This textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for all even-numbered problems will be made available to instructors.
Rezensionen / Stimmen
'A concise and engaging exposition of the mathematics necessary for physics students.' Juan Maldacena, Institute for Advanced Study '... an outstanding addition to the existing stock of books on mathematical methods. It is rigorous, yet readable, and up to date, covering topics like differential forms, which are more and more in use in many areas of physics. An invaluable part of the book that contributes greatly to its pedagogical mission is the vast collection of exercises and their solutions.' R. Shankar, Yale University 'This book takes the physics student along a well-planned trip through mathematics from high school geometry to graduate-level tensor calculus. The key concepts are introduced with a degree of care and precision that is unusual in a book for physicists - but the precision is well motivated, so not at all intimidating. The book is up to date in its contents, especially as it includes the calculus of differential forms, now an essential tool in the professional physicist's toolbox.' Michael Stone, University of Illinois '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
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Worked examples or Exercises; 25 Halftones, unspecified; 288 Line drawings, unspecified
Maße
Höhe: 251 mm
Breite: 197 mm
Dicke: 38 mm
Gewicht
ISBN-13
978-1-108-47122-0 (9781108471220)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Alexander Altland is Professor of Theoretical Physics at the Universitaet zu Koeln. 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 Universitaet zu Koeln. Jan von Delft is Professor of Theoretical Physics at the Arnold Sommerfeld Center for Theoretical Physics at the Ludwig-Maximilians-Universitaet 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.
Autor*in
Universitaet zu Koeln
Ludwig-Maximilians-Universitaet Muenchen
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.
