Elements of Partial Differential Equations.

Elements of Partial Differential Equations.

This book presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types o...

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Bibliographic Details
Main Author: Drábek, Pavel, 1968-
Other Authors: Holubová, Gabriela
Format: eBook
Language:English
Published: Berlin : De Gruyter, 2014.
Edition:2nd ed.
Series:De Gruyter textbook.
Subjects:
Differential equations, Partial > Textbooks.
Differential equations, Partial
Textbooks
Online Access:Click for online access
Table of Contents:
  • Preface ; Contents ; 1 Motivation, Derivation of Basic Mathematical Models ; 1.1 Conservation Laws ; 1.1.1 Evolution Conservation Law ; 1.1.2 Stationary Conservation Law ; 1.1.3 Conservation Law in One Dimension ; 1.2 Constitutive Laws ; 1.3 Basic Models.
  • 1.3.1 Convection and Transport Equation 1.3.2 Diffusion in One Dimension ; 1.3.3 Heat Equation in One Dimension ; 1.3.4 Heat Equation in Three Dimensions ; 1.3.5 String Vibrations and Wave Equation in One Dimension ; 1.3.6 Wave Equation in Two Dimensions
  • Vibrating Membrane.
  • 1.3.7 Laplace and Poisson Equations
  • Steady States 1.4 Exercises ; 2 Classification, Types of Equations, Boundary and Initial Conditions ; 2.1 Basic Types of Equations ; 2.2 Classical, General, Generic and Particular Solutions ; 2.3 Boundary and Initial Conditions.
  • 2.4 Well-Posed and Ill-Posed Problems 2.5 Classification of Linear Equations of the Second Order ; 2.6 Exercises ; 3 Linear Partial Differential Equations of the First Order ; 3.1 Equations with Constant Coefficients ; 3.1.1 Geometric Interpretation
  • Method of Characteristics.
  • 3.1.2 Coordinate Method 3.1.3 Method of Characteristic Coordinates ; 3.2 Equations with Non-Constant Coefficients ; 3.2.1 Method of Characteristics ; 3.2.2 Method of Characteristic Coordinates ; 3.3 Problems with Side Conditions ; 3.4 Solution in Parametric Form ; 3.5 Exercises.
  • 4 Wave Equation in One Spatial Variable
  • Cauchy Problem in R.

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