Book description
A visual, interdisciplinary approach to solving problems in numerical methods
Computing for Numerical Methods Using Visual C++ fills the need for a complete, authoritative book on the visual solutions to problems in numerical methods using C++. In an age of boundless research, there is a need for a programming language that can successfully bridge the communication gap between a problem and its computing elements through the use of visual-ization for engineers and members of varying disciplines, such as biologists, medical doctors, mathematicians, economists, and politicians. This book takes an interdisciplinary approach to the subject and demonstrates how solving problems in numerical methods using C++ is dominant and practical for implementation due to its flexible language format, object-oriented methodology, and support for high numerical precisions.
In an accessible, easy-to-follow style, the authors cover:
Numerical modeling using C++
Fundamental mathematical tools
MFC interfaces
Curve visualization
Systems of linear equations
Nonlinear equations
Interpolation and approximation
Differentiation and integration
Eigenvalues and Eigenvectors
Ordinary differential equations
Partial differential equations
This reader-friendly book includes a companion Web site, giving readers free access to all of the codes discussed in the book as well as an equation parser called "MyParser" that can be used to develop various numerical applications on Windows. Computing for Numerical Methods Using Visual C++ serves as an excellent reference for students in upper undergraduate- and graduate-level courses in engineering, science, and mathematics. It is also an ideal resource for practitioners using Microsoft Visual C++.
Table of contents
- Copyright
- TRADEMARKS
- PREFACE
- CODES FOR DOWNLOAD
- 1. Modeling and Simulation
- REFERENCES
- 2. Fundamental Tools for Mathematical Computing
- 3. Numerical Interface Designs
- 4. Curve Visualization
- 5. Systems of Linear Equations
- 6. Nonlinear Equations
- 7. Interpolation and Approximation
- 8. Differentiation and Integration
- 9. Eigenvalues and Eigenvectors
-
10. Ordinary Differential Equations
- 10.1. INTRODUCTION
- 10.2. INITIAL-VALUE PROBLEM FOR FIRST-ORDER ODE
- 10.3. TAYLOR SERIES METHOD
- 10.4. RUNGE-KUTTA OF ORDER 2 METHOD
- 10.5. RUNGE-KUTTA OF ORDER 4 METHOD
- 10.6. PREDICTOR-CORRECTOR MULTISTEP METHOD
- 10.7. SYSTEM OF FIRST-ORDER ODEs
- 10.8. SECOND-ORDER ODE
- 10.9. INITIAL-VALUE PROBLEM FOR SECOND-ORDER ODE
- 10.10. FINITE-DIFFERENCE METHOD FOR SECOND-ORDER ODE
- 10.11. DIFFERENTIATED BOUNDARY CONDITIONS
-
10.12. VISUAL SOLUTION: CODE10
- 10.12.1. Taylor Series of Order 3 Solution
- 10.12.2. Runge-Kutta of Order 2 Solution
- 10.12.3. Runge-Kutta of Order 4 Solution
- 10.12.4. Adams-Bashforth-Moulton Multistep Solution
- 10.12.5. ODE System Solution
- 10.12.6. ODE2 to ODE1 Solution
- 10.12.7. ODE2 Finite-Difference 1 Solution
- 10.12.8. ODE2 Finite-Difference 2 Solution
- 10.13. SUMMARY
- 10.14. NUMERICAL EXERCISES
- 10.15. PROGRAMMING CHALLENGES
- 11. Partial Differential Equations
Product information
- Title: Computing for Numerical Methods Using Visual C++
- Author(s):
- Release date: December 2007
- Publisher(s): Wiley-Interscience
- ISBN: 9780470127957
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