Partial differential equations : an introduction

Partial differential equations an introduction

Differential equations play a noticeable role in engineering, physics, economics, and other disciplines. They permit us to model changing forms in both mathematical and physical problems. These equations are precisely used when a deterministic relation containing some continuously varying quantities...

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Detalles Bibliográficos
Otros Autores: Shah, Nita H., author (author), Jani, Mrudul Y., author
Formato: Libro electrónico
Idioma:Inglés
Publicado: London ; New York, New York : Routledge [2021]
Edición:First edition
Colección:Mathematical engineering, manufacturing, and management sciences.
Materias:
Differential equations, Partial.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009644303006719
Tabla de Contenidos:
  • Intro
  • Half Title
  • Series Page
  • Title Page
  • Copyright Page
  • Contents
  • Acknowledgements
  • Preface
  • Authors
  • 1. Introduction of Partial Differential Equations
  • 1.1. Partial Differential Equations
  • 1.2. Formation of Partial Differential Equations
  • 1.3. Solution of Partial Differential Equations
  • 1.3.1. Direct Integration Method to Solve Partial Differential Equations
  • Exercises
  • Answers
  • 2. First-Order Partial Differential Equations
  • 2.1. Linear First-Order Partial Differential Equations
  • 2.1.1. Lagrange's Linear Equation of the First Order
  • 2.2. Non-Linear First-Order Partial Differential Equations
  • 2.2.1. Charpit Method
  • 2.2.2. Special Types of First-Order Partial Differential Equations
  • Exercises
  • Answers
  • 3. Second- and Higher-Order Linear Partial Differential Equations
  • 3.1. Homogeneous Linear Partial Differential Equations with Constant Coefficients
  • 3.2. Classification of Second-Order Linear Partial Differential Equations
  • 3.3. Method of Separation of Variables
  • Exercises
  • Answers
  • 4. Applications of Partial Differential Equations
  • 4.1. One-Dimensional Wave Equation
  • 4.1.1. The Solution of the Wave Equation by Separation of Variables
  • 4.1.2. D'Alemberts' Solution of the Wave Equation
  • 4.1.3. Duhamel's Principle for the One-Dimensional Wave Equation
  • 4.2. One-Dimensional Heat Equation
  • 4.3. Laplace's Equation
  • 4.3.1. Laplacian in Cylindrical Coordinates
  • 4.3.2. Laplacian in Spherical Coordinates
  • Exercises
  • Answers
  • Multiple-Choice Questions
  • Fill in the Blanks
  • Bibliography
  • Index.

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