Calculus of Several Variables (3rd ed. 1987)

The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured.

For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics.

Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula.

One can then finish with Chapter IX on double integration to round off the one-term course.

The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1.

This forms a coherent whole.