Higher Engineering Mathematics, 7/Ed > 수학/통계학

ntroduction;
Preface;
Website information;
Syllabus guidance;
1. Algebra;
2. Partial fractions;
3. Logarithms;
4. Exponential functions;
5. Inequalities; Revision Test 1;
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 numbers;
11. Boolean algebra and logic circuits; Revision Test 3;
12. Introduction to trigonometry;
13. Cartesian and polar co-ordinates;
14. The circle and its properties; Revision Test 4;
15. Trigonometric waveforms;
16. Hyperbolic functions;
17. Trigonometric identities and equations;
18. The relationship between trigonometric and hyperbolic functions;
19. Compound angles; Revision Test 5;
20. Functions and their curves;
21. Irregular areas, volumes and mean values of waveforms; Revision Test 6;
22. Complex numbers;
23. De Moivre’s theorem;
24. The theory of matrices and determinants;
25. Applications of matrices and determinants; Revision Test 7;
26. Vectors;
27. Methods of adding alternating waveforms;
28. Scalar and vector products; Revision Test 8;
29. Methods of differentiation;
30. Some applications of differentiation;
31. Differentiation of parametric equations;
32. Differentiation of implicit functions;
33. Logarithmic differentiation; Revision Test 9;
34. Differentiation of hyperbolic functions;
35. Differentiation of inverse trigonometric and hyperbolic functions;
36. Partial differentiation;
37. Total differential, rates of change and small changes;
38. Maxima, minima and saddle points for functions of two variables; Revision Test 10;
39. Standard integration;
40. Some applications of integration;
41. Integration using algebraic substitutions; Revision Test 11;
42. Integration using trigonometric and hyperbolic substitutions;
43. Integration using partial fractions;
44. The t = tan substitution; Revision Test 12;
45. Integration by parts;
46. Reduction formulae;
47. Double and triple integrals;
48. Numerical integration; Revision Test 13;
49. Solution of first order differential equations by separation of variables;
50. Homogeneous first order differential equations;
51.Linear first order differential equations;
52. Numerical methods for first order differential equations; Revision Test 14;
53. First order differential equations of the form;
54. First order differential equations of the form;
55. Power series methods of solving ordinary differential equations;
56. An introduction to partial differential equations; Revision Test 15;
57. Presentation of statistical data;
58. Mean, median, mode and standard deviation;
59. Probability; Revision Test 16;
60. The binomial and Poisson distributions;
61. The normal distribution;
62. Linear correlation;
63. Linear regression; Revision Test 17;
64. Sampling and estimation theories;
65. Significance testing;
66. Chi-square and distribution-free tests; Revision Test 18;
67. Introduction to Laplace transforms;
68. Properties of Laplace transforms;
69. Inverse Laplace transforms;
70. The Laplace transform of the Heaviside function;
71. The solution of differential equations using Laplace transforms;
72. The solution of simultaneous differential equations using Laplace transforms; Revision Test 19;
73. Fourier series for periodic functions of period 2p;
74. Fourier series for a non-periodic function over period 2p;
75. Even and odd functions and half-range Fourier series ;
76. Fourier series over any range;
77. A numerical method of harmonic analysis;
78. The complex or exponential form of a Fourier series;
Revision Test 20;
Essential formulae;
Answers to Practise Exercises;
Index