## Partial differential equations and boundary value problemsPacked with examples, this book provides a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material understandable even for readers with limited exposure to topics beyond calculus. Encourages the use of computer resources for illustrating results and applications, but is also suitable for use without computer access. Includes additional specialized topics that can be read as desired, and that can be read independently of each other. Denotes exercises requiring use of a computer with computer icons, asking readers to investigate problems using computer-generated graphics and to generate numerical data that cannot be computed by hand. Offers Mathematica files for download from the author's Web site; can be accessed through the Prentice Hall address http://www.prenhall.com/pubguide/. For engineers or anyone looking to brush up on their advanced mathematics skills. |

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27r-periodic 2p-periodic apply approximate associated Legendre Bessel functions Bessel series Bessel's equation boundary conditions boundary data boundary value problem compute converges uniformly coordinates cosine denote derive determine Dirichlet problem disk eigenfunction eigenfunction expansions eigenvalue Example Exercise 11 Figure formula Fourier coefficients Fourier series Fourier sine Fourier transform graph heat equation heat problem Hence Hint illustrate initial conditions initial temperature distribution initial velocity integral interval Laplace's equation Legendre functions Legendre polynomials Legendre series linear membrane nonhomogeneous nonzero normal mode obtain oo oo ordinary differential equations orthogonality Parseval's identity partial differential equation partial sums piecewise smooth Plot points of discontinuity Poisson problem positive zero product solutions PROJECT PROBLEM proof properties scries Section 4.8 separation constant separation of variables series expansion series solution Show sine series solve spherical harmonics steady-state temperature term by term Theorem tion uniform convergence wave equation