Higher Engineering Mathematics

 

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First edition 2010

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CONTENTS

    Preface

   Syllabus guidance

1 Algebra 

2 Partial fractions 

3 Logarithms 

4 Exponential functions 

  Revision Test 1 

5 Hyperbolic functions

6 Arithmetic and geometric progressions

7 The binomial series

  Revision Test2

8 Maclaurin’s series 

9 Solving equations by iterative methods

10 Binary, octal  and hexadecimal 

  Revision Test3

11 Introduction to trigonometry

12 Cartesian and polar co-ordinates

13 The circle and its properties

   RevisionTest4

14 Trigonometric waveforms

15 Trigonometric identities and equations

16 The relationship between trigonometric and hyperbolic functions

17 Compound angles 

   RevisionTest5

18 Functions and their curves

19 Irregular are as, volumes and mean values of waveforms

   RevisionTest6

20 Complex numbers 

21 De Moivre’s theorem

22 The theory of matrices and determinants

23 The solution of simultaneous equations by matrices and determinants

   Revision Test7 

24 Vectors

25 Methods of adding alternating waveforms

26 Scalar and vector products

   Revision Test8

27 Methods of differentiation

28 Some applications of differentiation 

29 Differentiation of parametric equations 

30 Differentiation of implicit functions 

31 Logarithmic differentiation 

   RevisionTest9

32 Differentiation of hyperbolic functions

33 Differentiation of inverse trigonometric and hyperbolic functions

33 Differentiation of inverse trigonometric and hyperbolic functions 

34 Partial differentiation

35 Total differential, rates of change and small changes 

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

   RevisionTest10

37 Standard integration 

38 Some applications of integration 

39 Integration using algebraic substitutions

RevisionTest11

40 Integration using trigonometric and hyperbolic substitutions 

41 Integration using partial fractions 

42 The t=tan

θ 2

substitution 

   Revision Test12 

43 Integration by parts 

44 Reduction formulae 

45 Numerical integration 

   Revision Test13 

46 Solution of first order differential equations by separation of variables

47 Homogeneous first order differential equations 

48 Linear first order differential equations 

49 Numerical methods for first order differential equations 

   Revision Test14 

50 Second order differential equations of the form 

51 Second order differential equations of the form 

52 Power series methods of solving ordinary differential equations 

53 An introduction to partial differential equations

   RevisionTest15

54 Presentation of statistical data 

55 Measures of central tendency and dispersion 

56 Probability 

   RevisionTest16

57 The binomial and Poisson distributions 

58 The normal distribution

59 Linear correlation 

60 Linear regression 

61 Introduction to Laplace transforms 

62 Properties of Laplace transforms 

63 Inverse Laplace transforms 

64 The solution of differential equations using Laplace transforms 

65 The solution of simultaneous differential equations using Laplace transforms

Revision Test18 

66 Fourier series for periodic functions of period2π 

67 Fourier series for a non-periodic function over range2π

68 Even and odd functions and half-range Fourier series 

69 Fourier series over any range 

70 A numerical method of harmonic analysis

71 The complex or exponential form of a Fourier series

  Revision Test19 

  Essential formulae 

  Index 

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