Numerical Methods: Nonlinear Equations, Numerical Calculus, & Differential Equations

Length: 230 pages
Edition: 1
Language: English
Publication Date: 2021-09-28
ISBN-10: B09HHFDRZB
Sales Rank: #0 (See Top 100 Books)

This is a combination of three books: Nonlinear Equations, Numerical Calculus, and Differential Equations. These three topics combine to form Numerical Methods. Nonlinear, integral, and differential equations are found throughout science and engineering across a wide variety of disciplines. These are a significant part of applied mathematics and much effort has been devoted to their study and solution. We will consider single and multi-variable problems. Various theories will be presented, but always with a focus on what works best—that is, robust algorithms.

Chapter 1. Single-Valued Functions of One Variable
Chapter 2. Multi-Valued Functions of One Variable
Chapter 3. Functions of Several Variables
Chapter 4: Bounding & Scaling
Chapter 5: Nonlinear Least-Squares
Chapter 6: Quasi-Newton Methods
Chapter 7. Broyden's Derivative-Free Algorithm
Chapter 8. Approximating Gradients and Hessians
Chapter 9. Multi-Dimensional Bisection Search
Chapter 10: Evolutionary Method
Chapter 11: Nonlinear Regression
Chapter 12: Hybrid Regression
Chapter 13. Data Analysis
Chapter 14. Newton-Cotes Integration
Chapter 15. Gauss Quadrature
Chapter 16. Chebyshev & Lobatto Quadrature
Chapter 17. Composite Rules
Chapter 18. Green's Lemma
Chapter 19. 2D and 3D Integrals
Chapter 20. Improper Integrals
Chapter 21 Applications
Chapter 22. Differential Equations
Chapter 23. Explicit Runge-Kutta Methods
Chapter 24. Marching Method Applications
Chapter 25. Step Length Control
Chapter 26. Finite Difference Method
Chapter 27. Finite Element Method
Chapter 28. Boundary Element Method
Appendix A: Steam Properties - A Practical Example
Appendix B: Graphical Representation
Appendix C: Data Transformation Program
Appendix D. Newton-Cotes Coefficient Program
Appendix E. Gauss Quadrature Weights & Abscissas
Appendix F. Cooling Tower Demand
Appendix G: Generalized Runge-Kutta Function
Appendix H: Finite Difference Operators
Appendix I: Processing and Checking Finite Element Models
Appendix J: Solving Large Systems of Linear Equations
Appendix K: Triangular Element Generating Program
Appendix L: SIAM Paper