Numerical Analysis Provides The Theoretical Foundation For The Numerical Algorithms We Rely On To Solve A Multitude Of Computational Problems In Science. Based On A Successful Course At Oxford University, This Book Covers A Wide Range Of Such Problems Ranging From The Approximation Of Functions And Integrals To The Approximate Solution Of Algebraic, Transcendental, Differential And Integral Equations. Throughout The Book, Particular Attention Is Paid To The Essential Qualities Of A Numerical Algorithm - Stability, Accuracy, Reliability And Efficiency. The Authors Go Further Than Simply Providing Recipes For Solving Computational Problems. They Carefully Analyse The Reasons Why Methods Might Fail To Give Accurate Answers, Or Why One Method Might Return An Answer In Seconds While Another Would Take Billions Of Years. This Book Is Ideal As A Text For Students In The Second Year Of A University Mathematics Course. It Combines Practicality Regarding Applications With Consistently High Standards Of Rigour. 1. Solution Of Equations By Iteration -- 2. Solution Of Systems Of Linear Equations -- 3. Special Matrices -- 4. Simultaneous Nonlinear Equations -- 5. Eigenvalues And Eigenvectors Of A Symmetric Matrix -- 6. Polynomial Interpolation -- 7. Numerical Integration I -- 8. Polynomial Approximation In The [infinity]-norm -- 9. Approximation In The 2-norm -- 10. Numerical Integration Ii -- 11. Piecewise Polynomial Approximation -- 12. Initial Value Problems For Odes -- 13. Boundary Value Problems For Odes -- 14. The Finite Element Method -- Appendix A. An Overview Of Results From Real Analysis -- Appendix B. Www Resources. Endre Süli And David F. Mayers. Includes Bibliographical References (p. 424-428) And Index. This textbook is written primarily for undergraduate mathematicians and also appeals to students working at an advanced level in other disciplines. The text begins with a clear motivation for the study of numerical analysis based on real-world problems. The authors then develop the necessary machinery including iteration, interpolation, boundary-value problems and finite elements. Throughout, the authors keep an eye on the analytical basis for the work and add historical notes on the development of the subject. There are numerous exercises for students. Based on a successful course at Oxford University, this book gives an authoritative introduction to numerical analysis. It is ideal as a text for students in the second year of a university mathematics course. It combines practicality regarding applications with consistently high standards of rigour. Numerous exercises are provided Equations of various kinds arise in a range of physical applications and a substantial body of mathematical research is devoted to their study.
introduction To Numerical Analysis Combining Rigour With Practical Applications. Numerous Exercises Plus Solutions.
