目次

Introduction;  Preface;  Website information;  Syllabus guidance;  1. Algebra;  2. Partial fractions;  3. Logarithms;  4. Exponential functions;  5. Inequalities;  Revision Test 1;  6. Arithmetic and geometric progressions;  7. The binomial series;  Revision Test 2;  8. Maclaurin’s series;  9. Solving equations by iterative methods;  10. Binary, octal and hexadecimal numbers;  11. Boolean algebra and logic circuits;  Revision Test 3;  12. Introduction to trigonometry;  13. Cartesian and polar co-ordinates;  14. The circle and its properties;  Revision Test 4;  15. Trigonometric waveforms;  16. Hyperbolic functions;  17. Trigonometric identities and equations;  18. The relationship between trigonometric and hyperbolic functions;  19. Compound angles;  Revision Test 5;  20. Functions and their curves;  21. Irregular areas, volumes and mean values of waveforms;  Revision Test 6;  22. Complex numbers;  23. De Moivre’s theorem;  24. The theory of matrices and determinants;  25. Applications of matrices and determinants;  Revision Test 7;  26. Vectors;  27. Methods of adding alternating waveforms;  28. Scalar and vector products;  Revision Test 8;  29. Methods of differentiation;  30. Some applications of differentiation;  31. Differentiation of parametric equations;  32. Differentiation of implicit functions;  33. Logarithmic differentiation;  Revision Test 9;  34. Differentiation of hyperbolic functions;  35. Differentiation of inverse trigonometric and hyperbolic functions;  36. Partial differentiation;  37. Total differential, rates of change and small changes;  38. Maxima, minima and saddle points for functions of two variables;  Revision Test 10;  39. Standard integration;  40. Some applications of integration;  41. Integration using algebraic substitutions;  Revision Test 11;  42. Integration using trigonometric and hyperbolic substitutions;  43. Integration using partial fractions;  44. The t = tan substitution;  Revision Test 12;  45. Integration by parts;  46. Reduction formulae;  47. Double and triple integrals;  48. Numerical integration;  Revision Test 13;  49. Solution of first order differential equations by separation of variables;  50. Homogeneous first order differential equations;  51.Linear first order differential equations;  52. Numerical methods for first order differential equations;  Revision Test 14;  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;  Revision Test 15;  57. Presentation of statistical data;  58. Mean, median, mode and standard deviation;  59. Probability;  Revision Test 16;  60. The binomial and Poisson distributions;  61. The normal distribution;  62. Linear correlation;   63. Linear regression;  Revision Test 17;  64. Sampling and estimation theories;  65. Significance testing;  66. Chi-square and distribution-free tests;  Revision Test 18;  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;  Revision Test 19;  73. Fourier series for periodic functions of period 2p;  74. Fourier series for a non-periodic function over period 2p;  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;  Revision Test 20;  Essential formulae;  Answers to Practise Exercises;  Index