Partial Differential Equations: Analytical and Numerical Methods

Contents: Preface. 1. Classification of Differential Equations. 2. Models in One Dimension. 3. Essential Linear Algebra. 4. Essential Ordinary Differential Equations. 5. Boundary Value Problems in Statics. 6. Heat Flow and Diffusion. 7. Waves. 8. First-Order PDEs and the Method of Characteristics. 9. Green s Functions. 10. Sturm Liouville Eigenvalue Problems. 11. Problems in Multiple Spatial Dimensions. 12. More about Fourier Series. 13. More about Finite Element Methods. Appendices. Bibliography. Index. This undergraduate textbook introduces students to the topic with a unique approach that emphasizes the modern finite element method alongside the classical method of Fourier analysis. Additional features of this new edition include: broader coverage of PDE methods and applications, with new chapters on the method of characteristics, Sturm Liouville problems, and Green's functions, a new section on the finite difference method for the wave equation; emphasis on linear algebra, particularly the idea of best approximation; realistic physical parameters and meaningful experiments for many of the examples and exercises; tutorials for the most popular software (MATLAB , Mathematica , and Maple ) that can be used to reproduce the examples and solve the exercises. The author continues to emphasize Fourier series and finite element methods, which were the primary scope of the first edition. This book is written for undergraduate courses usually titled Introduction to Partial Differential Equations or Fourier Series and Boundary Value Problems. (jacket). …