Boundary Value Problems for Linear Partial Differential Equations

Manuel Mañas, Luis Martínez Alonso

• Publisher: Chapman and Hall/CRC
• Year: 2024
• Print ISBN: 9781032662527
• eBook ISBN: 9781040026434
• Edition: 1
• Topic: Mathématiques
• Subtopic: Physique mathématique et informatique

Boundary value problems play a significant role in modeling systems characterized by established conditions at their boundaries. On the other hand, initial value problems hold paramount importance in comprehending dynamic processes and foreseeing future behaviors. The fusion of these two types of problems yields profound insights into the intricacies of the conduct exhibited by many physical and mathematical systems regulated by linear partial differential equations.

Boundary Value Problems for Linear Partial Differential Equations provides students with the opportunity to understand and exercise the benefits of this fusion, equipping them with realistic, practical tools to study solvable linear models of electromagnetism, fluid dynamics, geophysics, optics, thermodynamics and specifically, quantum mechanics. Emphasis is devoted to motivating the use of these methods by means of concrete examples taken from physical models.

Features

• No prerequisites apart from knowledge of differential and integral calculus and ordinary differential equations.
• Provides students with practical tools and applications
• Contains numerous examples and exercises to help readers understand the concepts discussed in the book.

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Dedication Page
• Table of Contents
• Preface
• About the authors
• Chapter 1. Introduction
• Chapter 2. Linear PDEs
• Chapter 3. Separation of Variables Method
• Chapter 4. Symmetric Differential Operators
• Chapter 5. Fourier Analysis
• Chapter 6. Eigenfunction Expansion Method
• Chapter 7. Special Functions
• Chapter 8. Cylindrical and Spherical BVPs
• Bibliography
• Subject Index
• Index of Capsule Biographies