Second year calculus. From celestial mechanics to special relativity. (English)

Springer, New York, NY (ISBN 0-387-97606-X). 397 p. (2001).

Textbook for multi-variable and vector calculus, emphasizing the historical physical problems from which the subject has grown, but couching much of it in the modern terminology of differential forms. The students learn to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. Contents: 1. Newton’s Mathematical Principals, 2. Vector algebra, 3. Celestial mechanics, 4. Differential forms, 5. Line integrals, double integrals, 6. Linear transformations, 7. Differential calculus, 8. Integration by pullback, 9. Techniques of differential calculus, 10. Fundamental theorem of calculus, 11. Albert Einstein’s theory of relativity.