Ordinary and Partial Differential Equations for the Beginner

This textbook is intended for college, undergraduate and graduate students, emphasizing mainly on ordinary differential equations. However, the theory of characteristics for first order partial differential equations and the classification of second order linear partial differential operators are also included. It contains the basic material starting from elementary solution methods for ordinary differential equations to advanced methods for first order partial differential equations.

In addition to the theoretical background, solution methods are strongly emphasized. Each section is completed with problems and exercises, and the solutions are also provided. There are special sections devoted to more applied tools such as implicit equations, Laplace transform, Fourier method, etc. As a novelty, a method for finding exponential polynomial solutions is presented which is based on the author's work in spectral synthesis. The presentation is self-contained, provided the reader has general undergraduate knowledge.

Contents:

• Ordinary Differential Equations
• Elementary Solution Methods
• Linear Differential Equations
• Functionally Dependence, Independence
• Higher Order Differential Equations
• First Order Partial Differential Equations
• Theory of Characteristics
• Higher Order Partial Differential Equations
• Second Order Quasilinear Partial Differential Equations
• Special Problems in Two Variables
• Table of Laplace Transforms
• Answers to Selected Problems

Readership: Undergraduate and graduate students interested in ordinary and partial differential equations.
Key Features:

• The book provides both theoretical and practical background to differential equations
• The Fourier transform for exponential polynomials provides a new tool to find particular solutions of differential equations
• Many problems and exercises with answers provide effective help for the reader to practise the presented methods