An introduction to partial differential equations
Publisher: Bookboon
Published: 2013
ISBN-13: 9788776819699
Table of contents: title: Part I First-order partial differential equations; title: List of examples; title: Preface; title: Introduction; title: Types of equation; title: Exercises 1; title: The quasi-linear equation; title: Of surfaces and tangents; title: The Cauchy (or initial value) problem; title: The semi-linear and linear equations; title: The quasi-linear equation in n independent variables; title: Exercises 2; title: The general equation; title: Geometry again; title: The method of solution; title: The general PDE with Cauchy data; title: The complete integral and the singular solution; title: Exercises 3; title: Answers; title: Part II Partial differential equations: classification and canonical forms; title: List of Equations; title: Preface; title: Introduction; title: Types of equation; title: First-order equations; title: The linear equation; title: The Cauchy problem; title: The quasi-linear equation; title: Exercises 2; title: The wave equation; title: Connection with first-order equations; title: Initial data; title: Exercises 3; title: The general semi-linear partial differential equation in two independent variables; title: Transformation of variables; title: Characteristic lines and the classification; title: Canonical form; title: Initial and boundary conditions; title: Exercises 4; title: Three examples from fluid mechanics; title: The Tricomi equation; title: General compressible flow; title: The shallow-water equations; title: Appendix: The hodograph transformation; title: Exercise 5; title: Riemann invariants and simple waves; title: Shallow-water equations: Riemann invariants; title: Shallow-water equations: simple waves; title: Answers; title: Part III Partial differential equations: method of separation of variables and similarity & travelling-wave solutions; title: List of Equations; title: Preface; title: Introduction; title: The Laplacian and coordinate systems; title: Overview of the methods; title: The method of separation of variables; title: Introducing the method; title: Two independent variables: other coordinate systems; title: Linear equations in more than two independent variables; title: Nonlinear equations; title: Exercises 2; title: Travelling-wave solutions; title: The classical, elementary partial differential equations; title: Equations in higher dimensions; title: Nonlinear equations; title: Exercises 3; title: Similarity solutions; title: Introducing the method; title: Continuous (Lie) groups; title: Similarity solutions of other equations; title: More general solutions from similarity solutions; title: Exercises 4; title: Answers; title: Index