Mathematics for Physicists: Introductory Concepts and Methods

ISBN-13: 9781108471220 / Angielski / Twarda / 2019 / 720 str.

Jan (Ludwig-Maximilians-Universitat Munchen) von Delft

Opis

This comprehensive textbook introduces fundamental concepts and computational methods of mathematics from the perspective of physicists.

Recenzje

'It contains all the material required in the undergraduate curriculum and emphasises a pedagogical strategy that presents a unified approach of concepts and methods, whereas most mathematics books for physicists tend to concentrate on methods.' Mike Glazer, Acta Crystallographica

Spis treści

Preface; Part I. Linear Algebra: 1. Mathematics before numbers; 2. Vector spaces; 3. Euclidean geometry; 4. Vector product; 5. Linear maps; 6. Determinants; 7. Matrix diagonalization; 8. Unitarity and hermiticity; 9. Linear algebra in function spaces; 10. Multilinear algebra; Problems: linear algebra; Part II. Calculus: 1. Differentiation of one-dimensional functions; 2. Integration of one-dimensional functions; 3. Partial differentiation; 4. Multi-dimensional integration; 5. Taylor series; 6. Fourier calculus; 7. Differential equations; 8. Functional calculus; 9. Calculus of complex functions; Problems: calculus; Part III. Vector Calculus: 1. Curves; 2. Curvilinear coordinates; 3. Fields; 4. Introductory concepts of differential geometry; 5. Alternating differential forms; 6. Riemannian differential geometry; 7. Case study: differential forms and electrodynamics; Problems: vector calculus; Solutions: linear algebra; Solutions: calculus; Solutions: vector calculus; Index.

O autorze

Altland, Alexander Alexander Altland is Professor of Theoretical Physics at the Universität zu Köln. His areas of specialization include quantum field theory and the physics of disordered and chaotic systems. He is co-author of the hugely successful textbook Condensed Matter Field Theory (2nd edition, Cambridge, 2010). He received the Albertus Magnus Teaching Award of the faculty of mathematics and natural sciences of Universität zu Köln. von Delft, Jan Jan von Delft is Professor of Theoretical Physics at the Arnold Sommerfeld Center for Theoretical Physics at the Ludwig-Maximilians-Universität Munchen. His research is focused on mesoscopic physics and strongly interacting electron systems. For his engagement in teaching, utilizing electronic chalk and 'example+practice' problem sheets including example problems with detailed solutions, he received a Golden Sommerfeld teaching award.