Differential Equations: A First Course on ODE and a Brief Introduction to PDE

Antonio Ambrosetti; Shair Ahmad

Published by De Gruyter 2024

Differential Equations

A First Course on ODE and a Brief Introduction to PDE

Antonio Ambrosetti and Shair Ahmad

In the series De Gruyter Textbook

https://doi.org/10.1515/9783111185675

Overview
Contents

About this book

The first part of this book is mainly intended as a textbook for students at the Sophomore-Junior level, majoring in mathematics, engineering, or the sciences in general. The book includes the basic topics in Ordinary Differential Equations, normally taught at the undergraduate level, such as linear and nonlinear equations and systems, Bessel functions, Laplace transform, stability, etc. It is written with ample flexibility to make it appropriate either as a course stressing application, or a course stressing rigor and analytical thinking. It also offers sufficient material for a one-semester graduate course, covering topics such as phase plane analysis, oscillation, Sturm-Liouville equations, Euler-Lagrange equations in Calculus of Variations, first and second order linear PDE in 2D. There are substantial lists of exercises at the ends of the chapters. In this edition complete solutions to all even number problems are given in the back of the book.
The 2nd edition also includes some new problems and examples. An effort has been made to make the material more suitable and self-contained for undergraduate students with minimal knowledge of Calculus. For example, a detailed review of matrices and determinants has been added to the chapter on systems of equations. The second edition also contains corrections of some misprints and errors in the first edition.

Covers solving linear and nonlinear equations and systems

Discusses theoretical aspects and qualitative analysis

New material includes a comprehensive table of the inverses of the Laplace transform

Additional applied examples and exercises

Author / Editor information

Antonio Ambrosetti, SISSA, Italy; Shair Ahmad, University of Texas at San Antonio, USA.

Topics

Frontmatter Publicly Available Download PDF	I
Memorial Dedicated to Professor Antonio Ambrosetti Publicly Available Download PDF	V
Preface Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	XI
1 A brief survey of some topics in calculus Requires Authentication Unlicensed Licensed Download PDF	1
2 First order linear differential equations Requires Authentication Unlicensed Licensed Download PDF	8
3 Analytical study of first order differential equations Requires Authentication Unlicensed Licensed Download PDF	23
4 Solving and analyzing some nonlinear first order equations Requires Authentication Unlicensed Licensed Download PDF	45
5 Exact differential equations Requires Authentication Unlicensed Licensed Download PDF	63
6 Second order linear differential equations Requires Authentication Unlicensed Licensed Download PDF	79
7 Higher order linear equations Requires Authentication Unlicensed Licensed Download PDF	103
8 Systems of first order equations Requires Authentication Unlicensed Licensed Download PDF	115
9 Phase plane analysis Requires Authentication Unlicensed Licensed Download PDF	143
10 Introduction to stability Requires Authentication Unlicensed Licensed Download PDF	167
11 Series solutions for linear differential equations Requires Authentication Unlicensed Licensed Download PDF	190
12 Laplace transform Requires Authentication Unlicensed Licensed Download PDF	207
13 A primer on equations of Sturm–Liouville type Requires Authentication Unlicensed Licensed Download PDF	221
14 A primer on linear PDE in 2D. I: first order equations Requires Authentication Unlicensed Licensed Download PDF	241
15 A primer on linear PDE in 2D. II: second order equations Requires Authentication Unlicensed Licensed Download PDF	256
16 The Euler–Lagrange equations in the Calculus of Variations: an introduction Requires Authentication Unlicensed Licensed Download PDF	288
Solutions Requires Authentication Unlicensed Licensed Download PDF	311
Bibliography Requires Authentication Unlicensed Licensed Download PDF	357
Index Requires Authentication Unlicensed Licensed Download PDF	359

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 2nd edition
Audience: A required course for graduate students in mathematics.
Pages
- Front matter: 16
- Main content: 362
Illustrations
- Illustrations: 4
- Coloured Illustrations: 88
Keywords: Differential equations; Laplace Transforms.; Lyapunov stability theory; qualitative theory; Sturm-Liouville problem

eBook

Published: December 18, 2023
ISBN: 9783111185675

Paperback

Published: December 18, 2023
ISBN: 9783111185248