Includes index.

Section A Number And Algebra -- 1. Basic arithmetic -- 2. Fractions -- 3. Decimals -- 4. Using a calculator -- 5. Percentages -- 6. Ratio and proportion -- 7. Powers, roots and laws of indices -- 8. Units, prefixes and engineering notation -- 9. Basic algebra -- 10. Further algebra -- 11. Solving simple equations -- 12. Transposing formulae -- 13. Solving simultaneous equations -- 14. Solving quadratic equations -- 15. Logarithms -- 16. Exponential functions -- 17. Inequalities -- 18. Polynomial division and the factor and remainder theorems -- 19. Number sequences -- 20. Binary, octal and hexadecimal numbers -- 21. Partial fractions -- 22. The binomial series -- 23. Maclaurin's series -- 24. Hyperbolic functions -- 25. Solving equations by iterative methods -- 26. Boolean algebra and logic circuits -- 27. Areas of common shapes -- 28. The circle and its properties -- 29. Volumes and surface areas of common solids -- 30. Irregular areas and volumes, and mean values -- 31. Straight line graphs -- 32. Graphs reducing non-linear laws to linear form -- 33. Graphs with logarithmic scales -- 34. Polar curves -- 35. Graphical solution of equations -- 36. Functions and their curves -- 37. Angles and triangles -- 38. Introduction to trigonometry --

39. Trigonometric waveforms -- 40. Cartesian and polar co-ordinates -- 41. Non-right-angled triangles and some practical applications -- 42. Trigonometric identities and equations -- 43. The relationship between trigonometric and hyperbolic functions -- 44. Compound angles -- 45. Complex numbers -- 46. De Moivre's theorem -- 47. The theory of matrices and determinants -- 48. Applications of matrices and determinants -- 49. Vectors -- 50. Methods of adding alternating waveforms -- 51. Scalar and vector products -- 52. Introduction to differentiation -- 53. Methods of differentiation -- 54. Some applications of differentiation -- 55. Differentiation of parametric equations -- 56. Differentiation of implicit functions -- 57. Logarithmic differentiation -- 58. Differentiation of hyperbolic functions -- 59. Differentiation of inverse trigonometric and hyperbolic functions -- 60. Partial differentiation -- 61. Total differential, rates of change and small changes -- 62. Maxima, minima and saddle points for functions of two variables -- 63. Standard integration -- 64. Integration using algebraic substitutions -- 65. Integration using trigonometric and hyperbolic substitutions -- 66. Integration using partial fractions --

67. The t = tan [theta]/2 substitution -- 68. Integration by parts -- 69. Reduction formulae -- 70. Double and triple integrals -- 71. Numerical integration -- 72. Areas under and between curves -- 73. Mean and root mean square values -- 74. Volumes of solids of revolution -- 75. Centroids of simple shapes -- 76. Second moments of area -- 77. Solution of first-order differential equations by separation of variables -- 78. Homogeneous first-order differential equations -- 79. Linear first-order differential equations -- 80. Numerical methods for first-order differential equations -- 81. Second-order differential equations of the form ad2y/dx2 + bdy/dx + cy = 0 -- 82. Second-order differential equations of the form ad2y/dx2 + bdy/dx + cy = f(x) -- 83. Power series methods of solving ordinary differential equations -- 84. An introduction to partial differential equations -- 85. Presentation of statistical data -- 86. Mean, median, mode and standard deviation -- 87. Probability -- 88. The binomial and Poisson distributions -- 89. The normal distribution -- 90. Linear correlation -- 91. Linear regression -- 92. Sampling and estimation theories -- 93. Significance testing -- 94. Chi-square and distribution-free tests -- 95. Introduction to Laplace transforms -- 96. Properties of Laplace transforms -- 97. Inverse Laplace transforms -- 98. The Laplace transform of the Heaviside function --

99. The solution of differential equations using Laplace transforms -- 100. The solution of simultaneous differential equations using Laplace transforms -- 101. Fourier series for periodic functions of period 2[pi] -- 102. Fourier series for a non-periodic function over range 2? -- 103. Even and odd functions and half-range Fourier series -- 104. Fourier series over any range -- 105. A numerical method of harmonic analysis -- 106. The complex or exponential form of a Fourier series