Advanced Mathematics for Engineers and Physicists

ISBN-13: 9783031215018 / Angielski / Twarda / 2023 / 827 str.

Sever Angel Popescu; Marilena Jianu

Opis

This book is designed to be an introductory course to some basic chapters of Advanced Mathematics for Engineering and Physics students, researchers in different branches of Applied Mathematics and anyone wanting to improve their mathematical knowledge by a clear, live, self-contained and motivated text.

Here, one can find different topics, such as differential (first order or higher order) equations, systems of differential equations, Fourier series, Fourier and Laplace transforms, partial differential equations, some basic facts and applications of the calculus of variations and, last but not least, an original and more intuitive introduction to probability theory. All these topics are carefully introduced, with complete proofs, motivations, examples, applications, problems and exercises, which are completely solved at the end of the book.We added a generous supplementary material (11.1) with a self-contained and complete introduction to normed, metric and Hilbert spaces. Since we used some topics from complex function theory, we also introduced in Chapter 11 a section (11.2) with the basic facts in this important field.What a reader needs for a complete understanding of this book? For a deep understanding of this book, it is required to take a course in undergraduate calculus and linear algebra. We mostly tried to use the engineering intuition instead of insisting on mathematical tricks. The main feature of the material presented here is its clarity, motivation and the genuine desire of the authors to make extremely transparent the "mysterious" mathematical tools that are used to describe and organize the great variety of impressions that come to the searching mind, from the infinite complexity of Nature.The book is recommended not only to engineering and physics students or researchers but also to junior students in mathematics because it shows the connection between pure mathematics and physical phenomena, which always supply motivations for mathematical discoveries.

Spis treści

- 1. First-Order Differential Equations. - 2. Higher-Order Differential Equations. - 3. Systems of Differential Equations. - 4. Fourier Series. - 5. Fourier Transform. - 6. Laplace Transform. - 7. Second-Order Partial Differential Equations. - 8. Introduction to the Calculus of Variations. - 9. Elements of Probability Theory. - 10. Answers and Solutions to Exercises. - 11. Supplementary Materials.

O autorze

Sever Angel Popescu. His scientific activity splits into two directions. One is Pure Mathematics, namely, in Algebra and Number theory, where he succeeded in obtaining some interesting results published by known mathematical journals such as Journal of Algebra, Mathematishe Zeitschrift, Mathematiche Nachrihten, Proc. of the Japan Academy, Manuscripta Mathematica, and Acta Arithmetica. (see Google Scholars for instance). The other is in Applied Mathematics, connected to his whole teaching activity at the Technical University of Civil Engineering Bucharest. Here, he tried to apply his mathematical experience to improve the syllabus of advanced mathematics for engineering students. This book covers all his experience in this direction. It is the last book in a series of many other books published in Romanian or in English as courses for engineering students (in Linear Algebra, Mathematical Analysis, Differential Equations, Calculus of Variations, Statistics, etc.). He also published some papers on applied mathematics topics such as differential equations, shift operators, the bridge and torch problem, etc.

Marilena Jianu received her M.Sc. degree in mathematics (statistics and probability) from the University of Bucharest, and her Ph.D. degree in civil engineering from the Technical University of Civil Engineering Bucharest. She has been teaching advanced mathematics to engineering students for over 20 years and has published several papers in pure and applied mathematics. She is an editorial board member of the Romanian Journal of Mathematics and Computer Science and a reviewer for Mathematical Reviews.