**Description**

**Content:-**

Preface

Syllabus guidance

**Section A: Number and Algebra**

1. Algebra

2. Inequalities

3. Partial fractions

4. Logarithms and exponential functions

5. Hyperbolic functions

6. Arithmetic and geometric progressions

7. The binomial series

8. Maclaurin’s series

9. Solving equations by iterative methods

10. Computer numbering systems

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. Trigonometric identities and equations

17. The relationship between trigonometric and hyperbolic functions

18. Compound angles

**Section C: Graphs**

19. Functions and their curves

20. Irregular areas, volumes and mean values of waveforms

**Section D: Vector geometry**

21. Vectors, phasors and the combination of waveforms

**Section E: Complex numbers**

23. Complex numbers

24. De Moivre’s theorem

**Section F: Matrices and Determinants**

25. The theory of matrices and determinants

26. The solution of simultaneous equations by matrices and determinants

**Section G: Differential calculus**

27. Methods of differentiation

28. Some applications of differentiation

29. Differentiation of parametric equations

30. Differentiation of implicit functions

31. Logarithmic differentiation

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

**Section H: Integral calculus**

37. Standard integration

38. Some applications of integration

39. Integration using algebraic substitutions

40. Integration using trigonometric and hyperbolic substitutions

41. Integration using partial fractions

42. The t =tanθ/2 substitution

43. Integration by parts

44. Reduction formulae

45. Numerical integration

**Section I: Differential equations**

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

50. Second order differential equations of the form a d2y/dx2 +b dy/dx +cy=0

51. Second order differential equations of the form a d2y/dx2 +b dy/dx +cy=f (x)

52. Power series methods of solving ordinary differential equations

53. An introduction to partial differential equations

**Section J: Statistics and probability**

54. Presentation of statistical data

55. Measures of central tendency and dispersion

56. Probability

57. The binomial and Poisson distributions

58. The normal distribution

59. Linear correlation

60. Linear regression

61. Sampling and estimation theories

62. Significance testing

63. Chi-square and distribution-free tests

**Section K: Laplace transforms**

64. Introduction to Laplace transforms

65. Properties of Laplace transforms

66. Inverse Laplace transforms

67. The solution of differential equations using Laplace transforms

68. The solution of simultaneous differential equations using Laplace transforms

**Section L: Fourier series**

69. Fourier series for periodic functions of period 2π

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

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

72. Fourier series over any range

73. A numerical method of harmonic analysis

74. The complex or exponential form of a Fourier series

Assignment 19

Essential formulae

Index

**Author Details**

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

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