# Complements of Higher Mathematics

• Marin Marin
• Andreas Öchsner

1. Front Matter
Pages i-viii
2. Marin Marin, Andreas Öchsner
Pages 1-51
3. Marin Marin, Andreas Öchsner
Pages 53-87
4. Marin Marin, Andreas Öchsner
Pages 89-110
5. Marin Marin, Andreas Öchsner
Pages 111-145
6. Marin Marin, Andreas Öchsner
Pages 147-207
7. Marin Marin, Andreas Öchsner
Pages 209-222
8. Marin Marin, Andreas Öchsner
Pages 223-252
9. Marin Marin, Andreas Öchsner
Pages 253-294
10. Marin Marin, Andreas Öchsner
Pages 295-318
11. Marin Marin, Andreas Öchsner
Pages 319-351
12. Back Matter
Pages 353-353

### Introduction

This book highlights the remarkable importance of special functions, operational calculus, and variational methods. A considerable portion of the book is dedicated to second-order partial differential equations, as they offer mathematical models of various phenomena in physics and engineering.

The book provides students and researchers with essential help on key mathematical topics, which are applied to a range of practical problems. These topics were chosen because, after teaching university courses for many years, the authors have found them to be essential, especially in the contexts of technology, engineering and economics. Given the diversity topics included in the book, the presentation of each is limited to the basic notions and results of the respective mathematical domain. Chapter 1 is devoted to complex functions. Here, much emphasis is placed on the theory of holomorphic functions, which facilitate the understanding of the role that the theory of functions of a complex variable plays in mathematical physics, especially in the modeling of plane problems.

In addition, the book demonstrates the importance of the theories of special functions, operational calculus, and variational calculus. In the last chapter, the authors discuss the basic elements of one of the most modern areas of mathematics, namely the theory of optimal control.

### Keywords

Special Functions Complex Functions Operational Calculus Laplace’s Transform Partial differential Equations Variational Calculus Equations of Chord Vibration PDE Partial differential Equations Heat Equation Optimal Control

#### Authors and affiliations

• Marin Marin
• 1
• Andreas Öchsner
• 2
1. 1.Dept. of Mathematics & Computer ScienceTransilvania University of BrasovBrasovRomania
2. 2.Faculty of Mechanical EngineeringEsslingen University of Applied Sciences Esslingen am NeckarGermany

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-74684-5
• Copyright Information Springer International Publishing AG, part of Springer Nature 2018
• Publisher Name Springer, Cham
• eBook Packages Engineering
• Print ISBN 978-3-319-74683-8
• Online ISBN 978-3-319-74684-5
• Buy this book on publisher's site