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This fifth edition of ‘Higher Engineering Mathematics’ covers essential mathematical material suitable for students studying Degrees, Foundation Degrees, Higher National Certificate and Diploma courses in Engineering disciplines. In this edition the material has been re-ordered into the following twelve convenient categories: number and algebra, geometry and trigonometry, graphs, vector geometry, complex numbers, matrices and determinants, differential calculus, integral calculus, differential equations, statistics and probability, Laplace transforms and Fourier series. New material has been added on inequalities, differentiation of parametric equations, the t =tan θ/2 substitution and homogeneous first order differential equations. Another new feature is that a free Internet download is available to lecturers of a sample of solutions (over 1000) of the further problems contained in the book.
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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