Instructor: Professor Anne Greenbaum Lewis tel: fax: greenbau amath. Discussion of how these arise in science and engineering. Transforms and Green's function methods.
Partial differential equations arise as basic models of flow, diffusion, dispersion, and vibration. Topics included in this first quarter include first and second order partial differential equations and their classification into types wave, diffusion, and potential equations , their origins in applications, and properties of solutions. Classical methods of calculus will be used to describe characteristics, maximum principles, Green's functions, eigenvalue problems, and Fourier expansions. After a brief discussion of ordinary differential equations, we will study initial-boundary-value problems for the first order transport equation, the wave equation, the diffusion equation, and some of their nonlinear extensions.
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied mathematics, and researchers will benefit greatly from this book. Equation of Continuity for Motion of a Fluid. Sound Waves Lecture 2. The Formulation of Problems of Mathematical Physics. The Dependence of the Solution on the Boundary Conditions.