Boundary and Eigenvalue Problems in Mathematical Physics (Dover Books on Physics)

About this book

This well-known text uses a limited number of basic concepts and techniques Hamiltons principle the theory of the first variation and Bernoullis separation method to develop complete solutions to linear boundary value problems associated with second order partial differential equations such as the problems of the vibrating string the vibrating membrane and heat conduction. It is directed to advanced undergraduate and beginning graduate students in mathematics applied mathematics physics and engineering who have completed a course in advanced calculus. In the first three chapters Professor Sagan introduces Hamiltons principle and the theory of the first variation; he then discusses the representation of the vibrating string the vibrating membrane and heat conduction (without convection) by partial differential equations. Bernoullis separation method and infinite series solutions of homogeneous boundary value problems are introduced as a means for solving these problems. The next three chapters take up Fourier series self-adjoint boundary value problems Legendre polynomials and Bessel functions. The concluding three chapters address the characterization of eigenvalues by a variational principle; spherical harmonics and the solution of the Schroedinger equation for the hydrogen atom; and the nonhomogeneous boundary value problem. Professor Sagan concludes most sections of this excellent text with selected problems (solutions provided for even-numbered problems) to reinforce the readers grasp of the theories and techniques presented.