Author: John Bird
Published March 2021
Higher Engineering Mathematics has helped thousands of students to succeed in their exams by developing problem-solving skills, It is supported by over 600 practical engineering examples and applications which relate theory to practice. The extensive and thorough topic coverage makes this a solid text for undergraduate and upper-level vocational courses. Its companion website provides resources for both students and lecturers, including lists of essential formulae, ands full solutions to all 2,000 further questions contained in the 277 practice exercises; and illustrations and answers to revision tests for adopting course instructors.
Table of Contents
Section A Number and algebra
1 Algebra
2 Partial fractions
3 Logarithms
4 Exponential functions
5 The binomial series
6.Solving equations by iterative methods
7 Boolean algebra and logic circuits
Section B Geometry and trigonometry
8 Introduction to trigonometry
9 Cartesian and polar co-ordinates
10 The circle and its properties
11 Trigonometric waveforms
12 Hyperbolic functions
13 Trigonometric identities and equations
14 The relationship between trigonometric and hyperbolic functions
15 Compound angles
Section C Graphs
16 Functions and their curves
17 Irregular areas, volumes and mean values of waveforms
Section D Complex numbers
18 Complex numbers
19 De Moivre’s theorem
Section E Matrices and determinants
20 The theory of matrices and determinants
21 Applications of matrices and determinants
Section F Vector geometry
22 Vectors
23 Methods of adding alternating waveforms
24 Scalar and vector products
Section G Differential calculus
25 Methods of differentiation
26 Some applications of differentiation
27 Differentiation of parametric equations
28 Differentiation of implicit functions
29 Logarithmic differentiation
30 Differentiation of hyperbolic functions
31 Differentiation of inverse trigonometric and hyperbolic functions
32 Partial differentiation
33 Total differentials, rates of change and small changes
34 Maxima, minima and saddle points for functions of two variables
Section H Integral calculus
35 Standard integration
36 Some applications of integration
37 Maclaurin’s series
38 Integration using algebraic substitutions
39 Integration using trigonometric and hyperbolic substitutions
40 Integration using partial fractions
41 The t = tan θ/2
42 Integration by parts
43 Reduction formulae
44 Double and triple integrals
45 Numerical integration
Section I Differential equations
46 Introduction to differential equations
47 Homogeneous first order differential equations
48 Linear first order differential equations
49 Numerical methods for first order differential equations
50 First order differential equations (1)
51 First order differential equations (2)
52 Power series methods of solving ordinary differential equations
53 An introduction to partial differential equations
Section J Laplace transforms
54 Introduction to Laplace transforms
55 Properties of Laplace transforms
56 Inverse Laplace transforms
57 The Laplace transform of the Heaviside function
58 The solution of differential equations using Laplace transforms
59 The solution of simultaneous differential equations using Laplace transforms
Section K Fourier series
60 Fourier series for periodic functions of period 2π
61 Fourier series for a non-periodic function over period 2π
62 Even and odd functions and half-range Fourier series
63 Fourier series over any range
64 A numerical method of harmonic analysis
65 The complex or exponential form of a Fourier series
Section L Z-transforms
66 An introduction to z-transforms
Section M Statistics and probability
67 Presentation of statistical data
68 Mean, median, mode and standard deviation
69 Probability
70 The binomial and Poisson distributions
71 The normal distribution
72 Linear correlation
73 Linear regression
74 Sampling and estimation theories
75 Significance testing
76 Chi-square and distribution-free tests
Essential formulae
Answers to Practice Exercises
