Mathematics for Physicists

基本信息

Format:Hardback 720 pages, Worked examples or Exercises; 25 Halftones, unspecified; 288 Line drawings, unspecified

Publisher:Cambridge University Press

Imprint:Cambridge University Press

ISBN:9781108471220

Published:14 Feb 2019

Weight:1690g

Dimensions:198 x 252 x 36 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

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.

• Presents abstract mathematical concepts and practical computational methods in unison and from a physically motivated perspective, making even advanced mathematics tangible

• Organized into three parts which are strongly interlinked and may be read in parallel, allowing reading orders to be chosen according to taste and time considerations

• Provides numerous worked examples, info sections offering physical context, biographical boxes introducing famous scientists, and several detailed case studies

• Includes over 300 problems, referenced from within the text at the location where they first become relevant, as well as fully worked solutions for all odd-numbered problems at the end of the book

目录

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.

作者简介

Alexander Altland, Universität zu Köln

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.

Jan von Delft, Ludwig-Maximilians-Universität München

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.