Preface
Syllabus guidance
Section A Number and algebra
1 Algebra
2 Partial fractions
3 Logarithms
4 Exponential functions
5 Inequalities
6 Arithmetic and geometric progressions
7 The binomial series
8 Maclaurin's series
9 Solving equations by iterative methods
10 Binary, octal and hexadecimal numbers
11 Boolean algebra and logic circuits
Section B Geometry and trigonometry
12 Introduction to trigonometry
13 Cartesian and polar co-ordinates
14 The circle and its properties
15 Trigonometric waveforms
16 Hyperbolic functions
17 Trigonometric identities and equations
18 The relationship between trigonometric and
hyperbolic functions
19 Compound angles
Section C Graphs
20 Functions and their curves
21 Irregular areas, volumes and mean values of waveforms
Section D Complex numbers
22 Complex numbers
23 De Moivre's theorem
Section E Matrices and determinants
24 The theory of matrices and determinants
25 Applications of matrices and determinants
Section F Vector geometry 303
26 Vectors
27 Methods of adding alternating waveforms
28 Scalar and vector products
Section G Introduction to calculus
29 Methods of differentiation
30 Some applications of differentiation
31 Standard integration
32 Some applications of integration
33 Introduction to differential equations
Section H Further differential calculus
34 Differentiation of parametric equations
35 Differentiation of implicit functions
36 Logarithmic differentiation
37 Differentiation of hyperbolic functions
38 Differentiation of inverse trigonometric and hyperbolic functions
39 Partial differentiation
40 Total differential, rates of change and small changes
41 Maxima, minima and saddle points for functions of two variables
Section I Further integral calculus
42 Integration using algebraic substitutions
43 Integration using trigonometric and hyperbolic substitutions
44 Integration using partial fractions
45 The t = tan /2
46 Integration by parts
47 Reduction formulae
48 Double and triple integrals
49 Numerical integration
Section J Further differential equations
50 Homogeneous first order differential equations
51 Linear first order differential equations
52 Numerical methods for first order differential equations
53 First order differential equations of the form
54 First order differential equations of the form
55 Power series methods of solving ordinary differential equations
56 An introduction to partial differential equations
Section K Statistics and probability
57 Presentation of statistical data
58 Mean, median, mode and standard deviation
59 Probability
60 The binomial and Poisson distributions
61 The normal distribution
62 Linear correlation
63 Linear regression
64 Sampling and estimation theories
65 Significance testing
66 Chi-square and distribution-free tests
Section L Laplace transforms
67 Introduction to Laplace transforms
68 Properties of Laplace transforms
69 Inverse Laplace transforms
70 The Laplace transform of the Heaviside function
71 The solution of differential equations using Laplace transforms
72 The solution of simultaneous differential equations using Laplace transforms
Section M Fourier series
73 Fourier series for periodic functions of period 2
74 Fourier series for a non-periodic function over period 2
75 Even and odd functions and half-range Fourier series
76 Fourier series over any range
77 A numerical method of harmonic analysis
78 The complex or exponential form of a Fourier series
Section N Z-transforms
79 An introduction to z-transforms
Essential formulae
Answers to Practice Exercises
Index
