1 Preliminaries 1.1 Review of Calculus 1.2 Binary Numbers 1.3 Error Analysis 2 Solution of Nonlinear Equations 2.1 Iteration for Solving x=g(x) 2.2 Bracketing Methods for Locating a Root 2.3 Initial Approximation and Convergence Criteria 2.4 Newton-Raphson and Secant Methods 2.5 Aitden's Process and Steffensen's and Muller's Methods 3 Solution of Linear Systems AX=B 3.1 Introduction to Vectors and Matrices 3.2 Properties of Vectors and Matrices 3.3 Upper-Triangular Linear Systems 3.4 Gaussian Elimination and Pivoting 3.5 Triangular Factorzation 3.6 Iterative Methods for Linear Systems 3.7 Iteration for Nonlinear Systems:Seidel and Newton's Methods 4 Interpolation and Polynomial Approximation 4.1 Taylor Series and Calculation of Functions 4.2 Introduction to Interpolation 4.3 Lagrange Approximation 4.4 Newton Polynomials 4.5 Chebyshev Polynomials 4.6 Pade Approximations 5 Curve Fitting 6 Numerical Differentiation 7 Numerical Integration 8 Numerical Optimization 9 Solution of Differential Equations 10 Solution of Partial Differential Equations 11 Eigenvalues and Eigenvectors Appendix:Introduction to MATLAB Answers to Selected Exercises Index
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