Bird’s Comprehensive Engineering Mathematics 2nd Edition by John Bird – Ebook PDF Instant Download/DeliveryISBN: 1351232852, 9781351232852
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ISBN-10 : 1351232852
ISBN-13 : 9781351232852
Author: John Bird
Studying engineering, whether it is mechanical, electrical or civil, relies heavily on an understanding of mathematics. This textbook clearly demonstrates the relevance of mathematical principles and shows how to apply them in real-life engineering problems. It deliberately starts at an elementary level so that students who are starting from a low knowledge base will be able to quickly get up to the level required. Students who have not studied mathematics for some time will find this an excellent refresher. Each chapter starts with the basics before gently increasing in complexity. A full outline of essential definitions, formulae, laws and procedures is presented, before real world practical situations and problem solving demonstrate how the theory is applied. Focusing on learning through practice, it contains simple explanations, supported by 1600 worked problems and over 3600 further problems contained within 384 exercises throughout the text. In addition, 35 Revision tests together with 9 Multiple-choice tests are included at regular intervals for further strengthening of knowledge. An interactive companion website provides material for students and lecturers, including detailed solutions to all 3600 further problems.
Bird’s Comprehensive Engineering Mathematics 2nd Table of contents:
1 Basic arithmetic
1.1 Introduction
1.2 Revision of addition and subtraction
1.3 Revision of multiplication and division
1.4 Highest common factors and lowest common multiples
1.5 Order of operation and brackets
2 Fractions
2.1 Introduction
2.2 Adding and subtracting fractions
2.3 Multiplication and division of fractions
2.4 Order of operation with fractions
Revision Test 1 Decimals, calculations and percentages
3 Decimals
3.1 Introduction
3.2 Converting decimals to fractions and vice-versa
3.3 Significant figures and decimal places
3.4 Adding and subtracting decimal numbers
3.5 Multiplying and dividing decimal numbers
4 Using a calculator
4.1 Introduction
4.2 Adding, subtracting, multiplying and dividing
4.3 Further calculator functions
4.4 Errors and approximations
4.5 Rational and irrational numbers
4.6 Evaluation of formulae
5 Percentages
5.1 Introduction
5.2 Percentage calculations
5.3 Further percentage calculations
5.4 More percentage calculations
Revision Test 2 Decimals, calculations and percentages
6 Ratio and proportion
6.1 Introduction
6.2 Ratios
6.3 Direct proportion
6.4 Inverse proportion
7 Powers, roots and laws of indices
7.1 Introduction
7.2 Powers and roots
7.3 Laws of indices
8 Units, prefixes and engineering notation
8.1 Introduction
8.2 SI units
8.3 Common prefixes
8.4 Standard form
8.5 Engineering notation
8.6 Metric conversions
8.7 Metric – US/Imperial conversions
Revision Test 3 Ratio, proportion, powers, roots, indices and units
9 Basic algebra
9.1 Introduction
9.2 Basic operations
9.3 Laws of indices
10 Further algebra
10.1 Introduction
10.2 Brackets
10.3 Factorisation
10.4 Laws of precedence
Multiple choice questions Test 1
11 Solving simple equations
11.1 Introduction
11.2 Solving equations
11.3 Practical problems involving simple equations
Revision Test 4 Algebra and simple equations
12 Transposing formulae
12.1 Introduction
12.2 Transposing formulae
12.3 Further transposing of formulae
12.4 More difficult transposing offormulae
13 Solving simultaneous equations
13.1 Introduction
13.2 Solving simultaneous equations in two unknowns
13.3 Further solving of simultaneous equations
13.4 Solving more difficult simultaneous equations
13.5 Practical problems involving simultaneous equations
13.6 Solving simultaneous equations in three unknowns
Revision Test 5 Transposition and simultaneous equations
14 Solving quadratic equations
14.1 Introduction
14.2 Solution of quadratic equations by factorisation
14.3 Solution of quadratic equations by ‘completing the square’
14.4 Solution of quadratic equations by formula
14.5 Practical problems involving quadratic equations
14.6 Solution of linear and quadratic equations simultaneously
Multiple choice questions Test 2
15 Logarithms
15.1 Introduction to logarithms
15.2 Laws of logarithms
15.3 Indicial equations
15.4 Graphs of logarithmic functions
16 Exponential functions
16.1 Introduction to exponential functions
16.2 The power series for
16.3 Graphs of exponential functions
16.4 Napierian logarithms
16.5 Laws of growth and decay
17 Inequalities
17.1 Introduction to inequalities
17.2 Simple inequalities
17.3 Inequalities involving a modulus
17.4 Inequalities involving quotients
17.5 Inequalities involving square functions
17.6 Quadratic inequalities
Revision Test 6 Quadratics, logarithms, exponentials and inequalities
Formulae/revision hints for Section A
Section B Further number and algebra
18 Polynomial division and the factor and remainder theorems
18.1 Polynomial division
18.2 The factor theorem
18.3 The remainder theorem
19 Partial fractions
19.1 Introduction to partial fractions
19.2 Worked problems on partial fractions with linear factors
19.3 Worked problems on partial fractions with repeated linear factors
19.4 Worked problems on partial fractions with quadratic factors
20 Number sequences
20.1 Simple sequences
20.2 The th term of a series
20.3 Arithmetic progressions
20.4 Geometric progressions
20.5 Combinations and permutations
Revision Test 7 Further algebra, partial fractions and number sequences
21 The binomial series
21.1 Pascal’s triangle
21.2 The binomial series
21.3 Worked problems onthe binomialseries
21.4 Further worked problems onthebinomial series
21.5 Practical problems involving thebinomial theorem
22 Maclaurin’s series
22.1 Introduction
22.2 Derivation of Maclaurin’s theorem
22.3 Conditions of Maclaurin’s series
22.4 Worked problems on Maclaurin’s series
22.5 Numerical integration using Maclaurin’s series
22.6 Limiting values
Revision Test 8 The binomial and Maclaurin’s series
23 Solving equations by iterative methods
23.1 Introduction to iterative methods
23.2 The bisection method
23.3 An algebraic method of successive approximations
23.4 The Newton–Raphson method
24 Hyperbolic functions
24.1 Introduction to hyperbolic functions
24.2 Graphs of hyperbolic functions
24.3 Hyperbolic identities
24.4 Solving equations involving hyperbolic functions
24.5 Series expansions for cosh x andsinh x
Revision Test 9 Iterative methods and hyperbolic functions
25 Binary, octal and hexadecimal numbers
25.1 Introduction
25.2 Binary numbers
25.3 Octal numbers
25.4 Hexadecimal numbers
26 Boolean algebra and logic circuits
26.1 Boolean algebra and switching circuits
26.2 Simplifying Boolean expressions
26.3 Laws and rules of Boolean algebra
26.4 De Morgan’s laws
26.5 Karnaugh maps
26.6 Logic circuits
26.7 Universal logic gates
Revision Test 10 Numbering systems, Boolean algebra and logic circuits
Multiple choice questions Test 3
Formulae/revision hints for Section B
Section C Areas and volumes
27 Areas of common shapes
27.1 Introduction
27.2 Common shapes
27.3 Areas of common shapes
27.4 Areas of similar shapes
28 The circle and its properties
28.1 Introduction
28.2 Properties of circles
28.3 Radians and degrees
28.4 Arc length and area of circles and sectors
28.5 The equation of a circle
28.6 Linear and angular velocity
28.7 Centripetal force
Revision Test 11 Areas of common shapes and the circle
29 Volumes and surface areas of common solids
29.1 Introduction
29.2 Volumes and surface areas ofcommon shapes
29.3 Summary of volumes and surface areas of common solids
29.4 More complex volumes and surface areas
29.5 Volumes and surface areas of frusta of pyramids and cones
29.6 The frustum and zone of a sphere
29.7 Prismoidal rule
29.8 Volumes of similar shapes
30 Irregular areas and volumes, and mean values
30.1 Areas of irregular figures
30.2 Volumes of irregular solids
30.3 Mean or average values of waveforms
Revision Test 12 Volumes, irregular areas and volumes, and mean values
Formulae/revision hints for Section C Areas and volumes
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