Mathematics

For introductory courses in PDEs taken by majors in engineering, physics, and mathematics.

Packed with examples, this text provides a smooth transition from a course in elementary ordinary differential equations to more advanced concepts in a first course in partial differential equations. Asmar's relaxed style and emphasis on applications make the material understandable even for students with limited exposure to topics beyond calculus. This computer-friendly text encourages the use of computer resources for illustrating results and applications, but it is also suitable for use without computer access. Additional specialized topics are included that are covered independently of each other and can be covered by instructors as desired.

• Jumps right into PDEs—Review material of ODEs is in Appendix A.

• Applied approach with proofs in Appendices.

• Large number of exercises per section—The more advanced ones include detailed hints to make them accessible to all students at this level.

  • Each set begins with a series of straightforward problems that reinforce basic concepts in that section; later exercises are more involved and lead to a deeper understanding of the concepts. Ex.___

• The most computer-friendly PDE text on the market—Asks students to investigate problems using computer-generated graphics and to generate numerical data that cannot be computed by hand.

  • Helps students visualize and understand even the most abstract notions covered in the course. Ex.___

• Marginal comments and remarks throughout the text—Offers insightful remarks, keys to following the material, and formulas recalled for the students' convenience.

• Mathematica files—Available for download from the author's website—Links through Prentice Hall address www.prenhall.com/pubguide/

• Includes material not covered in other texts—e.g., a chapter on quantum mechanics.

1. A Preview of Applications and Techniques.


2. Fourier Series.


Supplement on Convergence.


3. Partial Differential Equations in Rectangular Coordinates.


4. Partial Differential Equations in Polar and Cylindrical Coordinates.


Supplement on Bessel Functions.


5. Partial Differential Equations in Spherical Coordinates.


Supplement on Legendre Functions.


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.


Supplement on Orthogonal Polynomials.


Appendix A: Ordinary Differential Equations: Review of Concepts and Methods.


Appendix B: Tables of Transforms.


References.


Answers to Selected Exercises.


Index.

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  Partial Differential Equations and Boundary Value Problems with Fourier Series, 2/E
  Asmar
  ©2005 | Prentice Hall | Cloth; 816 pp | Instock
  ISBN-10: 0131480960 | ISBN-13: 9780131480964
  Brief Description | Buy from myPearsonStore

  

  For introductory courses in Partial Differential Equations (PDEs) taken by majors in engineering, physics, and mathematics.

  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.

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