Table of Content
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 θ/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 2π 74 Fourier series for a non-periodic function over period 2π 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
