Part 1 Modeling, Computers, and Error Analysis 1 Mathematical Modeling and Engineering Problem Solving 2 Programming and Software 3 Approximations and Round-Off Errors 4 Truncation Errors and the Taylor Series Epilogue: Part OnePart 2 Roots of Equations 5 Bracketing Methods 6 Open Methods 7 Roots of Polynomials 8 Case Studies: Roots of Equations Epilogue: Part TwoPart 3 Linear Algebraic Equations 9 Gauss Elimination 10 LU Decomposition and Matrix Inversion 11 Special Matrices and Gauss-Seidel 12 Case Studies: Linear Algebraic Equations Epilogue: Part ThreePart 4 Optimization 13 One-Dimensional Unconstrained Optimization 14 Multidimensional Unconstrained Optimization 15 Constrained Optimization 16 Case Studies: Optimization Epilogue: Part FourPart 5 Curve Fitting 17 Least-Squares Regression 18 Interpolation 19 Fourier Approximation 20 Case Studies: Curve Fitting Epilogue: Part FivePart 6 Numerical Differentiation and Integration 21 Newton-Cotes Integration Formulas 22 Integration of Equations 23 Numerical Differentiation 24 Case Studies: Numerical Integration and Differentiation Epilogue: Part SixPart 7 Ordinary Differential Equations 25 Runge-Kutta Methods 26 Stiffness and Multistep Methods 27 Boundary-Value and Eigenvalue Problems 28 Case Studies: Ordinary Differential Equations Epilogue: Part SevenPart 8 Partial Differential Equations 29 Finite Difference: Elliptic Equations 30 Finite Difference: Parabolic Equations 31 Finite-Element Method 32 Case Studies: Partial Differential Equations Epilogue: Part EightAppendix A: The Fourier Series Appendix B: Getting Started with Matlab Bibliography Index
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