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Title Details:
Applied Mathematics
Other Titles: Differential Equations, Complex Functions and Integral Transformations
Authors: Tsitsas, Nikolaos
Reviewer: Frantzeskakis, Dimitrios
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > FUNCTIONS OF A COMPLEX VARIABLE
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > FUNCTIONS OF A COMPLEX VARIABLE > SERIES EXPANSIONS
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > ORDINARY DIFFERENTIAL EQUATIONS > GENERAL THEORY
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PARTIAL DIFFERENTIAL EQUATIONS > GENERAL HIGHER-ORDER EQUATIONS AND SYSTEMS
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > ORDINARY DIFFERENTIAL EQUATIONS
Keywords:
Differential Equations
Complex Functions
Fourier Transform
Laplace Transform
Description:
Abstract:
The content of this book constitutes a unified presentation of concepts, methods, and results from Ordinary Differential Equations, Complex Functions, and Fourier Transformations, within which general frameworks are formulated, interpreted, and analyzed in various significant applications in the natural and technological sciences, as well as in computer science. The book is divided into three parts: I. Ordinary Differential Equations, II. Complex Functions, and III. Series and Fourier Transformations. Ordinary Differential Equations represent an extensive field in both pure and applied mathematics, focusing on the study of existence and uniqueness of solutions in pure mathematics and emphasizing computational methodologies in applied mathematics. Differential Equations also play a crucial role in mathematical modeling of physical, technological, and biological processes. The theory of Complex Functions is one of the most fascinating areas of mathematics. Many of the most powerful techniques used to formulate and study applications of mathematics in other sciences are based on the theory of Complex Functions. One of the purposes of the book is to present a wide range of applications and to comprehensively process techniques of Complex Functions that are used for their modeling. The concept of the Fourier Transformation consists of an integral representation of functions and is an extension of the representation of functions with the help of Fourier series. Fourier Transformations have many applications in the natural sciences and technology and are practically used for the transformation of functions between the fields of time or space and the field of frequencies.
Type: Undergraduate textbook
Creation Date: 2015
Item Details:
ISBN 978-960-603-257-8
License: http://creativecommons.org/licenses/by-nc-nd/3.0/gr
DOI http://dx.doi.org/10.57713/kallipos-936
Handle http://hdl.handle.net/11419/1131
Bibliographic Reference: Tsitsas, N. (2015). Applied Mathematics [Undergraduate textbook]. Kallipos, Open Academic Editions. https://dx.doi.org/10.57713/kallipos-936
Language: Greek
Consists of:
1. Ordinary Differential Equations: Introductory Concepts, Definitions, and Problem Modeling
2. First-order differential equations
3. Existence and uniqueness of solutions to first-order initial value problems
4. Second-order linear differential equations
5. Higher-order linear differential equations
6. Systems of first-order differential equations
7. Laplace Transform with applications to differential equations
8. Complex numbers
9. Sequences and series of complex numbers
10. Complex functions
11. Generating complex functions
12. Integrable complex functions
13. Complex powertrains and applications
14. Fourier series
15. Discrete Fourier transform
16. Fourier transform
Number of pages 505
Publication Origin: Kallipos, Open Academic Editions
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