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Partial Differential Equations

Methods, Applications and Theories

Overview

This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. They include the first-order equations and the three fundamental second-order equations, i.e. the heat, wave and Laplace equations. Through these equations we learn the types of problems, how we pose the problems, and the methods of solutions such as the separation of variables and the method of characteristics. The modeling aspects are explained as well. The methods introduced in earlier chapters are developed further in Chapters Six to Twelve. They include the Fourier series, the Fourier and the Laplace transforms, and the Green's functions. The equations in higher dimensions are also discussed in detail.

Struggles of the Heart

Rebecca Gromer is a sixteen-year-old girl who spends most of her time focused on school and keeping to herself. Her father is an accountant that spends most of his day in the office and is hardly at home. Her mother passed away in a plane crash when Rebecca was still very young, and every day she wishes that she could just have her back. She has…

This volume is application-oriented and rich in examples. Going through these examples, the reader is able to easily grasp the basics of PDE's.

Contents:
• First and Second Order Linear Equations — Preparation
• Heat Equation
• Wave Equation
• Laplace Equation
• First Order Equations Revisited
• Fourier Series and Eigenvalue Problems
• Separation of Variables in Higher Dimensions
• More Separation of Variables
• Fourier Transform
• Laplace Transform
• Higher Dimensional Problems — Other Approaches
• Green's Functions

Date release: January 28, 2013

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