Textbook: Essential Calculus: Early Transcendentals, 2nd Edition James Stewart McMaster University
ISBN-10: 1133112285 ISBN-13: 9781133112280
Catalog Description: This course includes vector calculus, vector-valued functions, tangents to curves, velocity vector, curl, partial derivatives, chain rule, gradients, implicit functions, extrema of functions of several variables, multiple integrals including change of order and applications, surface integrals, and path independent line integrals.
Prerequisites: MATH 2414 with a grade of “C”
or better, or equivalent. Other prerequisites include ENGL 0301 and READ 0303.
Semester Credit Hours: (4-4-0)
Course
Objectives: The student should be able to develop a conceptual understanding of the fundamental ideas underlying geometry in the space and vectors, derivatives of functions of two or more variables, multiple integrals and vector calculus.
Topics:
Introduction/3D Coordinate Systems
Vectors & Vector Algebra
Lines & Planes
Cylinders & Quadratic Surfaces
Vector Functions & Space Curves
Functions of Several Variables/Partial Derivatives
The Chain Rule
Directional Derivatives & The Gradient Vector
Maximum and Minimum Values & Lagrange Multipliers
Double Integrals/ Applications of Double Integrals
Triple Integrals/Applications of Triple Integrals
Change of Variables in Multiple Integrals
Vector Calculus/Line Integrals
Green’s Theorem, Curl & Gauss’s Divergence Theorem
Green’s Theorem, Curl & Gauss’s Divergence Theorem
Parametric Surfaces, Surface Integrals & Stoke’s Theorem