Victor Henner, Alexander Nepomnyashchy, Tatyana Belozerova, Mikhail Khenner

Ordinary Differential Equations (eBook, PDF)

Analytical Methods and Applications

• Format: PDF

Produktbeschreibung

The textbook presents a rather unique combination of topics in ODEs, examples and presentation style. The primary intended audience is undergraduate (2^nd, 3^rd, or 4^th year) students in engineering and science (physics, biology, economics). The needed pre-requisite is a mastery of single-variable calculus. A wealth of included topics allows using the textbook in up to three sequential, one-semester ODE courses. Presentation emphasizes the development of practical solution skills by including a very large number of in-text examples and end-of-section exercises. All in-text examples, be they of a mathematical nature or a real-world examples, are fully solved, and the solution logic and flow are explained. Even advanced topics are presented in the same undergraduate-friendly style as the rest of the textbook. Completely optional interactive laboratory-type software is included with the textbook.

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Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 606
• Erscheinungstermin: 5. Juni 2023
• Englisch
• ISBN-13: 9783031251306
• Artikelnr.: 68177710

Autorenporträt

Prof. Victor Henner got PhD degree in 1980 and Dr. of Science degree in theoretical and mathematical physics at Moscow State University, Russia in 1995. He has more than 35 years of teaching experience. He is the Professor at the Department of Theoretical Physics, Perm State University, Russia, and Adjunct Professor at the Department of Physics and Astronomy, University of Louisville, USA. His major research interests are high-energy physics and mathematical modeling of spin dynamics. He is the author and co-author of more than 100 research papers and 4 books.

Prof. Alexander Neponmyashchy got PhD degree at the Institute for Thermophysics, Novosibirsk, USSR in 1978. He has more than 40 years of teaching experience. He is Professor Emeritus at the Department of Mathematics, Technion, Israel, and Adjunct Professor at the Department of Engineering Sciences and Applied Mathematics, Northwestern University, USA. His major research interests are nonlinear stability theory, nonlinear waves, and mathematical modeling of interfacial phenomena. He is the author and co-author of more than 200 research papers and 6 books.

Dr. Tatyana Belozerova got PhD degree at Perm Technical University, Russia in 1996. She is the Senior Researcher at the Department of Mathematics, Perm State University, Russia, and the author and co-author of more than 30 research papers and 4 books.

Prof. Mikhail Khenner got PhD degree in Physical Applied Mathematics at Universite de la Mediterranee Aix-Marseille II, France and at Perm State University, Russia in 1998. He is Professor of Mathematics at Western Kentucky University, USA. He specializes in differential equations models of the dynamics of thin solid films and surfaces. He authored and co-authored more than fifty research papers and a textbook "Ordinary and Partial Differential Equations".

Inhaltsangabe

Introduction.- First-order Differential Equations.- Differential Equations of the Order n>1.- Systems of Differential Equations.- Qualitative Analysis and Atability of ODE Solutions.- Power series solutions of ODEs.- Laplace Transform.- Fourier series.- Boundary Value Problems for second-order ODEs.- Special Functions.- Integral Equations.- Calculus of Variations.- Partial Differential Equations.- Appendix 1: Picard's Existence and Uniqueness Theorem.- Appendix 2: A Primer on the Matrix Eigenvalue Problems and the Solutions of the Selected Examples.- Appendix 3: How to Use Software Associated with the Book.

Rezensionen

"The aim of this book is to develop skills for finding solutions and for investigating the qualitative theory of ordinary differential equations (ODEs). These skills help one to solve real-world problems. The book contains many examples, some of which are from mechanics, physics and biology. ... This book is arranged in such a way that students taking a distance learning course or studying the subject independently will benefit." (Narahari Parhi, Mathematical Reviews, September, 2024)

"The book introduces the reader to ordinary differential equations from the classical point of view. It is a basic first course for physics and engineers. In all chapters there is an introductory background with real examples, most of them solved. From the table of contents, it is clear what the reader will find." (Joan Torregrosa, zbMATH 1530.34003, 2024)