3 handouts section2-8-and_2-9
•
0 likes•212 views
The document defines the derivative of a function and explains how to find derivatives. It states that the derivative of a function f(x) at a point a is defined as the limit as h approaches 0 of (f(x+h) - f(x))/h, if the limit exists. This provides a geometric interpretation of the derivative as the slope of the tangent line to the function f(x) at the point a. The document also defines left and right derivatives and notes that for a derivative to exist at a point, the left and right derivatives must be the same at that point. Additionally, it mentions that differentiability requires a function to be continuous at a point.
Report
Share
Report
Share
Download to read offline
Recommended
Chapter 6.6
The document defines classes and methods in Java.
It discusses:
1) The syntax for defining a class with modifiers, data declarations, and method definitions.
2) How a class can contain data declarations and method declarations to store information and perform behaviors.
3) The structure of a method including the header, parameters, and body.
4) How to define constructors, static methods, and overload methods in a class.
Object and class in java
The document discusses key concepts in object-oriented programming including creating objects and object reference variables, constructors, modifiers, instance and class variables and methods, scope of variables, and using the this keyword. It provides examples of creating Circle and Mortgage classes to demonstrate these concepts. UML diagrams are used to illustrate graphical notations for classes, objects, fields, and methods.
3 handouts section3-8
1. This section discusses how to find derivatives of functions involving logarithms, including ln(u) and logb(u). It outlines the differentiation formulas for these functions and explains logarithmic differentiation.
2. Logarithmic differentiation can be used to differentiate functions that involve products, quotients, or powers, by taking the natural log of both sides, simplifying using properties of logarithms, and then differentiating.
3. Logarithmic differentiation is particularly useful for differentiating functions of the form v/u, where both u and v are functions of the variable. Examples are provided.
C++ classes tutorials
C++ classes allow programmers to encapsulate data and functions into user-defined types called classes. A class defines the data attributes and functions that operate on those attributes. Classes support object-oriented programming by allowing objects to be created from a class which store and manipulate data private to the class through public member functions.
COLLEGE OF COMPUTING AND INFORMATICS Assignment – 4
This document provides instructions for an assignment with 4 questions. It involves using stacks, queues, sets, maps and calculating hashcodes of strings. Students need to submit their responses by April 28th, 2016 for a total of 5 marks. Late or copied submissions will receive zero marks. The questions cover identifying real life examples of stack and queue usage, basic set operations in Java, storing and manipulating course data in a map, and writing a method to calculate string hashcodes based on a given formula.
Variational Auto Encoder and the Math Behind
The Math and internal workings of Variational Auto Encoders. It talks about Variational Inference and how VAEs take advantage of them to bypass having to calculate Marginal Probability distribution.
Bin Sorting And Bubble Sort By Luisito G. Trinidad
source from Wikipedia and other sites.. thanks to you guys.. sorry for note mentioning your names.. regards
OOP
This document provides an overview of object-oriented programming concepts in C++ including classes, objects, encapsulation, and templates. It introduces the stack data structure and shows how to implement it using structs in C and then classes in C++. It demonstrates how classes allow data and functions to be bundled together through methods and constructors. The document also discusses templates which allow classes to be parameterized for different data types.
Recommended
Chapter 6.6
The document defines classes and methods in Java.
It discusses:
1) The syntax for defining a class with modifiers, data declarations, and method definitions.
2) How a class can contain data declarations and method declarations to store information and perform behaviors.
3) The structure of a method including the header, parameters, and body.
4) How to define constructors, static methods, and overload methods in a class.
Object and class in java
The document discusses key concepts in object-oriented programming including creating objects and object reference variables, constructors, modifiers, instance and class variables and methods, scope of variables, and using the this keyword. It provides examples of creating Circle and Mortgage classes to demonstrate these concepts. UML diagrams are used to illustrate graphical notations for classes, objects, fields, and methods.
3 handouts section3-8
1. This section discusses how to find derivatives of functions involving logarithms, including ln(u) and logb(u). It outlines the differentiation formulas for these functions and explains logarithmic differentiation.
2. Logarithmic differentiation can be used to differentiate functions that involve products, quotients, or powers, by taking the natural log of both sides, simplifying using properties of logarithms, and then differentiating.
3. Logarithmic differentiation is particularly useful for differentiating functions of the form v/u, where both u and v are functions of the variable. Examples are provided.
C++ classes tutorials
C++ classes allow programmers to encapsulate data and functions into user-defined types called classes. A class defines the data attributes and functions that operate on those attributes. Classes support object-oriented programming by allowing objects to be created from a class which store and manipulate data private to the class through public member functions.
COLLEGE OF COMPUTING AND INFORMATICS Assignment – 4
This document provides instructions for an assignment with 4 questions. It involves using stacks, queues, sets, maps and calculating hashcodes of strings. Students need to submit their responses by April 28th, 2016 for a total of 5 marks. Late or copied submissions will receive zero marks. The questions cover identifying real life examples of stack and queue usage, basic set operations in Java, storing and manipulating course data in a map, and writing a method to calculate string hashcodes based on a given formula.
Variational Auto Encoder and the Math Behind
The Math and internal workings of Variational Auto Encoders. It talks about Variational Inference and how VAEs take advantage of them to bypass having to calculate Marginal Probability distribution.
Bin Sorting And Bubble Sort By Luisito G. Trinidad
source from Wikipedia and other sites.. thanks to you guys.. sorry for note mentioning your names.. regards
OOP
This document provides an overview of object-oriented programming concepts in C++ including classes, objects, encapsulation, and templates. It introduces the stack data structure and shows how to implement it using structs in C and then classes in C++. It demonstrates how classes allow data and functions to be bundled together through methods and constructors. The document also discusses templates which allow classes to be parameterized for different data types.
Structures
C programming language tutorial on structures:
1) Structures allow grouping of different data types under a single name and are used to represent records.
2) A structure is declared using the struct keyword and members can be accessed using the dot operator.
3) Structures can be passed to functions by passing individual members, passing the entire structure, or passing a pointer to the structure.
4) The typedef keyword allows creating new data type names for structures for easier declaration and use.
Lec 8 03_sept [compatibility mode]
This document discusses Java data types, variables, and methods. It covers primitive data types like int, float, and boolean. It describes rules for identifiers and conventions for naming variables and classes. The document defines parameter types, implicit and explicit parameters, and how to call methods. It explains constructing objects with the new operator and accessor and mutator methods. The summary concludes with a discussion of static methods and how to call them without an object.
Assignment 7
This document contains the solutions to 8 questions related to Java OOP concepts such as inheritance, polymorphism, method overriding and overloading.
The questions cover topics like determining the output of sample code, identifying true/false statements about OOP concepts, explaining the differences between method overriding and overloading, designing UML class diagrams to model relationships between classes, and writing Java programs to test class hierarchies and subclasses.
Detailed explanations and code samples are provided for each question to demonstrate concepts like invoking superclass constructors, determining pass/fail conditions for student grades based on average test scores, implementing abstract classes and interfaces, and creating subclasses that extend the functionality of base classes.
Machine learning
A brief overview of making recommendations using the K nearest neighbour algorithm and the Euclidean distance. Given at a Forward First Tuesday evening.
Chapter 13 introduction to classes
The document discusses object-oriented programming and class-based design. It explains that object-oriented programming focuses on modeling real-world objects as software objects with both data fields (attributes) and methods to operate on that data. A class defines a blueprint for objects, describing their attributes and methods. Objects are instances of classes that package both data and behaviors together. The document outlines key concepts like encapsulation, inheritance, polymorphism, and UML class diagrams.
Polymorphism
This document discusses the object-oriented programming concept of polymorphism in Java. It defines polymorphism as the ability for multiple methods to have the same name but implement different behaviors depending on the object type. The document provides examples of method overloading and late binding to demonstrate polymorphism. It also discusses upcasting and downcasting between base and derived classes.
Intro to modelling_wur
This document provides an introduction to biological modeling using ordinary differential equations (ODEs) and their solution in MATLAB. It discusses modeling techniques like deterministic, probabilistic, and discrete models. It also covers the basics of ODEs, analytical and numerical solutions, and how to implement a model in MATLAB including defining equations, parameters, initial values, and plotting results. Hands-on tutorials are provided to help students practice modeling different biological and physical systems using MATLAB.
Rakesh Bijawat , BCA Third Year
This document is a project report submitted by Rakesh Bijawat towards fulfilling the requirements for a BCA degree from Dezyne E'cole College. The project discusses wrapper classes in Java, which allow primitive data types to be handled as objects, and nesting of methods, where one method calls another method in the same class. It provides examples and outputs to demonstrate converting between primitive types and wrapper class objects, using wrapper class methods, and calling methods within other methods of the same class.
Rakesh Bijawat, BCA 2nd Year
Student Dezyne E'cole College, www.dezyneecole.com
Project on Wrapper Class and Nesting Method in Java
A MATLAB project on LCR circuits
This document discusses using MATLAB to solve differential equations related to electric circuits. It begins by explaining some advantages of MATLAB, such as its use of matrices, vectorized operations, and graphical output capabilities. It then provides an example of using MATLAB to solve the first order differential equation iR+Ldi/dt=E(t), which models an LCR circuit. The document also discusses solving second order differential equations manually and with MATLAB code. It provides an example of solving the second order equation d2q/dt2+10dq/dt+250q=0 both manually and using MATLAB code.
08slide
This document introduces key concepts of object-oriented programming in Java including classes, objects, encapsulation, and inheritance. It discusses how classes are used to define objects and their properties (data fields) and behaviors (methods). Constructors are introduced as special methods used to initialize objects. The document provides examples of defining classes like Circle and TV, creating objects, and accessing object data and methods. It also discusses reference variables, the null value, default values, and differences between primitive types and reference types. Finally, core classes like Date, Random, and JFrame from the Java library are mentioned.
Assessments
This document describes 8 lab assessments for a Java programming course. Each assessment involves modifying provided Java code to complete a programming problem related to topics covered in the Java Genesis textbook. Students must demonstrate their solutions to a tutor by a certain deadline to receive credit. The assessments involve tasks such as drawing shapes, searching arrays, animating objects, and building GUI programs.
3 handouts section2-7
1. The slope of the tangent line to a curve y=f(x) at a point (a, f(a)) is given by the limit as h approaches 0 of (f(a+h) - f(a))/h.
2. The instantaneous rate of change of a function f(x) at a point x=a is given by the limit as h approaches 0 of (f(a+h) - f(a))/h.
3. For a function s(t) that gives the position of an object at time t, the instantaneous velocity at time t is given by the limit as h approaches 0 of (s(t+h) - s
3 handouts section3-7
This document discusses higher order derivatives. It defines higher order derivatives as the successive differentiation of a function. For an explicitly defined function f(x), the kth derivative is written as ( )( ) ( 1)k kd f x f x dx − . Examples are provided to demonstrate finding higher order derivatives of both explicitly and implicitly defined functions. Notations for higher order derivatives are also introduced.
3 handouts section3-11
This document discusses linear approximations and differentials. It introduces:
1) Finding the linear approximation of non-linear functions by using the equation of the tangent line.
2) Finding the differential dy of a function y=f(x), which represents the change in y for an infinitesimal change dx in x.
3) Using differentials to approximate small changes or errors in a function when there is a small change in the input variable.
Bai giang Dao ham rieng
This document discusses partial derivatives of functions with multiple variables. It defines partial derivatives as derivatives of a function where all but one variable is held constant. For a function z=f(x,y), the partial derivatives with respect to x and y are defined. Higher order partial derivatives and partial derivatives of functions with more than two variables are also introduced. Examples are provided to demonstrate calculating first and second order partial derivatives.
3 handouts section2-2
1. The document defines the limit of a function as making the function values arbitrarily close to a limit L by taking the input value closer to a specific value.
2. It discusses one-sided limits and how the limit exists only when the left and right side limits are equal. Infinite limits result when direct substitution makes the denominator equal to zero.
3. Vertical asymptotes occur when the graph shoots to positive or negative infinity as the input approaches a particular value, or when factoring a rational function results in the denominator equaling zero at that input value.
7_Intro_to_Functions
The document discusses functions and how to determine if a relationship represents a function using the vertical line test. It defines what constitutes a function and introduces function notation. Examples are provided of evaluating functions for given values of the independent variable and using functions to model and express relationships between variables.
3 handouts section2-5
1. The document defines continuity and different types of discontinuities. A function is continuous if the limit exists and equals the function value at that point.
2. There are three types of discontinuities: removable (finite jump), infinite jump, and jump (finite discontinuity in function value).
3. Basic properties are that sums, products, scalar multiples of continuous functions are also continuous. Composition of continuous functions is continuous.
4. The intermediate value theorem states that if a continuous function takes on values between two numbers on an interval, it must take on all values in between.
Calculus 1 Lecture Notes (Functions and Their Graphs)
Calculus 1 Lecture Notes
Functions and Their Graphs
1 quadratic function
This document provides an agenda and activities for learning about quadratic functions that model real-world situations. It discusses using first and second differences to determine if a relationship is linear or quadratic. Activities include graphing quadratic functions in standard and vertex form, finding the domain and range, and converting between forms. Notes are provided on the standard form and how the parabola opens based on the value of a. The final activity has students write a quadratic function in vertex form.
More Related Content
What's hot
Structures
C programming language tutorial on structures:
1) Structures allow grouping of different data types under a single name and are used to represent records.
2) A structure is declared using the struct keyword and members can be accessed using the dot operator.
3) Structures can be passed to functions by passing individual members, passing the entire structure, or passing a pointer to the structure.
4) The typedef keyword allows creating new data type names for structures for easier declaration and use.
Lec 8 03_sept [compatibility mode]
This document discusses Java data types, variables, and methods. It covers primitive data types like int, float, and boolean. It describes rules for identifiers and conventions for naming variables and classes. The document defines parameter types, implicit and explicit parameters, and how to call methods. It explains constructing objects with the new operator and accessor and mutator methods. The summary concludes with a discussion of static methods and how to call them without an object.
Assignment 7
This document contains the solutions to 8 questions related to Java OOP concepts such as inheritance, polymorphism, method overriding and overloading.
The questions cover topics like determining the output of sample code, identifying true/false statements about OOP concepts, explaining the differences between method overriding and overloading, designing UML class diagrams to model relationships between classes, and writing Java programs to test class hierarchies and subclasses.
Detailed explanations and code samples are provided for each question to demonstrate concepts like invoking superclass constructors, determining pass/fail conditions for student grades based on average test scores, implementing abstract classes and interfaces, and creating subclasses that extend the functionality of base classes.
Machine learning
A brief overview of making recommendations using the K nearest neighbour algorithm and the Euclidean distance. Given at a Forward First Tuesday evening.
Chapter 13 introduction to classes
The document discusses object-oriented programming and class-based design. It explains that object-oriented programming focuses on modeling real-world objects as software objects with both data fields (attributes) and methods to operate on that data. A class defines a blueprint for objects, describing their attributes and methods. Objects are instances of classes that package both data and behaviors together. The document outlines key concepts like encapsulation, inheritance, polymorphism, and UML class diagrams.
Polymorphism
This document discusses the object-oriented programming concept of polymorphism in Java. It defines polymorphism as the ability for multiple methods to have the same name but implement different behaviors depending on the object type. The document provides examples of method overloading and late binding to demonstrate polymorphism. It also discusses upcasting and downcasting between base and derived classes.
Intro to modelling_wur
This document provides an introduction to biological modeling using ordinary differential equations (ODEs) and their solution in MATLAB. It discusses modeling techniques like deterministic, probabilistic, and discrete models. It also covers the basics of ODEs, analytical and numerical solutions, and how to implement a model in MATLAB including defining equations, parameters, initial values, and plotting results. Hands-on tutorials are provided to help students practice modeling different biological and physical systems using MATLAB.
Rakesh Bijawat , BCA Third Year
This document is a project report submitted by Rakesh Bijawat towards fulfilling the requirements for a BCA degree from Dezyne E'cole College. The project discusses wrapper classes in Java, which allow primitive data types to be handled as objects, and nesting of methods, where one method calls another method in the same class. It provides examples and outputs to demonstrate converting between primitive types and wrapper class objects, using wrapper class methods, and calling methods within other methods of the same class.
Rakesh Bijawat, BCA 2nd Year
Student Dezyne E'cole College, www.dezyneecole.com
Project on Wrapper Class and Nesting Method in Java
A MATLAB project on LCR circuits
This document discusses using MATLAB to solve differential equations related to electric circuits. It begins by explaining some advantages of MATLAB, such as its use of matrices, vectorized operations, and graphical output capabilities. It then provides an example of using MATLAB to solve the first order differential equation iR+Ldi/dt=E(t), which models an LCR circuit. The document also discusses solving second order differential equations manually and with MATLAB code. It provides an example of solving the second order equation d2q/dt2+10dq/dt+250q=0 both manually and using MATLAB code.
08slide
This document introduces key concepts of object-oriented programming in Java including classes, objects, encapsulation, and inheritance. It discusses how classes are used to define objects and their properties (data fields) and behaviors (methods). Constructors are introduced as special methods used to initialize objects. The document provides examples of defining classes like Circle and TV, creating objects, and accessing object data and methods. It also discusses reference variables, the null value, default values, and differences between primitive types and reference types. Finally, core classes like Date, Random, and JFrame from the Java library are mentioned.
Assessments
This document describes 8 lab assessments for a Java programming course. Each assessment involves modifying provided Java code to complete a programming problem related to topics covered in the Java Genesis textbook. Students must demonstrate their solutions to a tutor by a certain deadline to receive credit. The assessments involve tasks such as drawing shapes, searching arrays, animating objects, and building GUI programs.
What's hot (13)
Similar to 3 handouts section2-8-and_2-9
3 handouts section2-7
1. The slope of the tangent line to a curve y=f(x) at a point (a, f(a)) is given by the limit as h approaches 0 of (f(a+h) - f(a))/h.
2. The instantaneous rate of change of a function f(x) at a point x=a is given by the limit as h approaches 0 of (f(a+h) - f(a))/h.
3. For a function s(t) that gives the position of an object at time t, the instantaneous velocity at time t is given by the limit as h approaches 0 of (s(t+h) - s
3 handouts section3-7
This document discusses higher order derivatives. It defines higher order derivatives as the successive differentiation of a function. For an explicitly defined function f(x), the kth derivative is written as ( )( ) ( 1)k kd f x f x dx − . Examples are provided to demonstrate finding higher order derivatives of both explicitly and implicitly defined functions. Notations for higher order derivatives are also introduced.
3 handouts section3-11
This document discusses linear approximations and differentials. It introduces:
1) Finding the linear approximation of non-linear functions by using the equation of the tangent line.
2) Finding the differential dy of a function y=f(x), which represents the change in y for an infinitesimal change dx in x.
3) Using differentials to approximate small changes or errors in a function when there is a small change in the input variable.
Bai giang Dao ham rieng
This document discusses partial derivatives of functions with multiple variables. It defines partial derivatives as derivatives of a function where all but one variable is held constant. For a function z=f(x,y), the partial derivatives with respect to x and y are defined. Higher order partial derivatives and partial derivatives of functions with more than two variables are also introduced. Examples are provided to demonstrate calculating first and second order partial derivatives.
3 handouts section2-2
1. The document defines the limit of a function as making the function values arbitrarily close to a limit L by taking the input value closer to a specific value.
2. It discusses one-sided limits and how the limit exists only when the left and right side limits are equal. Infinite limits result when direct substitution makes the denominator equal to zero.
3. Vertical asymptotes occur when the graph shoots to positive or negative infinity as the input approaches a particular value, or when factoring a rational function results in the denominator equaling zero at that input value.
7_Intro_to_Functions
The document discusses functions and how to determine if a relationship represents a function using the vertical line test. It defines what constitutes a function and introduces function notation. Examples are provided of evaluating functions for given values of the independent variable and using functions to model and express relationships between variables.
3 handouts section2-5
1. The document defines continuity and different types of discontinuities. A function is continuous if the limit exists and equals the function value at that point.
2. There are three types of discontinuities: removable (finite jump), infinite jump, and jump (finite discontinuity in function value).
3. Basic properties are that sums, products, scalar multiples of continuous functions are also continuous. Composition of continuous functions is continuous.
4. The intermediate value theorem states that if a continuous function takes on values between two numbers on an interval, it must take on all values in between.
Calculus 1 Lecture Notes (Functions and Their Graphs)
Calculus 1 Lecture Notes
Functions and Their Graphs
1 quadratic function
This document provides an agenda and activities for learning about quadratic functions that model real-world situations. It discusses using first and second differences to determine if a relationship is linear or quadratic. Activities include graphing quadratic functions in standard and vertex form, finding the domain and range, and converting between forms. Notes are provided on the standard form and how the parabola opens based on the value of a. The final activity has students write a quadratic function in vertex form.
2.3 Functions
This document defines and discusses functions. It begins by defining a relation and function, noting that a function is a special type of relation where each input is mapped to exactly one output. It introduces function notation and discusses the domain, codomain, and range of a function. Examples are provided to illustrate determining if a relation defines a function. The document also covers identifying functions from equations or graphs, and the vertical line test. It concludes with a discussion of function notation and classwork assignments.
Unit 1.2
This document provides an overview of key concepts related to functions and their properties. It discusses function definition and notation, domain and range, continuity, increasing and decreasing functions, boundedness, local and absolute extrema, symmetry, asymptotes, and end behavior. Examples are provided to illustrate key concepts such as finding the domain and range of functions, identifying points of discontinuity, determining if a function is increasing or decreasing, and identifying local extrema. The document is intended to teach readers about important properties of functions.
Operations on function.pptx
The document discusses operations that can be performed on functions, including addition, subtraction, multiplication, division, and composition. It defines each operation and provides examples of how to find the sum, difference, product, quotient, and composite of functions. The domain of operations on functions is also discussed.
Functions and Relations
The document discusses functions and operations with functions. It defines a function as a relation where each input has a unique output. It introduces function notation using f(x) to represent the output of a function f given an input x. It then discusses how to evaluate functions using this notation. Finally, it discusses how functions can be combined using the basic operations of addition, subtraction, multiplication and division to create new functions.
U1 Cn2 Functions
Functions relate dependent and independent variables, where the dependent variable is determined by the independent variable. Functions can be expressed as equations, tables, or graphs. Even functions are symmetric about the y-axis and odd functions are symmetric about the origin. The domain of a function is the set of valid inputs and the range is the set of outputs. A function can be restricted to only certain domain values or composed of multiple functions.
R lecture co4_math 21-1
This document discusses concepts related to calculus including functions, limits, continuity, and derivatives. The objective is for students to be able to evaluate limits and determine derivatives of algebraic functions. It defines functions and function notation. It discusses limits, continuity, and the definition of the derivative. It provides examples of evaluating limits using theorems and the squeeze principle. It also defines types of discontinuities and conditions for continuity.
gfg
This document provides an introduction to symbolic math in MATLAB. It discusses differentiation and integration of functions using symbolic operators. Differentiation is defined as finding the rate of change of a function with respect to a variable. Integration finds the original function given its derivative. The document provides examples of differentiating and integrating simple functions in MATLAB's symbolic toolbox and exercises for the reader to practice.
1_Representation_of_Functions.pptx
This document covers representing functions including objectives like defining functions and related terms, determining if a relation is a function, defining piecewise functions, and representing real-life situations
1 representation of_functions
This document covers representing functions including objectives like defining functions and related terms, determining if a relation is a function, defining piecewise functions, and representing real-life situations
Math1000 section2.1
This document contains lecture notes from a Math 1000 class taught by Stuart Jones. It covers several topics related to functions, including definitions of functions, evaluating functions, piecewise functions, and the difference quotient. Key points covered include the definition of a function as a mapping from a domain to a range, evaluating functions at different inputs, how piecewise functions use different formulas in different intervals, and the formula for the difference quotient.
Lesson 8 the definite integrals
The document defines definite integrals and discusses their properties. It states that a definite integral evaluates to a single number by integrating a function over a closed interval from a lower limit to an upper limit. It gives examples of using definite integrals to find areas bounded by curves. The mean value theorem for integrals is also introduced, which states that there is a rectangle between the inscribed and circumscribed rectangles with an area equal to the region under the curve. Exercises are provided on evaluating definite integrals and applying the mean value theorem.
Similar to 3 handouts section2-8-and_2-9 (20)
Calculus 1 Lecture Notes (Functions and Their Graphs)
Calculus 1 Lecture Notes (Functions and Their Graphs)
More from International advisers
SNC 2020 MATHEMATICS Final.pptx
The Single National Curriculum for mathematics aims to develop mathematical literacy, logical thinking, and the ability to solve real-life problems. It is divided into four strands: numbers and operations, algebra, measurements and geometry, and data handling. The curriculum also emphasizes developing students' spiritual, moral, social, and cultural values through mathematics. It takes a concrete-pictorial-abstract approach and uses real-life situations, stories, mental math, and inquiry to engage students in mathematical reasoning from grades 1 to 5. Assessment includes formative methods like tests and projects as well as summative term and final exams. Teaching resources include manuals, workbooks, and online materials.
SNC 2020 MATHEMATICS Lesson plan.pptx
This document outlines a unit on number operations from the Single National Curriculum for Class 2. It includes 1) comprehensive student learning outcomes like adding two-digit numbers, 2) using conceptual understanding with examples, 3) integrated methodologies like a lab activity using spinners to practice addition, 4) student worksheets and homework assignments, and 5) assessment measures like a class quiz with addition word problems. Remedial assistance is also provided for students who need extra help mastering the key concepts.
SNC 2020 MATHEMATICS requirment.pptx
The document compares the mathematics curriculum and standards between the 2006 National Curriculum and the 2020 Single National Curriculum (SNC) in Pakistan. It shows that the core strands and standards of Numbers and Operations, Algebra, Geometry and Measurement, and Data Handling remain the same, but Reasoning and Logical Thinking is now underpinned across all strands in the SNC. The SNC also re-groups grades, updates benchmarks, standards, and student learning outcomes to emphasize application, problem-solving, and mathematical thinking over rote learning. Unit structures, weightages, and cognitive domains are also adjusted in the SNC.
SNC 2020 MATHEMATICS Final final.pptx
The 2020 curriculum focuses on developing logical and procedural fluency through reasoning and situational based questions compared to the 2006 curriculum which focused on conceptual understanding and real life applications. Some key differences include introducing new concepts through warm-up activities and using math labs rather than real-life situations, assessing students through portfolios and project-based work rather than just pen and paper tests, and incorporating ICT like GeoGebra. Both curricula aim to develop conceptual understanding, but the 2020 version emphasizes linking past experiences and deriving formulas independently through activities while the 2006 version focused more on memorizing formulas through worksheets.
GRAVITATION Day 1 final.pptx
This document discusses the key concepts of gravitation, including:
1) Isaac Newton discovered the law of universal gravitation after observing an apple fall from a tree, realizing all objects attract each other with a gravitational force.
2) Newton's law of universal gravitation states that every object in the universe attracts every other object with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
3) The gravitational force between two objects follows Newton's third law of motion, with equal but opposite forces between the objects.
GRAVITATION Day 1 sample.pptx
This document discusses Newton's law of universal gravitation. It begins by stating the aims of understanding force of gravitation and deriving the mathematical law. It then defines gravity as a force that causes every object in the universe to attract each other. The key points are that Newton's law states that the gravitational force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. The document derives the gravitational formula and notes that gravitational force is very small between everyday objects, which is why we do not notice it.
GRAVITATION Day 1 final own voice.pptx
This chapter discusses gravitation and covers:
- Isaac Newton discovered gravity by observing an apple fall from a tree.
- Newton concluded that a force called gravitation causes objects to attract each other, deriving the inverse square law of universal gravitation.
- The gravitational force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.
RATIO & PROPORTION.pptx
This document discusses ratios and proportions. It provides a hierarchy of ratio-related concepts including fractions, equivalent ratios, ratios, unitary method, proportions, direct proportions, and inverse proportions. It includes learning objectives about understanding ratios, using ratio notation, dividing quantities in a given ratio, and recognizing the relationship between ratios and proportions. It provides examples of setting up and comparing ratios between quantities like weights of objects. It also gives examples of ratio assessment questions and converting units to the same units to simplify ratios.
.ppt
The document discusses the difference between active and passive voice. In passive voice, the subject receives the action while in active voice, the subject performs the action. Passive voice uses helping verbs like "be" and "by" while active voice is more concise and direct. The document provides examples of sentences in both voices and offers tips on changing passive sentences to active sentences by identifying the subject and changing the verb form.
Chapter 19.ppt
The document summarizes sections from Chapter 19 of Magruder's American Government textbook about civil liberties protections in the United States Constitution. It discusses the rights to freedom of religion, speech, press, assembly, and petition as protected by the First Amendment, and how the Supreme Court has interpreted and placed limits on these rights over time. It also examines how principles of limited government and federalism have impacted civil liberties.
Checks and Balances.ppt
The document discusses checks and balances in the US government. It outlines the checks that each branch of government (Congress, the presidency, and the judiciary) has on the others, such as congressional oversight of the presidency and judicial review. Potential threats to checks and balances are also examined, like executive orders and signing statements. Finally, it notes that the US has a stronger system of checks and balances than the UK to limit government power.
AP Gov Federalism Lyberger 2015.pptx
Federalism divides power between the national and state governments in order to limit the power of government. The national government has enumerated powers listed in the Constitution like regulating interstate commerce, while states have reserve powers like regulating intrastate commerce. This system aims to promote political participation, innovation, and diversity while avoiding concentrated power. However, it can also lead to complexity, inequity between states, and conflicts between levels of government.
ap gov ppt ch01.ppt
This chapter introduces key concepts in the study of American government such as who governs, the purpose of government, and different theories of government. It defines political power, authority, and legitimacy. It also outlines different forms of democracy like direct and representative democracy and discusses the Framers' view of balancing popular views with limiting majority abuse of power. Finally, it summarizes theories of government like Marxism, elitism, bureaucratic, and pluralist theories.
Teacher Notes MODULE 25.pptx
The United States becomes involved in the Vietnam War to stop the spread of communism in Southeast Asia. Over time, the war becomes increasingly unpopular and divisive in the US as it drags on without clear progress. Protests and opposition to the war intensify during the 1960s. Finally, in the early 1970s, President Nixon begins withdrawing US troops from Vietnam as part of his Vietnamization policy. The last US troops depart in 1973 after over a decade of involvement, leaving South Vietnam to fight on its own.
Teacher Notes MODULE 28.pptx
This document is from an American history textbook and outlines several lessons on key issues facing the United States in the 21st century, including national security, foreign policy, poverty, and the environment. It introduces topics like terrorism, surveillance, globalization, and climate change. Each lesson contains subsections that provide more details on related policies, events, debates, and challenges. The overall document serves as a guide for students to learn about significant domestic and international concerns confronting America today.
Teacher Notes MODULE 20.pptx
Germany invades neighboring countries and launches the Holocaust, systematically killing millions of Jews and others. The United States remains neutral at first but begins providing military and economic aid to Britain and other Allied nations. In 1941, Japan attacks the US naval base at Pearl Harbor, bringing America fully into World War II against Germany, Italy and Japan.
Teacher Notes MODULE 21.pptx
The Cold War defined international affairs after World War 2, especially following the Korean War. The document outlines 6 lessons on the Cold War: 1) The Origins of the Cold War as the US and USSR emerged as superpowers with opposing political/economic systems; 2) The Cold War Heats Up as China became communist and Korea was divided; 3) The Cold War at Home and McCarthyism led to accusations against innocent US citizens; 4) Two Nations Live on the Edge as the nuclear arms race and brinksmanship brought the two countries to the edge of war; 5) Mounting Tensions in the Sixties led to further conflicts; and 6) The End of the Cold War in the late 1980s.
Teacher Notes MODULE 23.pptx
The document summarizes key events and policies during the Kennedy and Johnson administrations from the 1960s. It discusses Kennedy's New Frontier agenda which aimed to address social issues and confront the Soviet Union, but was cut short by his 1963 assassination. It then outlines Lyndon Johnson's Great Society programs that aimed to eliminate poverty and racial injustice through major civil rights laws and social welfare programs. However, Johnson also greatly escalated US involvement in the Vietnam War during this period of significant social change and cultural upheaval in America.
Teacher Notes MODULE 24.pptx
Activism and new civil rights legislation in the 1950s and 1960s advanced equal rights for African Americans. However, disagreements arose among civil rights groups about strategies and priorities, leading to a more violent period. Court decisions and laws banned segregation and expanded voting rights, but resistance remained strong in some areas.
Chapter_20.pptx
The document summarizes key aspects of US national security policymaking, including foreign policy instruments like the military, economics, and diplomacy. It outlines actors involved in foreign relations such as international organizations, regional groups, companies, NGOs, and individuals. It describes policymakers like the President, diplomats, national security establishment, and Congress. It provides an overview of periods in US foreign policy history from isolationism to the present War on Terror. It also briefly mentions military policy areas.
More from International advisers (20)
Recently uploaded
Top five deadliest dog breeds in America
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
How to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar KanvariaHow to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityAkanksha trivedi rama nursing college kanpur.
Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcDigital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments Unit - NGV Pavilion Concept Design
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...Nguyen Thanh Tu Collection
https://app.box.com/s/y977uz6bpd3af4qsebv7r9b7s21935vdExecutive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)Academy of Science of South Africa
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.CACJapan - GROUP Presentation 1- Wk 4.pdf
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
The Diamonds of 2023-2024 in the IGRA collection
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
DRUGS AND ITS classification slide share
Any substance (other than food) that is used to prevent, diagnose, treat, or relieve symptoms of a
disease or abnormal condition
The History of Stoke Newington Street Names
Presented at the Stoke Newington Literary Festival on 9th June 2024
www.StokeNewingtonHistory.com
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS Template 2023-2024 by: Irene S. Rueco
Recently uploaded (20)
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
Executive Directors Chat Leveraging AI for Diversity, Equity, and Inclusion
South African Journal of Science: Writing with integrity workshop (2024)
South African Journal of Science: Writing with integrity workshop (2024)
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
3 handouts section2-8-and_2-9
- 1. Section 2.8 Derivatives Section 2.9 The derivative as a function Learning outcomes After completing this section, you will inshaAllah be able to 1. explain the definition of derivative of a function 2. find derivatives using definition ( )1 2.8 2.9− • In the last section we saw that the rate of change of f(x) at a point ‘x’ is given by 0 ( ) ( ) lim h f a h f a m h→ + − = • Therefore such limits become very important. • The study of important limit of above type leads to the concept of derivative, which we study here.
- 2. Derivative of a function • Another notation: dy dx • ( )f a′ means derivative at the point a Geometric interpretation of derivative Checking differentiability graphically See examples 1, 2, 3 done in class See example 4 done in class The derivative of f(x) is defined by 0 ( ) ( ) ( ) lim h f x h f x f x h→ + − ′ = , if the limit exists. ( )2 2.8 2.9− See class explanation See class explanation
- 3. Left/Right derivative of a function Existence of a derivative • The next example uses all of these ideas. End of 2.8, 2.9 The left derivative of f(x) is defined by 0 ( ) ( ) ( ) lim h f a h f a f a h−− → + − ′ = ( )3 2.8 2.9− The right derivative of f(x) is defined by 0 ( ) ( ) ( ) lim h f a h f a f a h++ → + − ′ = See explanation given above for geometric interpretation of derivative The derivative ( )f a′ exists if the left and right derivatives are same. Also note the fact that “if a function is differentiable at a point then it is continuous at that point” i.e. the function will surely be not differentiable at a point where it is discontinuous See example 5 done in class