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Part One: Modeling, Computers, and Error Analysis

Chapter 1: Mathematical Modeling and Engineering Problem Solving

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

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