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Higher Education Science and Mathematics Mathematics

Partial Differential Equations and Boundary Value Problems with Fourier Series, 2/e

by

Nakhle H Asmar

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This example-rich text fosters a smooth transition from elementary ordinary differential equations courses to more advanced concepts in a first course on PDEs. Asmar's relaxed style and emphasis on applications make the material accessible even to students with limited exposure to topics beyond calculus. Computer use is encouraged for illustrating results and applications, but the text is also suitable for use without computer access. The Second Edition has added more engineering and physics applications more optional mathematical proofs a new chapter on Green's Theorem and Conformal Mappings and more geometric presentations throughout.


Features

• New examples of Fourier series and exercises • Complete proof of the Fourier Series Representation Theorem • New section on the application of Fourier series to the solution of forced vibrations of electrical and mechanical systems • New and expanded coverage of Partial Differential Equations in Polar and Cylindrical Coordinates • New coverage of Sturm-Liouville Theory with Engineering Applications • New material on the Fourier Transform and Its Applications • New chapter that deals with Green's functions and Conformal Mappings

Contents

1. A Preview of Applications and Techniques 2. Fourier Series 3. Partial Differential Equations in Rectangular Coordinates 4. Partial Differential Equations in Polar and Cylindrical Coordinates 5. Partial Differential Equations in Spherical Coordinates 6. Sturm-Liouville Theory with Engineering Applications 7. The Fourier Transform and Its Applications 8. The Laplace and Hankel Transforms with Applications 9. Finite Difference Numerical Methods 10. Sampling and Discrete Fourier Analysis with Applications to Partial Differential Equations 11. An Introduction to Quantum Mechanics 12. Green's Functions and Conformal Mappings 13. Appendix A: Ordinary Differential Equations: Review of Concepts and Methods 1 4. Appendix B: Tables of Transforms