Mathematics for Physicists Textbook – Introductory Concepts and Methods
Introductory Concepts and Methods
This mathematics for physicists textbook connects linear algebra, calculus, and geometry with undergraduate physics. Alexander Altland and Jan von Delft pair mathematical foundations with computational methods, worked examples, and problems that help readers practice each new idea.
- 720pages
- 313illustrations
- 300+problems
- 1stedition
This book is for you if you are
- an undergraduate physics student developing mathematical foundations
- a student connecting abstract definitions with calculations
- a reader reviewing mathematics before advanced physics courses
Why this book
A calculation becomes easier to follow when you understand both the operation and the structure behind it. This text develops those connections through linear algebra, calculus, and vector calculus, introducing mathematical ideas alongside the ways physicists use them. Readers progress from sets and vector spaces to differential equations, complex functions, and geometry, with worked examples providing opportunities to follow an argument closely.
The three main parts are linked, so students can revisit an earlier idea as it appears in another setting. For readers studying mathematical methods for physicists, this offers a route between an abstract definition and a practical calculation. Problem sections support independent practice, and worked solutions to odd-numbered problems help readers compare their reasoning with a complete approach.
The book is aimed at undergraduate physics students. It can support a mathematics course or help a reader review the foundations needed for more advanced physics.
What you'll learn
- Work with vector spaces and linear maps
- Connect matrix operations with geometric ideas
- Apply differentiation and integration methods
- Explore Fourier calculus and differential equations
- Study vector calculus and differential geometry
Not the right book for: Readers seeking a basic arithmetic workbook or an advanced graduate research monograph.
Questions about this book
What mathematical areas does it cover?
The main parts cover linear algebra, calculus, and vector calculus.
Are worked solutions included?
Worked solutions are provided for odd-numbered problems.
What level is the book intended for?
It is written for the undergraduate physics curriculum.
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Contents
- 1Mathematics before numbersp. 3
- 2Vector spacesp. 19
- 3Euclidean geometryp. 38
- 4Vector productp. 55
- 5Linear mapsp. 63
- 6Determinantsp. 86
- 7Matrix diagonalizationp. 98
- 8Unitarity and Hermiticityp. 109
- 9Linear algebra in function spacesp. 129
- 10Multilinear algebrap. 147
- 11Differentiation of one-dimensional functionsp. 208
- 12Integration of one-dimensional functionsp. 216
- 13Partial differentiationp. 229
- 14Multidimensional integrationp. 238
- 15Taylor seriesp. 259
- 16Fourier calculusp. 271
- 17Differential equationsp. 300
- 18Functional calculusp. 330
- 19Calculus of complex functionsp. 338
- 20Curvesp. 406
- 21Curvilinear coordinatesp. 414
- 22Fieldsp. 430
- 23Introductory concepts of differential geometryp. 463
- 24Alternating differential formsp. 477
- 25Riemannian differential geometryp. 502
- 26Case study: differential forms and electrodynamicsp. 518
Details
- Publisher
- Cambridge University Press
- Edition
- 1st edition, 2019
- Pages
- 720
- Language
- English
- Formats
- PDF (any other format on request)
- Licence
- Personal use, keep forever