Alice Gorguis

Vector Calculus: for College Students Alice Gorguis

This book of Vector calculus can be used as a text book for college level students. It is designed for a one-semester course in the Calculus of functions of several variables and vector analysis. The prerequisite for this course is the knowledge of the fundamentals of one-variable calculus, differentiation and integration of the standard functions. The text includes most of the basic theories as well as many related exercise throughout the text, which in my experience are than enough for a semester course in this subject. Each topic is followed by examples to illustrate and help the student to practice his/her skills. The material in this book is enough to be covered during a simple semester without a hassle, and students can work through the entire book with reasonable care. Most of the exercises are relatively routine computations to moderate and productive problems, to help the students understand the concept of each topic. The text covers calculus of vector field, in particular line integrals, surface integrals, the connection between these integrals and the single, double, and triple integrals which are given by the higher-dimensional analogue of the Fundamental Theorem of Calculus: Greens' Theorem, Stokes Theorem, and the Divergence Theorem.