Applied Calculus of Variations for Engineers, Third edition

3. Auflage 2022
ISBN: 978-1-032-33757-9
Verlag: CRC Press

Buch, Englisch, 292 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 447 g

Calculus of variations has a long history. Its fundamentals were laid down by icons of mathematics like Euler and Lagrange. It was once heralded as the panacea for all engineering optimization problems by suggesting that all
one needed to do was to state a variational problem, apply the appropriate Euler-Lagrange equation and solve the resulting differential equation.

This, as most all encompassing solutions, turned out to be not always true and the resulting differential equations are not necessarily easy to solve. On the other hand, many of the differential equations commonly used in various fields of engineering are derived from a variational problem. Hence it is an extremely important topic justifying the new edition of this book.

This third edition extends the focus of the book to academia and supports both variational calculus and mathematical modeling classes. The newly added sections, extended explanations, numerous examples and exercises aid the students in learning, the professors in teaching, and the engineers in applying variational concepts.

Zielgruppe

Academic and Professional Practice & Development

Autoren/Hrsg.

Komzsik, Louis

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Technische Wissenschaften Technik Allgemein Technik: Allgemeines
• Technische Wissenschaften Energietechnik | Elektrotechnik Elektrotechnik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Preface. Acknowledgments. Author. Introduction. I Mathematical foundation. The foundations of calculus of variations. Constrained variational problems. Multivariate functionals. Higher order derivatives. The inverse problem. Analytic solutions. Approximate methods. II Modeling applications. Differential geometry. Computational geometry. Variational equations of motion. Analytic mechanics. Computational mechanics. Solutions. Notations. List of Tables. List of Figures. References. Index

Über Autor(innen)

Dr. Louis Komzsik worked in the industry as an engineering mathematician for 42 years and during those years also lectured as a Visiting Professor at various southern California colleges and universities. Since his retirement he is lecturing in the Mathematics Department of the University of California at Irvine.