Partial Differential Equations: Theory and Completely Solved ProblemsFriesenPress, 2019 M05 15 - 688 páginas Provides more than 150 fully solved problems for linear partial differential equations and boundary value problems. Partial Differential Equations: Theory and Completely Solved Problems offers a modern introduction into the theory and applications of linear partial differential equations (PDEs). It is the material for a typical third year university course in PDEs. The material of this textbook has been extensively class tested over a period of 20 years in about 60 separate classes. The book is divided into two parts. Part I contains the Theory part and covers topics such as a classification of second order PDEs, physical and biological derivations of the heat, wave and Laplace equations, separation of variables, Fourier series, D’Alembert’s principle, Sturm-Liouville theory, special functions, Fourier transforms and the method of characteristics. Part II contains more than 150 fully solved problems, which are ranked according to their difficulty. The last two chapters include sample Midterm and Final exams for this course with full solutions. |
Contenido
| 6 | |
| 44 | |
| 92 | |
| 125 | |
Heat Wave and Laplace Equations | 157 |
Polar Coordinates | 193 |
Spherical Coordinates | 239 |
Fourier Transforms | 282 |
Fourier Transform Methods in PDEs | 323 |
Bibliography | 668 |
Otras ediciones - Ver todas
Partial Differential Equations: An Introduction to Theory and Applications Michael Shearer,Rachel Levy Vista previa limitada - 2015 |
Términos y frases comunes
assume a solution b(ac Bessel functions boundary condition gives boundary value problem boundary value—initial value boundedness condition coefficients coordinates corresponding eigenfunctions cosh cosine series cospla coswa defined Dirichlet Dirichlet’s theorem eigenvalues Example Exercise f is piecewise Fourier cosine series Fourier integral Fourier series Fourier sine series Fourier transform function f given heat equation hence initial condition interval jk;k Laplace's equation Legendre linear nonhomogeneous nontrivial solutions nºt Note nTac ordinary differential equations orthogonal partial differential equation piecewise continuous piecewise smooth Rayleigh quotient regular Sturm-Liouville problem satisfies the boundary second boundary condition separating variables separation constant separation of variables sinh ſº solve spherical Sturm-Liouville problem superposition principle temperature u(ac value—initial value problem waſ wave equation zero