# Understanding Engineering Mathematics

## Book Description

Studying engineering, whether it is mechanical, electrical or civil relies heavily on an understanding of mathematics. This new textbook clearly demonstrates the relevance of mathematical principles and shows how to apply them to solve 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 are introduced before real world situations, practicals and problem solving demonstrate how the theory is applied.

Focusing on learning through practice, it contains examples, supported by 1,600 worked problems and 3,000 further problems contained within exercises throughout the text. In addition, 34 revision tests are included at regular intervals.

An interactive companion website is also provided containing 2,750 further problems with worked solutions and instructor materials

### Table of Contents

Section A Number and Algebra

1 Basic arithmetic

2 Fractions

3 Decimals

4 Using a calculator

5 Percentages

6 Ratio and proportion

7 Powers, roots and laws of indices

8 Units, prefixes and engineering notation

9 Basic algebra

10 Further algebra

11 Solving simple equations

12 Transposing formulae

13 Solving simultaneous equations

14 Solving quadratic equations

15 Logarithms

16 Exponential functions

17 Inequalities

Section B Further number and algebra

18 Polynomial division and the factor and remainder theorems

19 Number sequences

20 Binary, octal and hexadecimal numbers

21 Partial fractions

22 The binomial series

23 Maclaurin’s series

24 Hyperbolic functions

25 Solving equations by iterative methods

26 Boolean algebra and logic circuits

Section C Areas and volumes

27 Areas of common shapes

28 The circle and its properties

29 Volumes and surface areas of common solids

30 Irregular areas and volumes, and mean values

Section D Graphs

31 Straight line graphs

32 Graphs reducing non-linear laws to linear form

33 Graphs with logarithmic scales

34 Polar curves

35 Graphical solution of equations

36 Functions and their curves

Section E Geometry and trigonometry

37 Angles and triangles

38 Introduction to trigonometry

39 Trigonometric waveforms

40 Cartesian and polar co-ordinates

41 Non-right-angled triangles and some practical applications

42 Trigonometric identities and equations

43 The relationship between trigonometric and hyperbolic functions

44 Compound angles

Section F Complex numbers

45 Complex numbers

46 De Moivre’s theorem

Section G Matrices and determinants

47 The theory of matrices and determinants

48 Applications of matrices and determinants

Section H Vector geometry

49 Vectors

50 Methods of adding alternating waveforms

51 Scalar and vector products

Section I Differential calculus

52 Introduction to differentiation

53 Methods of differentiation

54 Some applications of differentiation

55 Differentiation of parametric equations

56 Differentiation of implicit functions

57 Logarithmic differentiation

58 Differentiation of hyperbolic functions

59 Differentiation of inverse trigonometric and hyperbolic functions

60 Partial differentiation

61 Total differential, rates of change and small changes

62 Maxima, minima and saddle points for functions of two variables

Section J Integral calculus

63 Standard integration

64 Integration using algebraic substitutions

65 Integration using trigonometric and hyperbolic substitutions

66 Integration using partial fractions

67 The t=tanθ/2 substitution

68 Integration by parts

69 Reduction formulae

70 Double and triple integrals

71 Numerical integration

72 Areas under and between curves

73 Mean and root mean square values

74 Volumes of solids of revolution

75 Centroids of simple shapes

76 Second moments of area

Section K Differential equations

77 Solution of first-order differential equations by separation of variables

78 Homogeneous first-order differential equations

79 Linear first-order differential equations

80 Numerical methods for first-order differential equations

81 Second-order differential equations of the form a d2y/dx2+bdy/dx+cy=0

82 Second-order differential equations of the form ad2y/dx2+bdy/dx+cy=f(x)

83 Power seriesmethods of solving ordinary differential equations

84 An introduction to partial differential equations

Section L Statistics and probability

85 Presentation of statistical data

86 Mean, median, mode and standard deviation

87 Probability

88 The binomial and Poisson distributions

89 The normal distribution

90 Linear correlation

91 Linear regression

92 Sampling and estimation theories

93 Significance testing

94 Chi-square and distribution-free tests

Section M Laplace transforms

95 Introduction to Laplace transforms

96 Properties of Laplace transforms

97 Inverse Laplace transforms

98 The Laplace transform of the Heaviside function

99 The solution of differential equations using Laplace transforms

100 The solution of simultaneous differential equations using Laplace transforms

Section N Fourier series

101 Fourier series for periodic functions of period 2π

102 Fourier series for a non-periodic function over range 2π

103 Even and odd functions and half-range Fourier series

104 Fourier series over any range

105 A numerical method of harmonic analysis

106 The complex or exponential form of a Fourier series

## Book Details

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Download Link | Format | Size (MB) | Upload Date |
---|---|---|---|

Download from UsersCloud | True PDF | 7.3 | 12/25/2017 |