ABOUT THE AUTHORS
PREFACE
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
EPILOGUE: PART ONE
PART TWO. ROOTS OF EQUATIONS
CHAPTER 5. Bracketing Methods
CHAPTER 6. Open Methods
CHAPTER 7. Roots of Polynomials
CHAPTER 8. Case Studies: Roots of Equations
EPILOGUE: PART TWO
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. Case Studies: Linear Algebraic Equations
EPILOGUE: PART THREE
PART FOUR. OPTIMIZATION
CHAPTER 13. One-Dimensional Unconstrained Optimization
CHAPTER 14. Multidimensional Unconstrained Optimization
CHAPTER 15. Constrained Optimization
CHAPTER 16. Case Studies: Optimization
EPILOGUE: PART FOUR
PART FIVE. CURVE FITTING
CHAPTER 17. Least-Squares Regression
CHAPTER 18. Interpolation
CHAPTER 19. Fourier Approximation
CHAPTER 20. Case Studies: Curve Fitting
EPILOGUE: PART FIVE
PART SIX. NUMERICAL DIFFERENTIATION AND INTEGRATION
CHAPTER 21. Newton-Cotes Integration Formulas
CHAPTER 22. Integration of Equations
CHAPTER 23. Numerical Differentiation
CHAPTER 24. Case Studies: Numerical Integration and Differentiation
EPILOGUE: PART SIX
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. Case Studies: Ordinary Differential Equations
EPILOGUE: PART SEVEN
PART EIGHT. PARTIAL DIFFERENTIAL EQUATIONS
CHAPTER 29. Finite Difference: Elliptic Equations
CHAPTER 30. Finite Difference: Parabolic Equations
CHAPTER 31. Finite-Element Method
CHAPTER 32. Case Studies: Partial Differential Equations
EPILOGUE: PART EIGHT
APPENDIX A: THE FOURIER SERIES
APPENDIX B: GETTING STARTED WITH MATLAB
APPENDIX C: GETTING STARTED WITH MATHCAD
BIBLIOGRAPHY

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