Lipsman R.L., Rosenberg J.M. Multivariable Calculus with MatLAB. With Applications to Geometry and Physics

Springer, 2017. — 277 p.This book is a reworking and updating for MatLAB of our previous book (joint with Kevin R. Coombes) "Multivariable Calculus with Mathematica", Springer, 1998. It represents our attempt to enrich and enliven the teaching of multivariable calculus and mathematical methods courses for scientists and engineers. Most books in these subjects are not substantially different from those of fifty years ago. (Well, they may include fancier graphics and omit several topics, but those are minor changes.) This book is different. We do touch on most of the classical topics; however, we have made a particular effort to illustrate each point with a significant example. More importantly, we have tried to bring fundamental physical applications—Kepler’s laws, electromagnetism, fluid flow, energy estimation—back to a prominent position in the subject. From one perspective, the subject of multivariable calculus only exists because it can be applied to important problems in science. In addition, we have included a discussion of the geometric invariants of curves and surfaces, providing, in effect, a brief introduction to differential geometry. This material provides a natural extension to the traditional syllabus.Vectors and Graphics.
Geometry of Curves.
Kinematics.
Directional Derivatives.
Geometry of Surfaces.
Optimization in Several Variables.
Multiple Integrals.
Multidimensional Calculus.
Physical Applications of Vector Calculus.
MatLAB Tips.
Sample Solutions.