This textbook covers essential numerical techniques including basic methods for linear systems, root finding, interpolation, numerical integration and differentiation, least squares and Monte Carlo methods. This book balances the development, implementation, application and analysis of computational ideas and methods.
This textbook covers essential numerical techniques including basic methods for linear systems, root finding, interpolation, numerical integration and differentiation, least squares and Monte Carlo methods. This book balances the development, implementation, application and analysis of computational ideas and methods.
Sheng Xu is an Associate Professor of Mathematics at Southern Methodist University in Dallas, TX. His research areas are in the field of fluid mechanics and scientific computing, with specialization in computational fluid dynamics (CFD). He has written a few CFD packages to simulate fluid-solid interactions using the immersed interface method.
Inhaltsangabe
1. Overview of Scientific Computing 2. Taylor's Theorem 3. Roundoff Errors and Error Propagation 4. Direct Methods for Linear Systems 5. Root Finding for Nonlinear Equations 6. Interpolation 7. Numerical Integration 8. Numerical Differentiation 9. Initial Value Problems and Boundary Value Problems 10. Basic Iterative Methods for Linear Systems 11. Discrete Least Squares Problems 12. Monte Carlo Methods and Parallel Computing Appendix A. An Introduction of Matlab for Scientific Computing Appendix B. An Introduction of Python for Scientific Computing Index
1. Overview of Scientific Computing 2. Taylor's Theorem 3. Roundoff Errors and Error Propagation 4. Direct Methods for Linear Systems 5. Root Finding for Nonlinear Equations 6. Interpolation 7. Numerical Integration 8. Numerical Differentiation 9. Initial Value Problems and Boundary Value Problems 10. Basic Iterative Methods for Linear Systems 11. Discrete Least Squares Problems 12. Monte Carlo Methods and Parallel Computing Appendix A. An Introduction of Matlab for Scientific Computing Appendix B. An Introduction of Python for Scientific Computing Index
1. Overview of Scientific Computing 2. Taylor's Theorem 3. Roundoff Errors and Error Propagation 4. Direct Methods for Linear Systems 5. Root Finding for Nonlinear Equations 6. Interpolation 7. Numerical Integration 8. Numerical Differentiation 9. Initial Value Problems and Boundary Value Problems 10. Basic Iterative Methods for Linear Systems 11. Discrete Least Squares Problems 12. Monte Carlo Methods and Parallel Computing Appendix A. An Introduction of Matlab for Scientific Computing Appendix B. An Introduction of Python for Scientific Computing Index
1. Overview of Scientific Computing 2. Taylor's Theorem 3. Roundoff Errors and Error Propagation 4. Direct Methods for Linear Systems 5. Root Finding for Nonlinear Equations 6. Interpolation 7. Numerical Integration 8. Numerical Differentiation 9. Initial Value Problems and Boundary Value Problems 10. Basic Iterative Methods for Linear Systems 11. Discrete Least Squares Problems 12. Monte Carlo Methods and Parallel Computing Appendix A. An Introduction of Matlab for Scientific Computing Appendix B. An Introduction of Python for Scientific Computing Index
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