Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.
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About the Author
David Hilbert (1862 ? 1943) received his PhD from the University of K?nigsberg, Prussia (now Kaliningrad, Russia) in 1884. He remained there until 1895, after which he was appointed Professor of Mathematics at the University of G?ttingen. He held this professorship for most of his life. Hilbert is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. His own discoveries alone would have given him that honour, yet it was his leadership in the field of mathematics throughout his later life that distinguishes him. Hilbert's name is given to Infinite-Dimensional space, called Hilbert space, used as a conception for the mathematical analysis of the kinetic gas theory and the theory of radiations.
Richard Courant (1888 ? 1972) obtained his doctorate at the University of G?ttingen in 1910. Here, he became Hilbert?s assistant. He returned to G?ttingen to continue his research after World War I, and founded and headed the university?s Mathematical Institute. In 1933, Courant left Germany for England, from whence he went on to the United States after a year. In 1936, he became a professor at the New York University. Here, he headed the Department of Mathematics and was Director of the Institute of Mathematical Sciences - which was subsequently renamed the Courant Institute of Mathematical Sciences. Among other things, Courant is well remembered for his achievement regarding the finite element method, which he set on a solid mathematical basis and which is nowadays the most important way to solve partial differential equations numerically.
Richard Courant (1888 ? 1972) obtained his doctorate at the University of G?ttingen in 1910. Here, he became Hilbert?s assistant. He returned to G?ttingen to continue his research after World War I, and founded and headed the university?s Mathematical Institute. In 1933, Courant left Germany for England, from whence he went on to the United States after a year. In 1936, he became a professor at the New York University. Here, he headed the Department of Mathematics and was Director of the Institute of Mathematical Sciences - which was subsequently renamed the Courant Institute of Mathematical Sciences. Among other things, Courant is well remembered for his achievement regarding the finite element method, which he set on a solid mathematical basis and which is nowadays the most important way to solve partial differential equations numerically.
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7 of 8 people found the following review helpful:
4.0 out of 5 stars
Theory of advanced mathematics (not physics).,
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This review is from: Methods of Mathematical Physics, Vol. 1 (Paperback)
This book is intended for mathematicians and not for physicists. All of the mathematics is developed through proofs of theorems. The chapter on approximation of functions is the best in the book. There is also a short introduction to Lebesgue integration which is the best explanation of what it actually means that I have ever seen! (i.e. not having to develop the messy business of measure theory that fills up 10s of pages in most books).
If you want to learn graduate level mathematics (i.e. analysis and PDEs) in gorey detail then this is the book for you. If you want to understand applications, then it is not. I don't like the term "mathematical physics." It depend on which department teaches it. A mathematician will focus on the topics in this book. A physicist would focus on methods and not on proofs.
9 of 12 people found the following review helpful:
5.0 out of 5 stars
The best book available,
This review is from: Methods of Mathematical Physics, Vol. 1 (Paperback)
I would definitely not agree with any bad comments to this book. There are millions of books out there for you to workout problems and help you pass exams. But there is only one who actually teaches the subject and it's Courant. I don't expect literary genius out of a Mathematics book but clear development of the topics. The translation does a good job at it. Believe me if you really want to know the subject and get a feel for it read this book.This is not for the feckless as you will start defacing its stature with your comments. But the price tag is exorbitant and not many can afford to read this wonderful text. I had to borrow from my library as I cannot afford to buy one. 230+$ for two volumes is no joke especially for a student !!
10 of 17 people found the following review helpful:
4.0 out of 5 stars
This book is a classics, but perhaps not exhaustive,
By A Customer
This review is from: Methods of Mathematical Physics, Vol. 1 (Paperback)
I think that this book is better in its original german than in english langauge. As to its content, it may perhaps not include all items of this thema, but the items include are treated with genius. The lack of problems to solve may be a draw back, but for me that is not much trouble because there are many books with many problems to solve. The interest of this book lies in its being a source book, though historically written down in 1924, it still mantains its beauty and its present mathematical value.
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Inside This Book
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First Sentence:
In the present volume we shall be concerned with many topics in mathematical analysis which are intimately related to the theory of linear transformations and quadratic forms. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
given homogeneous boundary conditions, prescribed homogeneous boundary conditions, asymptotic dimension, pure imaginary zeros, piecewise continuous first derivatives, independent spherical harmonics, vanishing boundary values, extremum properties, degenerate kernels, eigenfunction series, homogeneous string, identical vanishing, complete orthogonal system, reciprocity formulas, expansion theorem, piecewise continuous derivatives, divergence expression, admissible functions, subsidiary conditions, isoperimetric problem, infinitely many variables, completeness relation, fundamental domain, natural boundary conditions, variational problem Key Phrases - Capitalized Phrases (CAPs): (learn more)
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In the present volume we shall be concerned with many topics in mathematical analysis which are intimately related to the theory of linear transformations and quadratic forms. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
given homogeneous boundary conditions, prescribed homogeneous boundary conditions, asymptotic dimension, pure imaginary zeros, piecewise continuous first derivatives, independent spherical harmonics, vanishing boundary values, extremum properties, degenerate kernels, eigenfunction series, homogeneous string, identical vanishing, complete orthogonal system, reciprocity formulas, expansion theorem, piecewise continuous derivatives, divergence expression, admissible functions, subsidiary conditions, isoperimetric problem, infinitely many variables, completeness relation, fundamental domain, natural boundary conditions, variational problem Key Phrases - Capitalized Phrases (CAPs): (learn more)
Cambridge University Press, General Remarks, New York New!
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Front Cover | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
100
books
cite this book:
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- A Course of Modern Analysis (Cambridge Mathematical Library) by E. T. Whittaker on page 392, page 396, and page 501
- Differential and Integral Calculus (2 Volume Set) by Richard Courant on page 74, and page 191
- A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library) by G. N. Watson on page 532
- Calculus of Variations (Carus Monograph) by Gilbert Ames Bliss on page 274
- Fouriersche Integrale by Salomon Bochner in Back Matter
- Mathematical Methods for Physicists, Fifth Edition by George B. Arfken on 4 pages
- Partial Differential Equations of First Order and Their Applications to Physics by Gustavo Lopez on page 36, page 89, and Back Matter
- Fractional Integrals and Derivatives: Theory and Applications by Stefan G. Samko in Back Matter (1), and Back Matter (2)
- Partial Differential Equations: Basic Theory (Texts in Applied Mathematics) by Michael E. Taylor on page 174, and page 412
- Applied Surface Thermodynamics (Surfactant Science) by Jan Spelt on page 50, and page 106
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