The author has managed admirably to bring to light both the beauty and the usefulness of the calculus of variations in many problems arising in applied sciences, thus creating a beautiful introduction to this field. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background. This nice book is likely to be especially successful. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. Unit VIII : Special Topics Calculus of Variations Integral Equations. Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. The calculus of variations has a long and rich history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly mechanics. It is written with the firm conviction that a good book is one that can be read. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. Between these two books, there is much excellent information. For a more rigorous text that covers higher variations also check out Gelfand & Fomins text. It mostly covers development of the first variation and applications. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. Calculus of variations: Robert Weinstocks Book is excellent and very cheap. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least. This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |