Bird's Higher Engineering Mathematics

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