Partial Differential Equations and Boundary Value ProblemsFor 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. |
Contents
Supplement on Convergence | 63 |
Partial Differential Equations in Rectangular Coordinates | 81 |
The Method of Separation of Variables | 92 |
Copyright | |
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Common terms and phrases
a²u applications approximate associated Legendre Bessel functions Bessel series Bessel's equation boundary conditions boundary value problem c₁ Chapter compute cosh cosine defined denote derive dimensional Dirichlet problem eigenfunction expansion eigenfunctions eigenvalues Example Exercise Figure finite formula Fourier coefficients Fourier series Fourier transform function f ƒ and g graph heat equation heat problem Hence Hint identity illustrate initial conditions initial temperature distribution integral interval Laplace transform Laplace's equation Legendre polynomials Legendre series linear membrane method nonzero obtain ordinary differential equation orthogonal Partial Differential Equations partial sums piecewise smooth Plot product solutions PROJECT PROBLEM proof properties Section 4.8 separation of variables series expansion series solution Show sin² sinh solve spherical harmonics string Sturm-Liouville problem Theorem tions uniform convergence vibrations wave equation y₁ ди пп