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Description
This sixth 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 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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