Course in Mathematics for Students of Physics 1

ISBN-13: 9780521406499 / Angielski / Miękka / 1991 / 424 str.

Paul Bamberg; Shlomo Sternberg

Opis

This text breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Aimed at physics students, it covers the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The exterior differential calculus is now being recognized by mathematicians and physicists as the best method of formulating the geometrical laws of physics, and the frontiers of physics have already begun to reopen fundamental questions about the geometry of space and time. Covering the basics of differential and integral calculus, the authors then apply the theory to interesting problems in optics, electronics (networks), electrostatics, wave dynamics, and finally to classical thermodynamics. The authors adopt the "spiral method" of teaching (rather than rectilinear), covering the same topic several times at increasing levels of sophistication and range of application.

Recenzje

'… there is to my knowledge no comparable book, and it is hard to imagine a more inspiring one.' The Times Higher Education Supplement

Spis treści

1. Linear transformations of the plane; 2. Eigenvectors and eigenvalues; 3. Linear differential equations in the plane; 4. Scalar products; 5. Calculus in the plane; 6. Applications of differential calculus; 7. Differential forms and line integrals; 8. Double integrals; 9. Gaussian optics; 10. Vector spaces and linear transformations; 11. Determinants; Index.