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MATH 2415 Calculus III



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.

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