Includes bibliographical references (p. 530-532) and index.

1. Numerical computation motivation and objectives ;
1. Number representation ;
2. Machine precision ;
3. Round-off error ;
4. Truncation error ;
5. Random number generation ;
6. Numerical software ;
7. Applications ;
8. Chapter summary ;
9. Problems 2. Linear algebraic systems motivation and objectives ;
10. Gauss-jordan elimination ;
11. Gaussian elimination ;
12. Lu decomposition ;
13. Ill-conditioned systems ;
14. Iterative methods ;
15. Applications ;
16. Chapter summary ;
17. Problems 3. Eigenvalues and eigenvectors motivation and objectives ;
18. The characteristic polynomial ;
19. Power methods ;
20. Jacobi''s method ;
21. Householder transformation ;
22. Qr method ;
23. Danilevsky''s method ;
24. Polynomial roots ;
25. Applications ;
26. Chapter summary ;
27. problems 4. Curve fitting motivation and objectives ;
28. Interpolation ;
29. Newton''s difference formula ;
30. Cubic splines ;
31. Least square ;
32. Two-dimensional interpolation ;
33. Applications ;
34. Chapter summary ;
35. Problems 5. Root finding motivation and objectives ;
36. Bracketing methods ;
37. Contraction mapping method ;
38. Secant method ;
39. Muller''s method ;
40. Newton''s method ;
41. Polynomial roots ;
42. Nonlinear systems of equations ;
43. Applications ;
44. Chapter summary ;
45. Problems 6. Optimization motivation and objectives ;
46. Local and global minima ;
47. Line searches ;
48. Steepest descent method ;
49. Conjugate-gradient method ;
50. Quasi-newton methods ;
51. Penalty functions ;
52. Simulated annealing ;
53. Applications ;
54. Chapter summary ;
55. Problems 7. Differentiation and integration motivation and objectives ;
56. Numerical differentiation ;
57. Noise-corrupted data ;
58. Newton-cotes integration formulas ;
59. Romberg integration ;
60. Gauss quadrature ;
61. Improper integrals ;
62. Multiple integrals ;
63. Applications ;
64. Chapter summary ;
65. Problems 8. Ordinary differential equations motivation and objectives ;
66. Euler''s method ;
67. Runge-kutta methods ;
68. Step size control ;
69. Multi-step methods ;
70. Bulirsch-stoer extrapolation methods ;
71. Stiff differential equations ;
72. Boundary
73. Value problems ;
74. Applications ;
75. Summary ;
76. Problems 9. Partial differential equations motivation and objectives ;
77. Elliptic equations ;
78. One-dimensional parabolic equations ;
79. Two-dimensional parabolic equations ;
80. One-dimensional hyperbolic equations ;
81. Two-dimensional hyperbolic equations ;
82. Applications ;
83. Chapter summary ;
84. Problems 10. Digital signal processing motivation and objectives ;
85. Fourier transform ;
86. Fast fourier transform (fft) ;
87. Correlation ;
88. Convolution digital filters ;
89. Two-dimensional fft ;
90. System identification ;
91. Applications ;
92. Chapter summary ;
93. Problems ;
94. References and further reading ;
95. Appendix 1: nlib using matlab? ;
96. A numerical toolbox: nlib ;
97. Main-program support ;
98. Linear algebraic systems ;
99. Eigenvalues and eigenvectors ;
100. Curve fitting ;
101. Root finding ;
102. Optimization ;
103. Differentiation and integration ;
104. Ordinary differential equations ;
105. Partial differential equations ;
106. Digital signal processing ;
107. Appendix 2: nlib using c ;
108. A numerical library: nlib ;
109. Nlib data types ;
110. Nlib core: nlib.c ;
111. Tabular display: show.c ;
112. Graphical display: draw.c ;
113. Linear algebraic systems: linear.c ;
114. Eigenvalues and eigenvectors: eigen.c ;
115. Curve fitting: curves.c ;
116. Root finding: roots.c ;
117. Optimization: optim.c ;
118. Differentiation and integration: integ.c ;
119. Ordinary differential equations: ode.c ;
120. Partial differential equations: pde.c ;
121. Digital signal processing: dsp.c ;
122. Appendix 3: vectors and matrices ;
123. Vector and matrix notation ;
124. Basic operations ;
125. Inverses ;
126. Eigenvalues and eigenvectors ;
127. Vector norms ;
128. Appendix 4: answers to selected problems ; index