Partial Differential Equations

Analytical Methods and Applications
1. Auflage 2023
ISBN: 978-1-032-47508-0
Verlag: Chapman and Hall/CRC

Buch, Englisch, 396 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 746 g

Reihe: Textbooks in Mathematics

Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners’ course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor.

This text introduces and promotes practice of necessary problem-solving skills. The presentation is concise and friendly to the reader. The "teaching-by-examples" approach provides numerous carefully chosen examples that guide step-by-step learning of concepts and techniques. Fourier series, Sturm-Liouville problem, Fourier transform, and Laplace transform are included. The book’s level of presentation and structure is well suited for use in engineering, physics and applied mathematics courses.

Highlights:

- Offers a complete first course on PDEs

- The text’s flexible structure promotes varied syllabi for courses

- Written with a teach-by-example approach which offers numerous examples and applications

- Includes additional topics such as the Sturm-Liouville problem, Fourier and Laplace transforms, and special functions

- The text’s graphical material makes excellent use of modern software packages

- Features numerous examples and applications which are suitable for readers studying the subject remotely or independently

Zielgruppe

General

Autoren/Hrsg.

Henner, Victor

Belozerova, Tatyana

Nepomnyashchy, Alexander

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Introduction

Basic definitions

Examples

First-order equations

Linear first-order equations

General solution

Initial condition

Quasilinear first-order equations

Characteristic curves

Examples

Second-order equations

Classification of second-order equations

Canonical forms

Hyperbolic equations

Elliptic equations

Parabolic equations

The Sturm-Liouville Problem

General consideration

Examples of Sturm-Liouville Problems

One-Dimensional Hyperbolic Equations

Wave Equation

Boundary and Initial Conditions

Longitudinal Vibrations of a Rod and Electrical Oscillations

Rod oscillations: Equations and boundary conditions

Electrical Oscillations in a Circuit

Traveling Waves: D'Alembert Method

Cauchy problem for nonhomogeneous wave equation

D'Alembert's formula

The Green's function

Well-posedness of the Cauchy problem

Finite intervals: The Fourier Method for Homogeneous Equations

The Fourier Method for Nonhomogeneous Equations

The Laplace Transform Method: simple cases

Equations with Nonhomogeneous Boundary Conditions

The Consistency Conditions and Generalized Solutions

Energy in the Harmonics

Dispersion of waves

Cauchy problem in an infinite region

Propagation of a wave train

One-Dimensional Parabolic Equations

Heat Conduction and Diffusion: Boundary Value Problems

Heat conduction

Diffusion equation

One-dimensional parabolic equations and initial

Über Autor(innen)

Victor Henner is a professor at the Department of Physics and Astronomy at the University of Louisville. He has Ph.Ds from the Novosibirsk Institute of Mathematics in Russia and Moscow State University. He co-wrote with Tatyana Belozerova Ordinary and Partial Differential Equations.

Tatyana Belozerova is a professor at Perm State University in Russia. Along with Ordinary and Partial Differential Equations, she co-wrote with Victor Henner Mathematical Methods in Physics: Partial Differential Equations, Fourier Series, and Special Functions.

Alexander Nepomnyashchy is a mathematics professor at Northwestern University and hails from the Faculty of Mathematics at Technion-Israel Institute of Technology. His research interests include non-linear stability theory and pattern formation.