## Periodic Functions and Distributions, Complex Analysis, Laplace Transform and Applications

• Richard Beals
Book

Part of the Graduate Texts in Mathematics book series (GTM, volume 12)

1. Front Matter
Pages i-xi
2. Richard Beals
Pages 1-33
3. Richard Beals
Pages 34-68
4. Richard Beals
Pages 69-102
5. Richard Beals
Pages 103-130
6. Richard Beals
Pages 131-154
7. Richard Beals
Pages 155-189
8. Richard Beals
Pages 190-222
9. Back Matter
Pages 223-232

### Introduction

Once upon a time students of mathematics and students of science or engineering took the same courses in mathematical analysis beyond calculus. Now it is common to separate" advanced mathematics for science and engi­ neering" from what might be called "advanced mathematical analysis for mathematicians." It seems to me both useful and timely to attempt a reconciliation. The separation between kinds of courses has unhealthy effects. Mathe­ matics students reverse the historical development of analysis, learning the unifying abstractions first and the examples later (if ever). Science students learn the examples as taught generations ago, missing modern insights. A choice between encountering Fourier series as a minor instance of the repre­ sentation theory of Banach algebras, and encountering Fourier series in isolation and developed in an ad hoc manner, is no choice at all. It is easy to recognize these problems, but less easy to counter the legiti­ mate pressures which have led to a separation. Modern mathematics has broadened our perspectives by abstraction and bold generalization, while developing techniques which can treat classical theories in a definitive way. On the other hand, the applier of mathematics has continued to need a variety of definite tools and has not had the time to acquire the broadest and most definitive grasp-to learn necessary and sufficient conditions when simple sufficient conditions will serve, or to learn the general framework encompass­ ing different examples.

### Keywords

Analysis calculus Complex analysis complex number differential equation distribution exponential function Fourier series function Hilbert space holomorphic function logarithm Logarithmus Mathematica mathematical analysis metric space

#### Authors and affiliations

• Richard Beals
• 1
1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4684-9886-8
• Copyright Information Springer-Verlag New York 1973
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-90066-7
• Online ISBN 978-1-4684-9886-8
• Series Print ISSN 0072-5285