Essentials of Mathematical Methods in Science and Engineering – S. Selcuk Bayin – 1st Edition


A complete introduction to the multidisciplinary applications of mathematical
In order to work with varying levels of engineering and physics research, it is important to have a firm understanding of key mathematical concepts such as , equations, analysis, and introductory mathematical physics. Essentials of Mathematical Methods in Science and Engineering provides a comprehensive introduction to these methods under one cover, outlining basic mathematical skills while also encouraging and practitioners to develop new, interdisciplinary approaches to their research.

The book begins with core topics from various branches of such as limits, integrals, and inverse functions. Subsequent chapters delve into the analytical tools that are commonly used in scientific and engineering studies, including vector analysis, generalized coordinates, determinants and matrices, algebra, complex numbers, complex analysis, and Fourier series.

The author provides an extensive chapter on probability theory with applications to statistical mechanics and thermodynamics that complements the following chapter on information theory, which contains coverage of Shannon’s theory, decision theory, game theory, and quantum information theory. A comprehensive list of references facilitates further exploration of these topics.

Throughout the book, numerous examples and exercises reinforce the presented concepts and techniques. In addition, the book is in a modular format, so each chapter covers its subject thoroughly and can be read independently. This structure affords flexibility for individualizing courses and teaching.

Providing a solid foundation and overview of the various mathematical methods and applications in multidisciplinary research, Essentials of Mathematical Methods in Science and Engineering is an excellent text for courses in physics, science, mathematics, and engineering at the upper-undergraduate and graduate levels. It also serves as a useful reference for scientists and who would like a practical review of mathematical methods.

Table of Contents



1. Functional Analysis.

2. Vector Analysis.

3. Generalized Coordinates and Tensors.

4. Determinants and Matrices.

5. Linear Algebra.

6. Sequences and Series.

7. Complex Numbers and Functions.

8. Complex Analysis.

9. Ordinary Differential Equations.

10. Second-Order Differential Equations and Special Functions.

11. Bessel's Equation and Bessel Functions.

12. Partial Differential Equations and Separation Variables.

13. Fourier Series.

14. Fourier and Laplace Transforms.

15. Calculus of Variations.

16. Probability Theory and Distributions.

17. Information Theory.


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