Partial Differential Equations An Introduction [Hardcover]

Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)—the wave, heat, and Laplace equations—this detailed text also presents a broad practical perspective that merges mathematical concepts with real-world application in diverse areas including molecular structure, photon and electron interactions, radiation of electromagnetic waves, vibrations of a solid, and many more.

Rigorous pedagogical tools aid in student comprehension; advanced topics are introduced frequently, with minimal technical jargon, and a wealth of exercises reinforce vital skills and invite additional self-study. Topics are presented in a logical progression, with major concepts such as wave propagation, heat and diffusion, electrostatics, and quantum mechanics placed in contexts familiar to students of various fields in science and engineering. By understanding the properties and applications of PDEs, students will be equipped to better analyze and interpret central processes of the natural world.

 (The starred sections form the basic part of the book.)

Chapter 1/Where PDEs Come From

1.1 What is a Partial Differential Equation? 1

1.2 First-Order Linear Equations 6

1.3 Flows, Vibrations, and Diffusions 10

1.4 Initial and Boundary Conditions 20

1.5 Well-Posed Problems 25

1.6 Types of Second-Order Equations 28

Chapter 2/Waves and Diffusions

2.1 The Wave Equation 33

2.2 Causality and Energy 39

2.3 The Diffusion Equation 42

2.4 Diffusil“M