An introduction to partial differential equations
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 Price: 129.00 kr
 Price: 129.00 kr
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About the book
Reviews
anonymous ★★★★★
Muy buen material para estudiar y diseñar clases.
Description
Most descriptions of physical systems, as used in physics, engineering and, above all, in applied mathematics, are in terms of partial differential equations. This text, presented in three parts, introduces all the main mathematical ideas that are needed for the construction of solutions. The material covers all the elements that are encountered in any standard university study: firstorder equations, including those that take very general forms, as well as the classification of secondorder equations and the development of special solutions e.g. travellingwave and similarity solutions.
Content
 Part I Firstorder partial differential equations
 List of examples
 Preface
 Introduction
 Types of equation
 Exercises 1
 The quasilinear equation
 Of surfaces and tangents
 The Cauchy (or initial value) problem
 The semilinear and linear equations
 The quasilinear equation in n independent variables
 Exercises 2
 The general equation
 Geometry again
 The method of solution
 The general PDE with Cauchy data
 The complete integral and the singular solution
 Exercises 3
 Answers
 Part II Partial differential equations: classification and canonical forms
 List of Equations
 Preface
 Introduction
 Types of equation
 Firstorder equations
 The linear equation
 The Cauchy problem
 The quasilinear equation
 Exercises 2
 The wave equation
 Connection with firstorder equations
 Initial data
 Exercises 3
 The general semilinear partial differential equation in two independent variables
 Transformation of variables
 Characteristic lines and the classification
 Canonical form
 Initial and boundary conditions
 Exercises 4
 Three examples from fluid mechanics
 The Tricomi equation
 General compressible flow
 The shallowwater equations
 Appendix: The hodograph transformation
 Exercise 5
 Riemann invariants and simple waves
 Shallowwater equations: Riemann invariants
 Shallowwater equations: simple waves
 Answers
 Part III Partial differential equations: method of separation of variables and similarity & travellingwave solutions
 List of Equations
 Preface
 Introduction
 The Laplacian and coordinate systems
 Overview of the methods
 The method of separation of variables
 Introducing the method
 Two independent variables: other coordinate systems
 Linear equations in more than two independent variables
 Nonlinear equations
 Exercises 2
 Travellingwave solutions
 The classical, elementary partial differential equations
 Equations in higher dimensions
 Nonlinear equations
 Exercises 3
 Similarity solutions
 Introducing the method
 Continuous (Lie) groups
 Similarity solutions of other equations
 More general solutions from similarity solutions
 Exercises 4
 Answers
 Index