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This document provides an overview of key concepts related to real numbers including rational numbers, irrational numbers, and operations involving them. It discusses that rational numbers can be expressed as fractions with integer numerators and denominators and give either terminating or recurring decimal expansions. Irrational numbers cannot be expressed as fractions and include numbers like √2. The document notes that when rational numbers are combined with irrational numbers through operations, the result is always irrational. It also defines highest common factor and least common multiple, providing examples of calculating each.
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Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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www.StokeNewingtonHistory.com
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Presentation (18).pptx
- 1. ART INTEGRATED PROJECT 2021-2022 MATHEMATICS CH-1 REAL NUMBERS • NAME : BHARATH.B • CLASS&SECTION : X-M • EXAM NO : 10M01 • COMPUTER NO : 80206 • SUBJECT : MATHS
- 2. TYPES OF NUMBERS • Natural Numbers (N) • Whole Numbers (W) • Integers (Z) • Rational numbers (Q) and Irrational Numbers • Real numbers (R)
- 3. RATIONAL NUMBERS AND DECIMALS • Any number is known as rational number if it is expressed as quotient or fraction pq. Of two integers where p is the numerator and q is the denominator. Since p and q are integers. So, q can also be equal to 1. So, every integer is a rational number. • Some of the examples of rational number are ½, 1/5, 3/4
- 4. DECIMAL EXPANSION OF RATIONAL NUMBER • A rational number gives either terminating or non- terminating recurring decimal expansion. Thus, we can say that a number whose decimal expansion is terminating or non-terminating recurring is rational. • Decimal numbers with the finite number of digits are called as terminating decimals while decimals with the infinite number of digits are called as non-terminating decimals.Example: 0.5, 2.456, 123.456, etc
- 5. IRRATIONAL NUMBERS • An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. ... Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.
- 6. OPERATIONS ON RATIONAL AND IRRATIONAL NUMBERS • When the addition or subtraction operation is done on a rational and irrational number, the result is an irrational number. • When the multiplication or division operation is done on a rational number with an irrational number, the result is an irrational number. • When two irrational numbers are added, subtracted, multiplied or divided, the result may be a rational or an irrational number.
- 7. HIGHEST COMMON FACTOR (HCF) • The HCF (Highest Common Factor) of two numbers is the highest number among all the common factors of the given numbers. For example, HCF of 12 and 36 is 12 because 12 is the highest common factor of 12 and 36.
- 8. LEAST COMMON MULTIPLE ( L.C.M ) * The least common multiple (L.C.M) of two or more number is the smallest number which can be exactly divided by each of the given number Let us find the LCM of 28 and 12 Multiples of 28 are 28 , 56 , 84 , 112 ……… Multiples of 12 are 12 , 24 , 36 , 48 , 60 , 72 , 84 , 96 ………. The least common multiple (L.C.M) of 28 and 12 is 84