A Course in Mathematics for Students of Physics: Volume 2
This textbook, available in two volumes, has been developed from a course taught at Harvard over the last decade. The course covers principally the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The authors adopt the 'spiral method' of teaching, covering the same topic several times at increasing levels of sophistication and range of application. Thus the reader develops a deep, intuitive understanding of the subject as a whole, and an appreciation of the natural progression of ideas. Topics covered include many items previously dealt with at a much more advanced level, such as algebraic topology (introduced via the analysis of electrical networks), exterior calculus, Lie derivatives, and star operators (which are applied to Maxwell's equations and optics). This then is a text which breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Any student, interpreted in the widest sense, with an interest in physics and mathematics, will gain from its study.
- Online resource
- 05 Nov 2015
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
- 408 b/w illus.
'... a very well readable and highly recommendable addition to the existing courses in mathematics for students of physics.' Zentralblatt fur Mathematik und Ihre Grenzgebiete '... there is to my knowledge no comparable book, and it is hard to imagine a more inspiring one.' The Times Higher Education Supplement '... this book will serve as a fundamental text not only for students in physics, but also for students in mathematics interested in the most evident applications of mathematical definitions, results and theories.' Padiatre and Padalogie 'Not only is the mathematics clean, elegant, andmodern, but the presentation is humane, especially for a mathematics text. Examples are provided before generalisation, and motivation and applications are kept firmly in view ... This is first rate!' American Journal of Physics
Table of contents
1. The theory of electric networks; 2. The method of orthogonal projection; 3. Higher-dimensional complexes; 4. Complexes situated in Rn; 5. Electrostatics in R3; 6. Currents, flows and magnetostatics; 7. The star operator; 8. Maxwell's equations; 9. Complex analysis; 10. Asymptotic analysis; Index.