A Course in Mathematics for Students of Physics Volume 1 [Paperback]

A textbook covering the theory and physical applications of linear algebra and the calculus of several variables.After the basic theories of differential and integral calculus are explained, they are applied to interesting problems in optics, electronics (networks), electrostatics, wave dynamics and finally, to classical thermodynamics.After the basic theories of differential and integral calculus are explained, they are applied to interesting problems in optics, electronics (networks), electrostatics, wave dynamics and finally, to classical thermodynamics.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.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. A Course in Mathematics by Bamberg and Sternberg is in a class by itself....The authors have drawn on their wide tel#i