# Introduction to Applied Mathematics

• Lawrence Sirovich
Book

Part of the Text in Applied Mathematics book series (TAM, volume 1)

1. Front Matter
Pages i-xii
2. Lawrence Sirovich
Pages 1-10
3. Lawrence Sirovich
Pages 11-26
4. Lawrence Sirovich
Pages 27-76
5. Lawrence Sirovich
Pages 77-133
6. Lawrence Sirovich
Pages 134-167
7. Lawrence Sirovich
Pages 168-222
8. Lawrence Sirovich
Pages 223-260
9. Lawrence Sirovich
Pages 261-293
10. Lawrence Sirovich
Pages 294-362
11. Back Matter
Pages 363-370

### Introduction

From the Preface: "The material in this book is based on notes for a course which I gave several times at Brown University. The target of the course was juniors and seniors majoring in applied mathematics, engineering and other sciences. My basic goal in the course was to teach standard methods, or what I regard as a basic "bag of tricks". In my opinion the material contained here, for the most part, does not depart widely from traditional subject matter. One such departure is the discussion of discrete linear systems. Besides being interesting in its own right, this topic is included because the treatment of such systems leads naturally to the use of discrete Fourier series, discrete Fourier transforms, and their extension, the Z-transform. On making the transition to continuous systems we derive their continuous analogues, viz., Fourier series, Fourier transforms, Fourier integrals and Laplace transforms. A main advantage to the approach taken is that a wide variety of techniques are seen to result from one or two very simple but central ideas. Above all, this course is intended as being one which gives the student a "can-do" frame of mind about mathematics. Students should be given confidence in using mathematics and not be made fearful of it. I have, therefore, forgone the theorem-proof format for a more informal style. Finally, a concerted effort was made to present an assortment of examples from diverse applications with the hope of attracting the interest of the student, and an equally dedicated effort was made to be kind to the reader."

### Keywords

Extension Fourier series Fourier transform differential equation mathematics partial differential equation

#### Authors and affiliations

• Lawrence Sirovich
• 1
1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-4580-3
• Copyright Information Springer-Verlag New York 1988
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-8932-6
• Online ISBN 978-1-4612-4580-3
• Series Print ISSN 0939-2475
• Series Online ISSN 2196-9949