**Description**

In this edition the material has been ordered into the following twelve convenient categories: number and algebra, geometry and trigonometry, graphs, complex numbers, matrices and determinants, vector geometry, differential calculus, integral calculus, differential equations, statistics and probability, Laplace transforms and Fourier series. New material has been added on logarithms and exponential functions, binary, octal and hexadecimal, vectors and methods of adding alternating waveforms. Another feature is that a free Internet download is available of a sample (over 1100) of the further problems contained in the book.

**Content:-**

Preface

Syllabus guidance

1. Algebra

2. Partial fractions

3. Logarithms

4. Exponential functions

**Revision Test 1**

5. Hyperbolic functions

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

**Revision Test 3**

11. Introduction to trigonometry

12. Cartesian and polar co-ordinates

13. The circle and its properties

**Revision Test 4**

14. Trigonometric waveforms

15. Trigonometric identities and equations

16. The relationship between trigonometric and hyperbolic functions

17. Compound angles

**Revision Test 5**

18. Functions and their curves

19. Irregular areas, volumes and mean values of waveforms

**Revision Test 6**

20. Complex numbers

21. De Moivre’s theorem

22. The theory of matrices and determinants

23. The solution of simultaneous equations by matrices and determinants

**Revision Test 7**

24. Vectors

25. Methods of adding alternating waveforms

26. Scalar and vector products

**Revision Test 8**

27. Methods of differentiation

28. Some applications of differentiation

29. Differentiation of parametric equations

30. Differentiation of implicit functions

31. Logarithmic differentiation

**Revision Test 9**

32. Differentiation of hyperbolic functions

33. Differentiation of inverse trigonometric and hyperbolic functions

34. Partial differentiation

35. Total differential, rates of change and small changes

36. Maxima, minima and saddle points for functions of two variables

**Revision Test 10**

37. Standard integration

38. Some applications of integration

39. Integration using algebraic substitutions

**Revision Test 11**

40. Integration using trigonometric and hyperbolic substitutions

41. Integration using partial fractions

42. The t =tanθ/2 substitution

**Revision Test 12**

43. Integration by parts

44. Reduction formulae

45. Numerical integration

**Revision Test 13**

46. Solution of first order differential equations by separation of variables

47. Homogeneous first order differential equations

48. Linear first order differential equations

49. Numerical methods for first order differential equations

**Revision Test 14**

50. Second order differential equations of the form

51. Second order differential equations of the form

52. Power series methods of solving ordinary differential equations

53. An introduction to partial differential equations

**Revision Test 15**

54. Presentation of statistical data

55. Measures of central tendency and dispersion

56. Probability

**Revision Test 16**

57. The binomial and Poisson distributions

58. The normal distribution

59. Linear correlation

60. Linear regression

**Revision Test 17**

61. Introduction to Laplace transforms

62. Properties of Laplace transforms

63. Inverse Laplace transforms

64. The solution of differential equations using Laplace transforms

65. The solution of simultaneous differential equations using Laplace transforms

**Revision Test 18**

66. Fourier series for periodic functions of period 2π

67. Fourier series for a non-periodic function over range 2π

68. Even and odd functions and half-range Fourier series

69. Fourier series over any range

70. A numerical method of harmonic analysis

71. The complex or exponential form of a Fourier series

**Revision Test 19**

Essential formulae

Index

**Author Details**

**"John Bird",**BSc (Hons), CMath, CEng, CSci, FIMA, FIET, MIEE, FIIE, FCollT

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