Previous edition: 2014. Includes index.

PrefaceSyllabus guidanceSection A Number and algebra1 Algebra2 Partial fractions3 Logarithms4 Exponential functions5 Inequalities6 Arithmetic and geometric progressions7 The binomial series8 Maclaurin's series9 Solving equations by iterative methods10 Binary, octal and hexadecimal numbers11 Boolean algebra and logic circuitsSection B Geometry and trigonometry12 Introduction to trigonometry13 Cartesian and polar co-ordinates14 The circle and its properties15 Trigonometric waveforms16 Hyperbolic functions17 Trigonometric identities and equations18 The relationship between trigonometric andhyperbolic functions19 Compound anglesSection C Graphs20 Functions and their curves21 Irregular areas, volumes and mean values of waveforms Section D Complex numbers22 Complex numbers 23 De Moivre's theorem Section E Matrices and determinants24 The theory of matrices and determinants 25 Applications of matrices and determinants Section F Vector geometry 30326 Vectors 27 Methods of adding alternating waveforms 28 Scalar and vector productsSection G Introduction to calculus29 Methods of differentiation30 Some applications of differentiation31 Standard integration32 Some applications of integration33 Introduction to differential equationsSection H Further differential calculus34 Differentiation of parametric equations35 Differentiation of implicit functions36 Logarithmic differentiation37 Differentiation of hyperbolic functions38 Differentiation of inverse trigonometric and hyperbolic functions 39 Partial differentiation40 Total differential, rates of change and small changes41 Maxima, minima and saddle points for functions of two variablesSection I Further integral calculus42 Integration using algebraic substitutions43 Integration using trigonometric and hyperbolic substitutions44 Integration using partial fractions45 The t = tan θ/246 Integration by parts47 Reduction formulae48 Double and triple integrals49 Numerical integration Section J Further differential equations50 Homogeneous first order differential equations51 Linear first order differential equations52 Numerical methods for first order differential equations53 First order differential equations of the form54 First order differential equations of the form55 Power series methods of solving ordinary differential equations56 An introduction to partial differential equationsSection K Statistics and probability57 Presentation of statistical data58 Mean, median, mode and standard deviation59 Probability60 The binomial and Poisson distributions61 The normal distribution62 Linear correlation63 Linear regression64 Sampling and estimation theories65 Significance testing66 Chi-square and distribution-free testsSection L Laplace transforms67 Introduction to Laplace transforms68 Properties of Laplace transforms69 Inverse Laplace transforms70 The Laplace transform of the Heaviside function71 The solution of differential equations using Laplace transforms72 The solution of simultaneous differential equations using Laplace transformsSection M Fourier series73 Fourier series for periodic functions of period 2Ï 74 Fourier series for a non-periodic function over period 2Ï 75 Even and odd functions and half-range Fourier series76 Fourier series over any range77 A numerical method of harmonic analysis78 The complex or exponential form of a Fourier seriesSection N Z-transforms79 An introduction to z-transformsEssential formulaeAnswers to Practice ExercisesIndex