Part One: Modeling, Computers, and Error Analysis
Chapter 1: Mathematical Modeling and Engineering Problem Solving
Two parts: simple model, conservation laws
Chapter 2: Programming and Software
Chapter 3: Approximations and Round-Off Errors
Chapter 4: Truncation Errors and the Taylor Series
Part One Epilogue
Part Two: Roots of Equations
Chapter 5: Bracketing Methods
Chapter 6: Open Methods
Chapter 7: Roots of Polynomials
Chapter 8: Engineering Applications: Roots of Equations
Part Two Epilogue
Part Three: Linear Algebraic Equations
Chapter 9: Gauss Elimination
Chapter 10: LU Decomposition and Matrix Inversion
Chapter 11: Special Matrices and Gauss-Seidel
Chapter 12: Engineering Applications: Linear Algebraic Equations
Part Three Epilogue
Part Four: Optimization
Chapter 13: One-Dimensional Unconstrained Optimization
Chapter 14: Multidimensional Unconstrained Optimization
Chapter 15: Constrained Optimization
Chapter 16: Engineering Applications: Optimization
Part Four Epilogue
Part Five: Curve Fitting
Chapter 17: Least-Squares Regression
Chapter 18: Interpolation
Chapter 19: Fourier Approximation
Chapter 20: Engineering Applications: Curve Fitting
Part Five Epilogue
Part Six: Numerical Differentiation and Integration
Chapter 21: Newton-Cotes Integration Formulas
Chapter 22: Integration of Equations
Chapter 23: Numerical Differentiation
Chapter 24: Engineering Applications: Numerical Integration and Differentiation
Part Six Epilogue
Part Seven: Ordinary Differential Equations
Chapter 25: Runge-Kutta Methods
Chapter 26: Stiffness and Multistep Methods
Chapter 27: Boundary-Value and Eigenvalue Problems
Chapter 28: Engineering Applications: Ordinary Differential Equations
Part Seven Epilogue
Part Eight: Partial Differential Equations
Chapter 29: Finite Difference: Elliptic Equations
Chapter 30: Finite Difference: Parabolic Equations
Chapter 31: Finite Element Method
Chapter 32: Engineering Applications: Partial Differential Equations
Part Eight Epilogue