Mathematical Physics: A Modern Introduction to Its Foundations / Edition 1

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This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained. Intended for advanced undergraduate or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.
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Editorial Reviews

From the Publisher

From the book reviews:

“Mathematical Physics: A Modern Introduction to Its Foundations is intended for adoption in a course or a sequence of ‘methods of mathematical physics’ at the advanced undergraduate or beginning graduate level. … this is a textbook that every library must have (with a large number of copies in reserve), and it will be a valuable aid for committed students, researchers, and instructors of science and applied mathematics.” (Eleftherios Kirkinis, SIAM Review, Vol. 56 (3), September, 2014)

“Hassani uses the concept of a vector space to build all of the discussions for the basic ideas about the subject. … Hassani writes well and does a very good job of connecting the various topics presented. Each of the 30 chapters contains clear, worked-out examples and problems at the end. Summing Up: Recommended. Upper-division undergraduates and graduate students.” (E. Kincanon, Choice, Vol. 51 (11), July, 2014)

Some praise for the previous edition:

PAGEOPH [Pure and Applied Geophysics]

Review by Daniel Wojcik, University of Maryland

"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. … I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."


Review by G.Roepstorff, University of Aachen, Germany

"… Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. … A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. … For the physics student in the middle of his training, it will certainly prove to be extremely useful."


Review by Paul Davies, Orion Productions, Adelaide, Australia

"I am pleased to have so many topics collected in a single volume. All the tricks are there of course, but supported by sufficient rigour and substantiation to make the dedicated mathematical physicist sigh with delight."


"This book is a condensed exposition of the mathematics that is met in most parts of physics. The presentation attains a very good balance between the formal introduction of concepts, theorems and proofs on one hand, and the applied approach on the other, with many examples, fully or partially solved problems, and historical remarks. An impressive amount of mathematics is covered. … This book can be warmly recommended as a basic source for the study of mathematics for advanced undergraduates or beginning graduate students in physics and applied mathematics, and also as a reference book for all working mathematicians and physicists."

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Product Details

  • ISBN-13: 9780387985794
  • Publisher: Springer New York
  • Publication date: 2/28/2002
  • Edition description: 1st ed. 1999. Corr. 3rd printing 2002
  • Edition number: 1
  • Pages: 1026
  • Product dimensions: 6.70 (w) x 9.80 (h) x 2.00 (d)

Meet the Author

Sadri Hassani, Department of Physics, Illinois State University,
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Table of Contents

Note to the Reader
Mathematical Preliminaries
I Finite-Dimensional Vector Spaces
1 Vectors and Transformations
2 Operator Algebra
3 Matrices: Operator Representations
4 Spectral Decomposition
II Infinite-Dimensional Vector Spaces
5 Hilbert Spaces
6 Generalized Functions
7 Classical Orthogonal Polynomials
8 Fourier Analysis
III Complex Analysis
9 Complex Calculus
10 Calculus of Residues
11 Complex Analysis: Advanced Topics
IV Differential Equations
12 Separation of Variables in Spherical Coordinates
13 Second-Order Linear Differential Equations
14 Complex Analysis of SOLDEs
15 Integral Transforms and Differential Equations
V Operators on Hilbert Spaces
16 An Introduction to Operator Theory
17 Integral Equations
18 Sturm-Liouville Systems: Formalism
19 Sturm-Liouville Systems: Examples
VI Green's Functions
20 Green's Functions in One Dimension
21 Multidimensional Green's Functions: Formalism
22 Multidimensional Green's Functions: Applications
VII Groups and Manifolds
23 Group Theory
24 Group Representation Theory
25 Algebra of Tensors
26 Analysis of Tensors
VIII Lie Groups and Their Applications
27 Lie Groups and Lie Algebras
28 Differential Geometry
29 Lie Groups and Differential Equations
30 Calculus of Variations, Symmetries, and Conservation Laws
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