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 and limiting values 38 Integration using algebraic substitutions 39 Integration using trigonometric and hyperbolic substitutions 40 Integration using partial fractions 41 The t = tan θ/2 substitution 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 Second-order differential equations (1) 51 Second-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