Boundary value problems

This Book Has Been Designed For A One-year Graduate Course On Boundary Value Problems For Students Of Mathematics, Engineering, And The Physical Sciences. It Deals Mainly With The Three Fundamental Equations Of Mathematical Physics, Namely The Heat Equation, The Wave Equation, And Laplace's Equation. The Goal Of The Book Is To Obtain A Formal Solution To A Given Problem Either By The Method Of Separation Of Variables Or By The Method Of General Solutions And To Verify That The Formal Solution Possesses All The Required Properties. To Provide The Mathematical Justification For This Approach, The Theory Of Sturm–liouville Problems, The Fourier Series, And The Fourier Transform Are Fully Developed. The Book Assumes A Knowledge Of Advanced Calculus And Elementary Differential Equations. Contents: Linear Partial Differential Equationsthe Wave Equationgreen's Function And Sturm–liouville Problemsfourier Series And Fourier Transformsthe Heat Equationlaplace's Equation And Poisson's Equationproblems In Higher Dimensions Readership: Graduate Students In Applied Mathematics, Engineering And The Physical Sciences. Keywords:boundary Value Problems;green's Function;sturm-liouville Problems;symmetric Integral Operator;eigenvalues And Eigenfunctions;fourier Series And Fourier Transforms;heat Equation;wave Equation;laplace's Equation;bessel Functions;legendre Polynomials This volume covers some of the most recent and significant advances in computer mathematics. Researchers, engineers, academics and graduate students interested in doing mathematics using computers will find it good reading as well as a valuable reference Linear partial differential equations; the wave equation; Green's function and Sturm-Liouville problems; Fourier series and Fourier transforms; the heat equation; Laplace's equation and Poisson's equation; problems in higher dimensions This text has been designed for use on a one-year graduate course on boundary value problems. It deals mainly with the three fundamental equations of mathematical physics, namely the heat equation, the wave equation, and Laplace's equation. Chi Y. Lo. Includes Bibliographical References (p. 255) And Index.