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.

**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.

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

Appendix B: Tables of Transforms.

References.

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