Second Year Calculus: From Celestial Mechanics to Special Relativity

by David M. Bressoud

Second Year From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.

Genres: Mathematics, Calculus

404 pages, Paperback

First published August 8, 1991

Reviews

[Karl · Rating 4 out of 5]

As all mathematicians know, the real way to make the classical integral theorems of multivariable calculus come together is by viewing them through the modern lens of differential forms. This would be a textbook that one could use to teach Calculus 3 from that vantage, but still allowing the students to learn the basic skills - computing surface integrals, gradients, etc. Bressoud has an historical approach, culminating in a discussion of Maxwell's equations and Einstein's special relativity - a good motivation to view the world from Bressoud's angle at any rate. You know you want to teach it this way - go for it!

[Naomi · Rating 4 out of 5]

Good book for beginning vector analysis