# Scalar Wave Theory

## Green’s Functions and Applications

• John A. DeSanto
Book

Part of the Springer Series on Wave Phenomena book series (SSWAV, volume 12)

1. Front Matter
Pages III-XIII
2. John A. DeSanto
Pages 1-31
3. John A. DeSanto
Pages 33-77
4. John A. DeSanto
Pages 79-99
5. John A. DeSanto
Pages 101-141
6. John A. DeSanto
Pages 143-186
7. Back Matter
Pages 187-193

### Introduction

This book comprises some of the lecture notes I developed for various one-or two-semester courses I taught at the Colorado School of Mines. The main objective of all the courses was to introduce students to the mathematical aspects of wave theory with a focus on the solution of some specific fundamental problems. These fundamental solutions would then serve as a basis for more complex wave propagation and scattering problems. Although the courses were taught in the mathematics department, the audience was mainly not mathematicians. It consisted of gradu­ ate science and engineering majors with a varied background in both mathematics and wave theory in general. I believed it was necessary to start from fundamental principles of both advanced applied math­ ematics as well as wave theory and to develop them both in some detail. The notes reflect this type of development, and I have kept this detail in the text. I believe it essential in technical careers to see this detailed development at least once. This volume consists of five chapters. The first two on Scalar Wave Theory (Chapter 1) and Green's Functions (Chapter 2) are mainly mathematical although in Chapter 1 the wave equation is derived from fundamental physical principles. More complicated problems involving spatially and even temporally varying media are briefly introduced.

### Keywords

Green's Functions Propagation Scalar Waves Scattering Waveguides wave wave equation

#### Authors and affiliations

• John A. DeSanto
• 1
1. 1.Department of Mathematical and Computer SciencesColorado School of MinesGoldenUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-84738-7
• Copyright Information Springer-Verlag Berlin Heidelberg 1992
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-642-84740-0
• Online ISBN 978-3-642-84738-7
• Series Print ISSN 0931-7252