and related rates.
3) The assessment tasks and grading criteria are also presented, including quizzes, classwork, and a final examination. Minimum averages for satisfactory performance are provided.
MIT Math Syllabus 10-3 Lesson 1: Sets and the real number systemLawrence De Vera
1) The document discusses sets and the real number system in algebra. It defines a set as a well-defined collection of distinct objects and describes important sets like the set of real numbers.
2) It explains different ways to describe sets using roster/listing and rule/set-builder notation with examples. It also covers set relationships like subsets, intersections, unions and uses Venn diagrams to illustrate these relationships.
3) The last part defines operations on sets such as union, intersection, complement, difference and Cartesian product with examples. It concludes by defining the real number system as the union of rational and irrational numbers.
Analisa Isu-Isu Strategis RPJMD Propinsi Maluku UtaraOswar Mungkasa
Dokumen tersebut membahas analisis isu-isu strategis yang menjadi dasar penyusunan Rencana Pembangunan Jangka Menengah Provinsi Maluku Utara periode 2014-2018. Isu-isu strategis yang diidentifikasi antara lain pembangunan infrastruktur seperti jalan dan jembatan serta upaya meningkatkan daya saing ekonomi provinsi.
This short document does not contain any meaningful information to summarize in 3 sentences or less. It only contains blank lines and the words "THANK YOU", which provides no context or details about any topic.
Indonesia is an archipelago located in Southeast Asia consisting of over 17,000 islands with a population of over 238 million people. It has a diverse cuisine that varies by region and has been influenced by Indian, Middle Eastern, Chinese, and European cuisines. Some popular Indonesian dishes include nasi goreng, gado-gado, sate, and soto, which are considered national dishes. Fast food prices range from approximately 5,000 to 100,000 rupiah while meal prices are slightly higher, ranging from 8,000 to 150,000 rupiah.
Indonesia is an archipelago located in Southeast Asia known for its beaches, volcanoes, and diverse cuisine including nasi goreng, batagor, and ayam goreng kuning. The country is also home to endangered wildlife like tigers, elephants, and komodo dragons, as well as orangutans. Indonesia has a tropical climate and uses rupiah as its currency, with a long history dating back to ancient Hindu-Buddhist kingdoms and the spread of Islam in later centuries.
A short talk about Indonesia.
Useful for Indonesian students to introduce their countries to foreigners. :)
Also, some travel itineraries suggestions to explore the heritages and precious gems in Indonesia.
The document provides information about resume formats and samples for civil engineers. It includes summaries and examples of 8 common resume types: chronological, functional, curriculum vitae (CV), combination, targeted, professional, new graduate, and executive resumes. It also lists additional resources on resume writing tips and interview questions and answers that may be useful for civil engineers.
Indonesia is an archipelago country made up of over 17,000 islands located in Southeast Asia. It has a population of over 240 million people and its capital and largest city is Jakarta. The national language is Indonesian but there are over 700 local languages spoken. Indonesia has a diverse landscape and climate with tropical rainforests, over 10% of the world's flowering plants, and 17% of bird species. It also has significant natural resources like oil, natural gas and minerals.
Pancasila is Indonesia's national philosophy based on five principles of belief in God, just and civilized humanity, the unity of Indonesia, democracy guided by wisdom of deliberations among representatives, and social justice for all people of Indonesia. It was established in 1945 as the foundational philosophy to unite Indonesia's diversity of over 17,000 islands and hundreds of ethnic and religious groups. Indonesia has over 400 volcanoes, making it prone to volcanic eruptions, and is located on the seismically active Ring of Fire. It has a rich variety of endemic flora and fauna as well as cultural traditions across its many islands.
UNICEF Digital Citizenship and Safety- Indonesia presentationAkshay Sinha
This document summarizes information about digital citizenship and safety in Indonesia. It provides an overview of Indonesia's population and economy. It then discusses characteristics of internet usage in Indonesia, including its growth, mobile usage, and digital divide. The document outlines common online activities of Indonesians like social networking, blogging, and streaming. It also examines safety risks such as piracy, sexual content, child exploitation, and terrorism online. The document concludes with recommendations for improving digital safety in Indonesia.
This Indonesia Power Point highlights these facts and much more including: 20 Points on General Information, 8 Points on Family Life, 20 Points on Food, 20 Points on Food Etiquette, 13 Points on Social Etiquette, 27 Points on Business Etiquette, and 14 Points on Trivia.
The document provides information on various types of reference materials like almanacs, atlases, brochures, dictionaries, directories, encyclopedias, experts, magazines, newspapers, and thesauruses. It also discusses different types of writing like narrative and informational. Additionally, it outlines how to use resources in a book including the table of contents, index, glossary, headings, subtitles, captions, footnotes, and taking notes.
The document defines sequences and their different types, including arithmetic and geometric sequences. It provides examples of finding the nth term or general term of sequences given initial terms. It also discusses how to find the common difference of arithmetic sequences and common ratio of geometric sequences. The document explains how to calculate arithmetic means, harmonic means, and geometric means of sequences. It provides information on finding the sums of finite and infinite arithmetic, harmonic, and geometric sequences.
The document discusses polynomial functions. It defines a polynomial function and distinguishes it from other function types. It lists the objectives of understanding degree, using theorems to determine factors and roots, and approximating graphs of polynomial functions. Key points are that every polynomial equation has at least one real or complex root based on the Fundamental Theorem of Algebra, and that a polynomial of degree n will have n roots.
This document defines functions and relations. It discusses identifying the domain and range of functions and relations, evaluating functions, and performing operations on functions such as addition, subtraction, multiplication, division, and composition. It also covers graphing functions, including piecewise functions, absolute value functions, greatest and least integer functions. Key examples are provided to illustrate how to identify domains and ranges, evaluate functions, perform operations on functions, and graph different types of functions.
Malaysian and Indonesian literature share a common linguistic ancestor before the arrival of Islam in the 14th century. Early Malay literature was influenced by Indian epics, while 19th century works included religious texts, romances, and tales. Indonesian literature can be divided into periods such as the Pujangga Lama (Old Poets) and AngkatanBalaiPustaka (Colonial Office for Popular Literature generation). Major genres include syair (narrative poetry), pantun (quatrains), and hikayat (stories and chronicles). By the 1920s, fiction and Western-style works replaced earlier forms. Thai traditional literature focused on Buddhism and Hinduism through various emotive verse forms, exempl
This document covers exponential and logarithmic functions, including their definitions, graphs, properties, and applications. Some key points are:
- Exponential functions have the form f(x) = bx where b is the base. Their graphs stretch upwards and have asymptotes at the x-axis.
- The natural exponential function is f(x) = ex.
- Logarithmic functions are the inverses of exponential functions and have the form f(x) = logbx. Their graphs stretch downwards and have asymptotes at the y-axis.
- Properties of exponents and logarithms include the change of base formula and rules for simplifying expressions.
- Exponential and logarithmic equations can be solved
Spherical trigonometry concerns triangles on the surface of a sphere, with formulas to solve for unknown sides and angles of spherical triangles based on relationships between opposite, adjacent, and included parts. Formulas are provided for right, oblique, and general spherical triangles, along with the six cases for solving oblique triangles based on given parts. Examples demonstrate applying the formulas to solve various spherical triangle problems.
The document derives the Law of Sines and Law of Cosines, which relate the angles and sides of triangles. It discusses using these laws to solve oblique triangles given certain information like two angles and a side, two sides and the angle opposite one of the sides, two sides and the angle between them, or all three sides. It also covers finding the area of a triangle given two sides and the included angle, or using Heron's Formula with all three sides. Application problems demonstrate using these concepts to solve real-world geometry problems.
Trigonometric equations involve trigonometric functions and can be solved using algebraic techniques like isolating variables, collecting like terms, and factoring. There are two types of trigonometric equations: identical equations that are true for all values of the variable, and conditional equations that are true for some but not all values. To solve trigonometric equations, one should use identities to obtain a single function, substitute values to solve for an angle, or use the quadratic formula if a single function is quadratic.
The document defines inverse trigonometric functions. It states that trigonometric functions are not one-to-one but their domains can be restricted to make them one-to-one, allowing inverses. The inverses of sinx, cosx, tanx, cotx, secx, and cscx are then defined. Examples are given of finding exact values of inverse trigonometric functions.
The document provides information about solving systems of linear and nonlinear equations:
- It discusses the three types of solutions to systems of linear equations in two and three variables - one solution, no solution, and infinitely many solutions. Methods for solving include substitution, elimination, and graphing.
- Systems of nonlinear equations like quadratics are also introduced.
- Several examples of application problems involving systems of equations with two or three variables are presented and solved.
This document provides an overview of trigonometric identities and examples of their applications. It discusses basic identities, verifying identities, and advanced identities involving sums, differences, doubles angles, and half angles. Examples are provided for applying product-to-sum and sum-to-product identities. The objectives are to review and apply various trigonometric identities to simplify expressions and evaluate functions.
The document discusses inequalities and their solutions. It defines absolute and conditional inequalities and explains how to represent solutions using interval, set, and graphical notation. Methods are presented for solving linear, polynomial, rational, and absolute value inequalities. Key steps include determining intervals where an expression is positive or negative, identifying valid intervals based on inequality signs, and expressing the solution in interval notation. Examples are provided throughout to demonstrate these techniques.
The document discusses various methods for solving quadratic equations, including factoring, square root method, completing the square, and the quadratic formula. It also covers solving other types of equations that are quadratic in form, such as radical equations, through transformations. The objectives are to solve quadratic, radical, and other equations that are quadratic in form and to find sums and products of roots, the quadratic equation given roots, and solve application problems involving these equation types.
The document provides an overview of lessons on linear equations for a math class over 3 days. Key points covered include:
- Day 1 focuses on defining linear equations, properties of equality, and solving linear and rational equations.
- Day 2 covers solving equations involving radicals, absolute values, and literal equations.
- Day 3 involves word problems including number, geometry, digit, investment, age, mixture, uniform motion, work, and clock problems that can be modeled and solved using linear equations.
Kong Zi was a philosopher who proposed a socio-political-moral philosophy based on benevolence, righteousness, propriety, wisdom, and sincerity. He aimed to create an ideal, harmonious society with well-ordered structure and citizens with mutual obligations. Kong Zi transmitted ancient wisdom through instruction, rather than proposing new ideas or religion. His teachings were recorded in Lun Yu as instructive sayings between Kong Zi and his disciples. Key concepts in his philosophy included Ren (benevolence or goodness), Zhong (rectitude), Yi (duty), Li (ritual propriety), and Zhi (wisdom and virtue).
This document discusses different types of variation that can be used to model relationships between quantities: direct variation occurs when one quantity is directly proportional to another; inverse variation occurs when one quantity is inversely proportional to another; joint variation occurs when one quantity is proportional to the product of two or more other quantities; and combined variation occurs when one quantity is directly proportional to some quantities and inversely proportional to others. Examples are provided to illustrate direct, inverse, joint and combined variation and how to write equations to describe each type of variation. Classwork and homework exercises are assigned for students to practice applying these concepts.
This document discusses graphs of trigonometric functions. It aims to teach students how to develop properties of trig functions, find the amplitude, period, phase shift and vertical shift from equations, and graph trig functions. Examples are provided to illustrate finding these characteristics from trig function equations and using them to graph the functions.
The educational system in the Philippines took over 3 and a half centuries to develop after the Spanish colonized the islands. The Spanish friars first introduced parochial schools modeled after those used in Europe during the Dark Ages. In 1591, Governor Dasmarinas ordered that taxes from land grants be used to support schools, though the friars taught in native dialects rather than Spanish. The early schools run by friars were simple primary schools focused on religious instruction, not graded systems, and were governed by the friars with little oversight. Formal schools began emerging in the 18th and 19th centuries focused on subjects like artillery, navigation, commerce, and the arts.
1) This document provides lesson objectives and examples for solving right triangles using trigonometric functions, the Pythagorean theorem, and angle relationships. It defines trigonometric ratios, angle of elevation/depression, bearing, and course.
2) Examples are provided to solve right triangles, find missing angles and sides, and solve real-world problems involving width of a stream, height of a flagpole, camera angle of depression, and height of a tower.
3) Additional examples solve problems involving slant distance to a sunken ship, plane bearings and courses between locations, and references are provided for further reading.
This document discusses trigonometric functions of right triangles. It defines the six trigonometric functions as ratios of the sides of a right triangle. It also discusses reciprocal functions, the Pythagorean theorem, functions of complementary angles, and the trigonometric functions of specific angles like 45°, 30° and 60° degrees. Examples are provided to evaluate trigonometric functions and to solve right triangles.
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Introducing Milvus Lite: Easy-to-Install, Easy-to-Use vector database for you...Zilliz
Join us to introduce Milvus Lite, a vector database that can run on notebooks and laptops, share the same API with Milvus, and integrate with every popular GenAI framework. This webinar is perfect for developers seeking easy-to-use, well-integrated vector databases for their GenAI apps.
Enchancing adoption of Open Source Libraries. A case study on Albumentations.AIVladimir Iglovikov, Ph.D.
Presented by Vladimir Iglovikov:
- https://www.linkedin.com/in/iglovikov/
- https://x.com/viglovikov
- https://www.instagram.com/ternaus/
This presentation delves into the journey of Albumentations.ai, a highly successful open-source library for data augmentation.
Created out of a necessity for superior performance in Kaggle competitions, Albumentations has grown to become a widely used tool among data scientists and machine learning practitioners.
This case study covers various aspects, including:
People: The contributors and community that have supported Albumentations.
Metrics: The success indicators such as downloads, daily active users, GitHub stars, and financial contributions.
Challenges: The hurdles in monetizing open-source projects and measuring user engagement.
Development Practices: Best practices for creating, maintaining, and scaling open-source libraries, including code hygiene, CI/CD, and fast iteration.
Community Building: Strategies for making adoption easy, iterating quickly, and fostering a vibrant, engaged community.
Marketing: Both online and offline marketing tactics, focusing on real, impactful interactions and collaborations.
Mental Health: Maintaining balance and not feeling pressured by user demands.
Key insights include the importance of automation, making the adoption process seamless, and leveraging offline interactions for marketing. The presentation also emphasizes the need for continuous small improvements and building a friendly, inclusive community that contributes to the project's growth.
Vladimir Iglovikov brings his extensive experience as a Kaggle Grandmaster, ex-Staff ML Engineer at Lyft, sharing valuable lessons and practical advice for anyone looking to enhance the adoption of their open-source projects.
Explore more about Albumentations and join the community at:
GitHub: https://github.com/albumentations-team/albumentations
Website: https://albumentations.ai/
LinkedIn: https://www.linkedin.com/company/100504475
Twitter: https://x.com/albumentations
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Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
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1. COURSE CALENDAR AND SUMMARY SCORE SHEET - DIFFERENTIAL EQUATIONS
Second Qtr SY 2008 - 2009
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS PROBLEM SET AND PROJECT SCORES
1 9/29/2008 Orientation S A
2 10/1/2008 Definitions/Elimination of Arbitrary Constants pp. 1 - 5/pp. 6 - 10 7th ed A1 20/10, 24/10
3 10/3/2008 Families of Curves/ Separation of Variables pp. 10 - 16 7th ed/ pp. 18 - 23 8th ed. A2 15/15, 21/15 // 9/23, 21/23
4 10/6/2008 Equations with Homogeneous Coefficients pp. 25 - 29 A3 9/28, 17/28
5 10/8/2008 Exact Equations pp. 29 - 34 A4 15/34, 19/34
6 10/10/2008 The Linear Equation of Order One pp. 35 - 43 A5 21/40, 23/40
7 10/13/2008 Integrating Factors Found by Inspection pp. 75 - 79 A6 19/78, 25/78
8 10/15/2008 The Determination of Integrating Factors pp. 79 - 83 A7 11/83, 19/84
9 10/17/2008 LONG QUIZ 1 SCORE LQ1: /100 TOTAL PROBLEM SET A
10 10/20/2008 Substitution Suggested by the Equation pp. 84 - 86
11 10/22/2008 Bernoulli’s Equation pp. 86 - 89 B1 10/88, 15/89, 19/89
12 10/24/2008 Coefficients Linear in the Two Variables pp. 89 - 94 B2 9/93, 19/93
13 10/27/2008 Orthogonal Trajectories/ Newton's Law of Cooling pp. 59 - 62 7th ed/ pp.64 - 65 8th. Ed B3 19/62, 23/62 // 7/66
14 10/29/2008 Law of Growth and Decay/ Simple Interest pp. 65 - 69 B4 9/66, 15/67
15 10/31/2008 Newtons Second law of Motion/ Mixture Problems pp. 65 - 69 B5 22/68
16 11/3/2008 Logistic Growth pp. 69 - 73 B6 3/72,
17 11/5/2008 Simple Electric Circuits pp. 68 # 20 and 21
18 11/7/2008 LONG QUIZ 2 SCORE LQ2: /100 TOTAL PROBLEM SET B
19 11/10/2008 Differential Operators pp. 109 - 116
20 11/12/2008 Linear Equations with Constant Coefficients pp. 117 - 133 P1 pp.131-132, all odd
21 11/14/2008 The Method of Undetermined Coefficients pp. 139 - 144 P2 pp.142-143, 1-43 all odd
22 11/17/2008 Variation of Parameters pp. 156 - 164 P3 pp.162, 1-18 all odd
23 11/19/2008 Inverse Differential Operators pp 152 - 158 7th ed.
24 11/21/2008 Laplace Transforms pp. 252 - 257
25 11/24/2008 Definition of an Inverse Transforms pp. 274 - 277
26 11/26/2008 Partial Fractions pp. 277 - 280 P4 pp.280, 1-10
27 11/28/2008 LONG QUIZ 3 SCORE LQ3: /100 TOTAL PROJECT
28 12/1/2008 Initial Value Problem pp. 280 - 285
29 12/3/2008 A Step Function pp. 286 - 293
30 12/5/2008 Submission of Portfolio and Grade Verification /300 GRAND TOTAL
31 12/8/2008 FINAL EXAMS WEEK AVERAGE
Faculty in Charge: Dr. DANTE L. SILVA
Mapua Institute of Technology - Mathematics Department
Textbook: ELEMENTARY DIFFERENTIAL EQUATIONS, 7th and 8th EDITION
by: Rainville, Bedient, Bedient
2. COURSE CALENDAR AND SUMMARY SCORE SHEET - DIFFERENTIAL EQUATIONS
Third Qtr SY 2008 - 2009
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS PROBLEM SETS SCORES
1 1/5/2009 Orientation S A
2 1/7/2009 Definitions/Elimination of Arbitrary Constants pp. 1 - 5/pp. 6 - 10 7th ed A1 19/10, 21/10
3 1/9/2009 Families of Curves/ Separation of Variables pp. 10 - 16 7th ed/ pp. 18 - 23 8th ed. A2 16/15, 20/15 // 10/23, 32/23
4 1/12/2009 Equations with Homogeneous Coefficients pp. 25 - 29 8th ed A3 10/28, 20/28
5 1/14/2009 Exact Equations pp. 29 - 34 8th ed A4 16/34, 17/34
6 1/16/2009 The Linear Equation of Order One pp. 35 - 43 8th ed A5 22/40, 28/40
7 1/19/2009 Integrating Factors Found by Inspection pp. 75 - 79 8th ed A6 18/78, 20/78
8 1/21/2009 The Determination of Integrating Factors pp. 79 - 83 8th ed A7 12/83, 20/84
9 1/23/2002 LONG QUIZ 1 SCORE LQ1: /100 TOTAL PROBLEM SET A
10 1/26/2009 Substitution Suggested by the Equation pp. 84 - 86 8th ed
11 1/28/2009 Bernoulli’s Equation pp. 86 - 89 8th ed B1 11/88, 20/89
12 1/30/2009 Coefficients Linear in the Two Variables pp. 89 - 94 8th ed B2 10/93, 18/93
13 2/2/2009 Orthogonal Trajectories/ Newton's Law of Cooling pp. 59 - 62 7th ed/ pp.64 - 65 8th. Ed B3 19/62, 23/62 // 7/66
14 2/4/2009 Law of Growth and Decay/ Simple Interest pp. 65 - 69 8th ed B4 9/66, 15/67
15 2/6/2009 Newtons Second law of Motion/ Mixture Problems pp. 65 - 69 8th ed B5 22/68
16 2/9/2009 Logistic Growth/Prices of Commodities pp. 69 - 73 8th ed B6 3/72, 9/73
17 2/11/2009 Simple Electric Circuits pp. 68 # 20 and 21 8th ed
18 2/13/2009 LONG QUIZ 2 SCORE LQ2: /100 TOTAL PROBLEM SET B
19 2/16/2009 Uniqueness Theorem/Differential Operators pp. 100 - 109//pp. 109 - 116 8th ed C1 5/102, 7/105, 3/115
20 2/18/2009 Linear Equations with Constant Coefficients pp. 117 - 133 8th ed C2 15/119, 18/123, 17/130
21 2/20/2009 Construction of Homogeneous Equation pp. 134 - 136 8th ed C3 5/136, 18/136
22 2/23/2009 The Method of Undetermined Coefficients pp. 139 - 144 8th ed C4 27/143, 39/143
23 2/25/2009 Variation of Parameters pp. 156 - 164 8th ed C5 4/162, 6/162
24 2/27/2009 Inverse Differential Operators pp 152 - 158 7th ed.
25 3/2/2009 Laplace Transforms pp. 252 - 257 8th ed
26 3/4/2009 Definition of an Inverse Transforms pp. 274 - 277 8th ed
27 3/6/2009 LONG QUIZ 3 SCORE LQ3: /100 TOTAL PROBLEM SET C
28 3/9/2009 Partial Fractions pp. 277 - 280 8th ed P1 pp.280, 1-10
29 3/11/2009 Initial Value Problem pp. 280 - 285 8th ed
30 3/13/2009 Submission of Portfolio and Grade Verification
31 3/16/2009 FINAL EXAM /300 GRAND TOTAL
Faculty in Charge: Dr. DANTE L. SILVA Textbook: ELEMENTARY DIFFERENTIAL EQUATIONS, 7th and 8th EDITION
Mapua Institute of Technology - Mathematics Department by: Rainville, Bedient, Bedient
3. COURSE CALENDAR AND SUMMARY SCORE SHEET - DIFFERENTIAL EQUATIONS
Fourth Qtr SY 2008 - 2009
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS PROBLEM SETS SCORES
1 4/20/2009 Orientation S A
2 4/22/2009 Definitions/Elimination of Arbitrary Constants pp. 1 - 5/pp. 6 - 10 7th ed A1 19/10, 21/10
3 4/24/2009 Families of Curves/ Separation of Variables pp. 10 - 16 7th ed/ pp. 18 - 23 8th ed. A2 16/15, 20/15 // 10/23, 32/23
4 4/27/2009 Equations with Homogeneous Coefficients pp. 25 - 29 8th ed A3 10/28, 20/28
5 4/28/2009 Exact Equations pp. 29 - 34 8th ed A4 16/34, 17/34
6 5/1/2009 The Linear Equation of Order One pp. 35 - 43 8th ed A5 22/40, 28/40
7 5/4/2009 Integrating Factors Found by Inspection pp. 75 - 79 8th ed A6 18/78, 20/78
8 5/6/2009 The Determination of Integrating Factors pp. 79 - 83 8th ed A7 12/83, 20/84
9 5/8/2009 LONG QUIZ 1 SCORE LQ1: /100 TOTAL PROBLEM SET A
10 5/11/2009 Substitution Suggested by the Equation pp. 84 - 86 8th ed
11 5/13/2009 Bernoulli’s Equation pp. 86 - 89 8th ed B1 11/88, 20/89
12 5/15/2009 Coefficients Linear in the Two Variables pp. 89 - 94 8th ed B2 10/93, 18/93
13 5/18/2009 Orthogonal Trajectories/ Newton's Law of Cooling pp. 59 - 62 7th ed/ pp.64 - 65 8th. Ed B3 19/62, 23/62 // 7/66
14 5/20/2009 Law of Growth and Decay/ Simple Interest pp. 65 - 69 8th ed B4 9/66, 15/67
15 5/22/2009 Newtons Second law of Motion/ Mixture Problems pp. 65 - 69 8th ed B5 22/68
16 5/25/2009 Logistic Growth/Prices of Commodities pp. 69 - 73 8th ed B6 3/72, 9/73
17 5/27/2009 Simple Electric Circuits pp. 68 # 20 and 21 8th ed
18 5/29/2009 LONG QUIZ 2 SCORE LQ2: /100 TOTAL PROBLEM SET B
19 6/1/2009 Uniqueness Theorem/Differential Operators pp. 100 - 109//pp. 109 - 116 8th ed C1 5/102, 7/105, 3/115
20 6/3/2009 Linear Equations with Constant Coefficients pp. 117 - 133 8th ed C2 15/119, 18/123, 17/130
21 6/5/2009 Construction of Homogeneous Equation pp. 134 - 136 8th ed C3 5/136, 18/136
22 6/8/2009 The Method of Undetermined Coefficients pp. 139 - 144 8th ed C4 27/143, 39/143
23 6/10/2009 Variation of Parameters pp. 156 - 164 8th ed C5 4/162, 6/162
24 6/12/2009 Inverse Differential Operators pp 152 - 158 7th ed.
25 6/15/2009 Laplace Transforms pp. 252 - 257 8th ed
26 6/17/2009 Definition of an Inverse Transforms pp. 274 - 277 8th ed
27 6/19/2009 LONG QUIZ 3 SCORE LQ3: /100 TOTAL PROBLEM SET C
28 6/22/2009 Partial Fractions pp. 277 - 280 8th ed P1 pp.280, 1-10
29 6/24/2009 Initial Value Problem pp. 280 - 285 8th ed
30 6/26/2009 Submission of Portfolio and Grade Verification
31 6/29/2009 FINAL EXAM /300 GRAND TOTAL
Faculty in Charge: Dr. DANTE L. SILVA Textbook: ELEMENTARY DIFFERENTIAL EQUATIONS, 7th and 8th EDITION
Mapua Institute of Technology - Mathematics Department by: Rainville, Bedient, Bedient
4. COURSE CALENDAR AND SUMMARY SCORE SHEET - DIFFERENTIAL EQUATIONS
First Qtr SY 2009 - 2010
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS PROBLEM SETS SCORES
1 7/20/2009 Orientation S A
2 7/22/2009 Definitions/Elimination of Arbitrary Constants pp. 1 - 5/pp. 6 - 10 7th ed A1 11/10, 17/10
3 7/24/2009 Families of Curves/ Separation of Variables pp. 10 - 16 7th ed/ pp. 18 - 23 8th ed. A2 10/15, 16/15 // 7/23, 28/23
4 7/27/2009 Equations with Homogeneous Coefficients pp. 25 - 29 8th ed A3 5/28, 7/28
5 7/29/2009 Exact Equations pp. 29 - 34 8th ed A4 12/34, 14/34
6 7/31/2009 The Linear Equation of Order One pp. 35 - 43 8th ed A5 18/40, 20/40
7 8/3/2009 Integrating Factors Found by Inspection pp. 75 - 79 8th ed A6 6/78, 8/78
8 8/5/2009 The Determination of Integrating Factors pp. 79 - 83 8th ed A7 2/83, 10/83
9 8/7/2009 LONG QUIZ 1 SCORE LQ1: /100 TOTAL PROBLEM SET A
10 8/10/2009 Substitution Suggested by the Equation pp. 84 - 86 8th ed
11 8/12/2009 Bernoulli’s Equation pp. 86 - 89 8th ed B1 4/88, 6/88
12 8/14/2009 Coefficients Linear in the Two Variables pp. 89 - 94 8th ed B2 4/92, 8/92
13 8/17/2009 Orthogonal Trajectories/ Newton's Law of Cooling pp. 59 - 62 7th ed/ pp.64 - 65 8th. Ed B3 4/61, 9/62 // 7/66
14 8/19/2009 Law of Growth and Decay pp. 65 - 69 8th ed B4 9/66, 15/67
15 8/21/2009 Simple Interest
16 8/24/2009 Newtons Second law of Motion pp. 65 - 69 8th ed B5 22/68
17 8/26/2009 Mixture Problems
18 8/28/2009 LONG QUIZ 2 SCORE LQ2: /100 TOTAL PROBLEM SET B
19 8/31/2009 Differential Operators pp. 100 - 109//pp. 109 - 116 8th ed C1 2/115, 4/115
20 9/2/2009 The Method of Undetermined Coefficients pp. 139 - 144 8th ed C2 8/143, 10/143
21 9/4/2009 Variation of Parameters pp. 156 - 164 8th ed C3 3/162, 7/162
22 9/7/2009 Inverse Differential Operators pp 152 - 158 7th ed.
23 9/9/2009 Laplace Transforms pp. 252 - 257 8th ed
24 9/11/2009 Definition of an Inverse Transforms pp. 274 - 277 8th ed
25 9/14/2009 Partial Fractions pp. 277 - 280 8th ed
26 9/16/2009 Initial Value Problem pp. 280 - 285 8th ed
27 9/18/2009 LONG QUIZ 3 SCORE LQ3: /100 TOTAL PROBLEM SET C
28 9/21/2009 Grade Verification
29 9/23/2009 Submission of Project
30 9/25/2009 Submission of Portfolio
31 9/28/2009 FINAL EXAM /300 GRAND TOTAL
Faculty in Charge: Dr. DANTE L. SILVA Textbook: ELEMENTARY DIFFERENTIAL EQUATIONS, 7th and 8th EDITION
Mapua Institute of Technology - Mathematics Department by: Rainville, Bedient, Bedient
5. COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 10-1
First Quarter 2011 - 2012
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY DATE TOPICS READINGS HOMEWORKS SCORES
1 11-Jul Orientation S A
2 13-Jul Sets and the Real Number System SEC 0.1 pp 4 - 15
3 15-Jul Alg Expressions, Properties of Exponents, Polynomials SEC0.1 p9/SEC0.3 pp27-30/SEC 4.3
4 18-Jul Operations on Polynomials, Synthetic Division SEC 0.1 p. 9 / SEC 0.3 pp 27 -30
5 20-Jul Special Products SEC 0.3 pp 31 - 34
6 22-Jul Common Factorsof Polynomials and Factors of Binomials SEC 0.4 pp 37 - 46
7 25-Jul Factors of Trinomials and Factoring by Grouping SEC 0.4 pp 37 - 46
8 27-Jul LONG QUIZ 1 SCORE LQ1: /100
9 29-Jul Simplify, Multiply, and Divide of Rational Expressions SEC0.1 pp 13 - 14/SEC0.5 pp 50 - 62
10 1-Aug Add and Subtract Rational Expressions/Complex Fractions SEC0.1 pp 13 - 14/SEC0.5 pp 50 - 62
11 3-Aug Rational Exponent and Radicals SEC 0.6 pp 63 - 71
12 5-Aug Linear Equations SEC1.1 pp 90-96/SEC1.2 pp 100-109
13 8-Aug Applications of Linear Equations SEC1.1 pp 90-96/SEC1.2 pp 100-109
14 10-Aug LONG QUIZ 2 SCORE LQ2: /100
15 12-Aug Quadratic Equations SEC 1.3 pp 113-123
16 15-Aug Applications of Quadratic Equations SEC 1.3 pp 113-123
17 17-Aug Inequalities SEC 1.5, 1.6 and 1.7 pp 136 - 163
18 19-Aug Inequalities in Two Variables SEC 9.4 917 - 919
19 22-Aug Matrices and Determinants SEC 10.1 - 10.4 pp946 - 1017
20 24-Aug Systems of Linear Equations SEC 9.1 pp 876 - 892
21 26-Aug Systems of Inequalities SEC 9.4 pp 917 - 927
22 29-Aug App of Systems of Linear Equations and Inequalities SEC9.1pp876-829/SEC9.4pp917-927
23 31-Aug LONG QUIZ 3 SCORE LQ3: /100
24 2-Sep Partial Fractions SEC 9.3 pp 905 - 913
25 5-Sep Functions and Relations, Operations on Functions SEC 3.1 - 3.5 pp 226 - 303
26 7-Sep Inverse of Functions, Graphs of Functions SEC 3.1 - 3.5 pp 226 - 303
27 9-Sep Ratio, Proportion, and Variation SEC 3.6 pp. 304 - 308
28 12-Sep Combinatorial Mathematics: Permutation SEC 12.6 pp 1169 - 1171, 1172 - 1173
29 14-Sep Combinatorial Mathematics: Combination SEC 12.6 pp 1171 - 1172
30 16-Sep LONG QUIZ 4 SCORE LQ4: /100
31 FINAL EXAM
Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young
Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________
6. COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 10-2
First Quarter 2011 - 2012
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS HOMEWORKS SCORES
1 12-Jul Orientation S A
2 14-Jul The Real Number System SEC 0.1 pp 4 - 15
3 16-Jul Algebraic Expressions SEC 0.1 p. 9 / SEC 0.3 pp 27 -28
4 19-Jul Laws of Integer Exponents SEC 0.2 pp18 - 25
5 21-Jul Addition, Subtraction, and Simplifying Alg Expressions SEC 0.3 p 29
6 23-Jul Multiplication and Division of Algebraic Expressions SEC 0.3 p 30 / SEC 4.3 pp 358 - 363
7 26-Jul Binomial Special Products SEC 0.3 pp 31 - 34
8 28-Jul Cube of a Binomial and Square of a Trinomial SEC 0.3 pp 31 - 34
9 30-Jul Common Factors of Polynomials and Factors of Binomials SEC 0.4 pp 37 - 46
10 2-Aug Factoring Trinomials SEC 0.4 pp 37 - 46
11 4-Aug LONG QUIZ 1 SCORE LQ1: /100
12 6-Aug Rational Expressions SEC0.1 pp 13 - 14/SEC0.5 pp 50 - 52
13 9-Aug Multiplication and Division of Rational Expressions, LCM SEC 0.5 pp 52 - 59
14 11-Aug Addition and Subtraction of Rational Expressions SEC 0.5 pp 52 - 59
15 13-Aug Complex Fractions SEC 0.5 pp 52 - 59
16 16-Aug Radicals, Simplifying and Rationalizing Radical Expressions SEC 0.6 pp 63 - 71
17 18-Aug Operations Involving Radical Expressions SEC 0.6 pp 63 - 71
18 20-Aug LONG QUIZ 2 SCORE LQ2: /100
19 23-Aug Linear Equations and Properties of Equality
20 25-Aug Linear Eqns in One Variable, Equations Leading to ax+b=0 SEC1.1 pp 90-96/SEC1.2 pp 100-109
21 27-Aug Applications of Linear Equations in One Variable SEC1.1 pp 90-96/SEC1.2 pp 100-109
22 30-Aug Quadratic Equations 1 SEC 1.3 pp 113-123
23 1-Sep Systems of Linear Equations in One Variable SEC 9.1 pp 876 - 888
24 3-Sep Solving Systems of Linear Equations in One Variable SEC 9.1 pp 876 - 888
25 6-Sep Ratio and Proportion SEC 3.6 pp. 304 - 308
26 8-Sep Transformation of a Proportion SEC 3.6 pp. 304 - 308
27 10-Sep Variation SEC 3.6 pp. 304 - 308
28 13-Sep LONG QUIZ 3 SCORE LQ3: /100
29 15-Sep Review/Preparation of Portfolio
30 17-Sep Review/Preparation of Portfolio
31 FINAL EXAM
Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young
Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________
7.
8. COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 10
1st Qtr 2011 - 2012
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS HOMEWORKS SCORES
1 11-Jul Orientation S A
2 13-Jul Equations and Linear Equations in One Variable SEC 1.1 pp. 90 - 99
3 15-Jul Equations Leading to Linear Equations in One Variable SEC 1.1 pp. 90 - 99
4 18-Jul Number, Digit, Geometric, and Money and Coin Problems SEC 1.2 pp. 100 - 113
5 20-Jul Investment, Age, and Mixture Problems SEC 1.2 pp. 100 - 113
6 22-Jul Uniform Motion, Work, and Clock Problems SEC 1.2 pp. 100 - 113
7 25-Jul Ratio, Proportion, and Variation SEC 3.6 pp. 304 - 313
8 27-Jul LONG QUIZ 1 SCORE LQ1: /100
9 29-Jul Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135
10 1-Aug Equations Leading to Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135
11 3-Aug Equations Leading to Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135
12 5-Aug Applications of Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135
13 8-Aug Inequalities and Linear Equalities in One Variable SEC 1.5, 1.6 and 1.7 pp 136 - 163
14 10-Aug Nonlinear Inequalities in One Variable SEC 1.5, 1.6 and 1.7 pp 136 - 163
15 12-Aug LONG QUIZ 2 SCORE LQ2: /100
16 15-Aug Systems of Equations/Systems of Linear Equations in Two Variables SEC 9.1 pp 876 - 892
17 17-Aug Systems of Nonlinear Equations in Two Variables SEC 9.1 pp 876 - 892
18 19-Aug Applications of Systems of Linear Equations SEC 9.1 pp 876 - 892
19 22-Aug Systems of Inequalities in Two Variables SEC 9.4 pp 917 - 927
20 24-Aug Applications of Systems of Inequalities in Two Variables SEC 9.4 pp 917 - 927
21 26-Aug LONG QUIZ 3 SCORE LQ3: /100
22 29-Aug Functions and Relations, Types of Functions, Domain and Range SEC 3.1 - 3.5 pp 226 - 303
23 31-Aug Graphs of Functions, Operations on Functions, One-to-One Functions SEC 3.1 - 3.5 pp 226 - 303
24 2-Sep Synthetic Division, Remainder and Factor Theorems, Fundamental Theorem of Algebra SEC 4.1 - 4.5 pp 326 - 389
25 5-Sep Zeroes of Polynomials, Decartes Rule of Signs, Rational Zeroes SEC 4.1 - 4.5 pp 326 - 389
26 7-Sep LONG QUIZ 4 SCORE LQ4: /100
27 9-Sep Sequences and Series, Arithmetic Sequences SEC 12.1 - 12.4 pp 1122 - 1158
28 12-Sep Harmonic Sequences and Geometric Sequences SEC 12.1 - 12.4 pp 1122 - 1158
29 14-Sep Factorial of a Number, Binomial Theorem SEC 12.1 pp 1124 - 1125 / SEC 12.5
30 16-Sep LONG QUIZ 5 SCORE LQ5: /100
31 FINAL EXAM
Faculty in Charge: Floro Deogracias G. Llacuna Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young
Chairman, Mathematics Department: Dr. Lilibeth D. Sabino
Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________
9. COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 10
First Quarter 2011 - 2012
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS HOMEWORKS SCORES
1 12-Jul Orientation S A
2 14-Jul Equations and Linear Equations in One Variable SEC 1.1 pp. 90 - 99
3 16-Jul Equations Leading to Linear Equations in One Variable SEC 1.1 pp. 90 - 99
4 19-Jul Number, Digit, Geometric, and Money and Coin Problems SEC 1.2 pp. 100 - 113
5 21-Jul Investment, Age, and Mixture Problems SEC 1.2 pp. 100 - 113
6 23-Jul Uniform Motion, Work, and Clock Problems SEC 1.2 pp. 100 - 113
7 26-Jul Ratio, Proportion, and Variation SEC 3.6 pp. 304 - 313
8 28-Jul LONG QUIZ 1 SCORE LQ1: /100
9 30-Jul Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135
10 2-Aug Equations Leading to Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135
11 4-Aug Equations Leading to Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135
12 6-Aug Applications of Quadratic Equations in One Variable SEC 1.3 and 1.4 pp 113 - 135
13 9-Aug Inequalities and Linear Equalities in One Variable SEC 1.5, 1.6 and 1.7 pp 136 - 163
14 11-Aug Nonlinear Inequalities in One Variable SEC 1.5, 1.6 and 1.7 pp 136 - 163
15 13-Aug LONG QUIZ 2 SCORE LQ2: /100
16 16-Aug Systems of Equations/Sys of Linear Eqns in Two Variables SEC 9.1 pp 876 - 892
17 18-Aug Systems of Nonlinear equations in Two Variables SEC 9.1 pp 876 - 892
18 20-Aug Applications of Systems of Linear Equations SEC 9.1 pp 876 - 892
19 23-Aug Systems of Inequalities in Two Variables SEC 9.4 pp 917 - 927
20 25-Aug Applications of Systems of Inequalities in Two Variables SEC 9.4 pp 917 - 927
21 27-Aug LONG QUIZ 3 SCORE LQ3: /100
22 30-Aug Functions and Relations, Types of Fxns, Domain and Range SEC 3.1 - 3.5 pp 226 - 303
23 1-Sep Graphs of Fxns, Operations on Fxns, One-to-One Fxns SEC 3.1 - 3.5 pp 226 - 303
24 3-Sep Syn Div, Remdr and Factor Theorem, Fund Theorem of Alg SEC 4.1 - 4.5 pp 326 - 389
25 6-Sep Zeroes of Poly's, Decartes Rule of Signs, Rational Zeroes SEC 4.1 - 4.5 pp 326 - 389
26 8-Sep LONG QUIZ 4 SCORE LQ4: /100
27 10-Sep Sequences and Series, Arithmetic Sequences SEC 12.1 - 12.4 pp 1122 - 1158
28 13-Sep Harmonic Sequences and Geometric Sequences SEC 12.1 - 12.4 pp 1122 - 1158
29 15-Sep Factorial of a Number, Binomial Theorem SEC 12.1 pp 1124 - 1125/SEC 12.5
30 17-Sep LONG QUIZ 5 SCORE LQ5: /100
31 FINAL EXAM
Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young
Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________
10. COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 12
First Quarter 2011 - 2012
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS HOMEWORKS SCORES
1 11-Jul Orientation S A
2 13-Jul Angle Measure, Standard Position, Coterminal Angles pp492-494, pp537-542, pp568-572
3 15-Jul Length of a Circular Arc, Linear and Angular Speeds pp 573-585
4 18-Jul Trigonometeric Ratios and Ratios for Special Angles pp509-512, pp516-519
5 20-Jul Solutions of Right Triangles pp495-503, pp524-527
6 22-Jul Angle of Elevation/Depression and Bearing and Course pp 528-530
7 25-Jul Signs of Trigo Fxns and Trigo Ratios of Quadrant Angles pp546-548, pp552-556, pp586-591
8 27-Jul Evaluating Trigonometric Fxns Using the Reference Angle pp556-563
9 29-Jul LONG QUIZ 1 SCORE LQ1: /100
10 1-Aug Graphs of Sin and Cos Fxns/Tan and Cot Fxns pp595-618, pp624-638
11 3-Aug Graphs of Tan ans Cot Fxnx/Sec and Csc Fxns pp624-638
12 5-Aug Trigonometric Identities and Prooving pp660-716
13 8-Aug Definition of Inverse Trigonometric Functions pp719-734
14 10-Aug Graphs of Inverse Trigonometric Functions pp719-734
15 12-Aug Evaluating Inverse Trigonometric Functions pp719-734
16 15-Aug Solving Trigonometric Equations pp739-750
17 17-Aug Applications of Trigonometric Equations pp739-750
18 19-Aug LONG QUIZ 2 SCORE LQ2: /100
19 22-Aug Solutions to Oblique Triangles and the Law of Sines pp770-781
20 24-Aug Applications of the Law of Sines, Law of Cosines pp770-781, pp785-791
21 26-Aug Applications of the Law of Cosines pp785-791
22 29-Aug Definitions in Spherical Trigonometry TBA
23 31-Aug Law of Sine and Cosine in Spherical Trigonometry TBA
24 2-Sep Napier's Analogies and The Terrestrial Sphere TBA
25 5-Sep LONG QUIZ 3 SCORE LQ3: /100
26 7-Sep Exponential Functions and Their Graphs pp422-433
27 9-Sep Logarithmic Functions and Properties of Logarithms pp437-447, pp451-457
28 12-Sep Solving Exponential and Logarithmic Equations pp460-467
29 14-Sep Applications Involving Exponential and Logarithmic Fxns pp460-467
30 16-Sep LONG QUIZ 4 SCORE LQ4: /100
31 FINAL EXAM
Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young
Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________
11. COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 12-L
First Quarter 2011 - 2012
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS HOMEWORKS SCORES
1 12-Jul Orientation and Review of Basic Terms S A
2 19-Jul Angle Measure
3 26-Jul Trigonometery of Right Triangles
4 2-Aug Trigo Functions and Angles / LONG QUIZ 1 SCORE LQ1: /100
5 9-Aug Graphs of Trigonometric Functions
6 16-Aug Trigonometric Identities
7 23-Aug Inverse Trigo Fxns and Trigonometric Equations
8 30-Aug LONG QUIZ 2 / Solutions to Oblique Triangles SCORE LQ2: /100
9 6-Sep Appn's of Sin and Cos Laws and Spherical Trigo
10 13-Sep FINAL EXAM / Exp and Log Equations
Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young
Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________
12. COURSE CALENDAR AND SUMMARY SCORE SHEET - MATH 12-L
First Quarter 2011 - 2012
Surname: ______________________Firstname___________________________MI_______
Section: __________ Time : ____________ Room: ____________ Seat Number: ____________ Contact Number: _____________________
DAY # DATE TOPICS READINGS HOMEWORKS SCORES
1 16-Jul Orientation and Review of basic Terms S A
2 23-Jul Angle Measure
3 30-Jul Trigonometery of Right Triangles
4 6-Aug Trigo Functions and Angles / LONG QUIZ 1 SCORE LQ1: /100
5 13-Aug Graphs of Trigonometric Functions
6 20-Aug Trigonometric Identities
7 27-Aug Inverse Trigo Fxns and Trigonometric Equations
8 3-Sep LONG QUIZ 2 / Solutions to Oblique Triangles SCORE LQ2: /100
9 10-Sep Appn's of Sin and Cos Laws and Spherical Trigo
10 17-Sep FINAL EXAM / Exp and Log Equations
Faculty in Charge: Engr. Antonio D. Sayaboc, Jr. Textbook: Algebra and Trigonometry, 2nd ed., Cynthia Young
Mapua Institute of Technology - Mathematics Department Student Signature: ____________________________
17. TOPICS DAY # DATE
Orientation 16 15-Aug
Sets and the Real Number System 17 17-Aug
Alg Exp 1 (Concepts, Exponents, Polynomials) 18 19-Aug
Alg Exp 2 (Oper'ns on Polynomials and Syn Div) 19 22-Aug
Special Products 20 24-Aug
Factoring 1 21 26-Aug
Factoring 2 22 29-Aug
LONG QUIZ 1 23 31-Aug
Rat'l Exp 1 (Simplifying, Multiplication and Division) 24 2-Sep
Rat'l Exp 2 (Add'n, Sub'n, and Complex Fractions) 25 5-Sep
Rational Exponent and Radicals 26 7-Sep
Linear Equations 27 9-Sep
Applications of Linear Equations 28 12-Sep
LONG QUIZ 2 29 14-Sep
Quadratic Equations 30 16-Sep
31
TOPICS DAY # DATE
Orientation 16 15-Aug
Equations, Properties of Equality, Equivalent Eqn's 17 17-Aug
Linear Equations in One Variable 18 19-Aug
Modelling/ Number, Digit, and Geometric Problems 19 22-Aug
Money, Investment, Age, and Mixture Problems 20 24-Aug
Uniform Motion, Work, and Clock Problems 21 26-Aug
Ratio, Proportion, and Variation 22 29-Aug
LONG QUIZ 1 23 31-Aug
Quadratic Equations in One Variable 24 2-Sep
Equations Leading to Quadratic Equations 1 25 5-Sep
Equations Leading to Quadratic Equations 2 26 7-Sep
Applications of Quadratic Equations in One Variable 27 9-Sep
Inequalities 1 28 12-Sep
Inequalities 2 29 14-Sep
LONG QUIZ 2 30 16-Sep
31
18. TOPICS DAY # DATE
Orientation 16 15-Aug
Angle Measure 1 17 17-Aug
Angle Measure 2 18 19-Aug
Trigonometry of Right Triangles 1 19 22-Aug
Trigonometry of Right Triangles 2 20 24-Aug
Trigonometry of Right Triangles 3 21 26-Aug
Trigonometric Functions of Angles 1 22 29-Aug
Trigonometric Functions of Angles 2 23 31-Aug
LONG QUIZ 1 24 2-Sep
Graphs of Trigonometric Functions 1 25 5-Sep
Graphs of Trigonometric Functions 2 26 7-Sep
Trigonometric Identities 27 9-Sep
Inverse Trigonometric Functions 1 28 12-Sep
Inverse Trigonometric Functions 2 29 14-Sep
Inverse Trigonometric Functions 3 30 16-Sep
31
TOPICS DAY # DATE
Orientation 16 16-Aug
The Real Number System 17 18-Aug
Algebraic Expressions 18 20-Aug
Laws of Integer Exponents 19 23-Aug
Operations on Alg Exp 1 (Add'n, Sub'n, Symplifying) 20 25-Aug
Operations on Alg Exp 2 (Mult, Div, and Syn Div) 21 27-Aug
Special Products 1 22 30-Aug
Special Products 2 23 1-Sep
Factoring 1 24 3-Sep
Factoring 2 25 6-Sep
LONG QUIZ 1 26 8-Sep
Rational Expressions 27 10-Sep
Operations on Rational Expressions 1 28 13-Sep
Operations on Rational Expressions 2 29 15-Sep
Operations on Rational Expressions 3 30 17-Sep
31
TOPICS
19. Orientation and Review of basic Terms
Angle Measure
Trigonometery of Right Triangles
Trig of Right Triangles / LONG QUIZ 1
Graphs of Trigonometric Functions
Trigonometric Identities
Inverse Trigo Fxns and Trigonometric Equations
LONG QUIZ 2 / Solutions to Oblique Triangles
Appn's of Sin and Cos Laws and Spherical Trigo
FINAL EXAM / Exp and Log Equations
TOPICS
Orientation and Review of basic Terms
Angle Measure
Trigonometery of Right Triangles
Trig of Right Triangles / LONG QUIZ 1
Graphs of Trigonometric Functions
Trigonometric Identities
Inverse Trigo Fxns and Trigonometric Equations
LONG QUIZ 2 / Solutions to Oblique Triangles
Appn's of Sin and Cos Laws and Spherical Trigo
FINAL EXAM / Exp and Log Equations
TOPICS DAY # DATE
Orientation 16 16-Aug
Equations, Properties of Equality, Equivalent Eqn's 17 18-Aug
Linear Equations in One Variable 18 20-Aug
Modelling/ Number, Digit, and Geometric Problems 19 23-Aug
Money, Investment, Age, and Mixture Problems 20 25-Aug
Uniform Motion, Work, and Clock Problems 21 27-Aug
Ratio, Proportion, and Variation 22 30-Aug
LONG QUIZ 1 23 1-Sep
Quadratic Equations in One Variable 24 3-Sep
Equations Leading to Quadratic Equations 1 25 6-Sep
Equations Leading to Quadratic Equations 2 26 8-Sep
Applications of Quadratic Equations in One Variable 27 10-Sep
Inequalities 1 28 13-Sep
Inequalities 2 29 15-Sep
21. TOPICS
Applications of Quadratic Equations
Inequalities
Inequalities in Two Variables
Matrices and Determinants
Systems of Linear Equations
Systems of Inequalities
App of Sys of Linear Equations and Inequalities
LONG QUIZ 3
Partial Fractions
Functions and Relations 1 (Def'ns and Oper'ns)
Functions and Relations 2 (Inverse Fxn and Graphs)
Ratio, Proportion, and Variation
Combinatorial Mathematics: Permutation
Combinatorial Mathematics: Combination
LONG QUIZ 4
FINAL EXAM
TOPICS
Systems of Equations and Inequalities 1
Systems of Equations and Inequalities 2
Systems of Equations and Inequalities 3
Systems of Equations and Inequalities 4
Systems of Equations and Inequalities 5
LONG QUIZ 3
Relations Functions and Graphs 1
Relations Functions and Graphs 2
Polynomial Functions 1
Polynomial Functions 2
LONG QUIZ 4
Sequences and Series, Arithmetic Sequences
Harmonic sequence, Geometric Sequence
Factorial of a Number, Binomial Theorem
LONG QUIZ 5
FINAL EXAM
22. TOPICS
Trigonometric Equations 1
Trigonometric Equations 2
LONG QUIZ 2
Solutions of Oblique Triangles 1
Solutions of Oblique Triangles 2
Solutions of Oblique Triangles 3
Spherical Trigonometry 1
Spherical Trigonometry 2
Spherical Trigonometry 3
LONG QUIZ 3
Exponential Functions
Logarithmic Function 1
Logarithmic Function 2
Exponential and Logarithmic Equations
LONG QUIZ 4
FINAL EXAM
TOPICS
Rational Exponents 1
Rational Exponents 2
LONG QUIZ 2
Linear Equations 1
Linear Equations 2
Linear Equations 3
Quadratic Equations 1
Quadratic Equations 2
Quadratic Equations 3
Ratio, Proportion, and Variation 1
Ratio, Proportion, and Variation 2
Ratio, Proportion, and Variation 3
LONG QUIZ 3
Review/Preparation of Portfolio
Review/Preparation of Portfolio
FINAL EXAM
23. TOPICS
Systems of Equations and Inequalities 1
Systems of Equations and Inequalities 2
Systems of Equations and Inequalities 3
Systems of Equations and Inequalities 4
Systems of Equations and Inequalities 5
LONG QUIZ 3
Relations Functions and Graphs 1
Relations Functions and Graphs 2
Polynomial Functions 1
Polynomial Functions 2
LONG QUIZ 4
Sequences and Series, Arithmetic Sequences
Harmonic sequence, Geometric Sequence
Factorial of a Number, Binomial Theorem