Textbook: Stewart, Calculus - Early Transcendentals, 4th Edition, Brooks/Cole
1999
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3. MATH-2630 COURSE OUTLINE
Chapter 12..................................................................5
12.3, 12.4 & 12.5 Review of Vector Algebra, Lines and Planes--------------2
12.6 Cylinders and Quadratic Surfaces-------------------------------------2
12.7 Cylindrical and Spherical Coordinates (with Review of Section 10.4,
Polar Coordinates)--------------------------------------------------------1
Chapter 13..................................................................6
13.1 Vector Functions and Space Curves (with Review of Sections 10.1/2,
Parametric Curves)--------------------------------------------------------2
13.2 Derivatives and Integrals of Vector Functions------------------------1
13.3 Arc Length and Curvature (with Review of Section 8.1)----------------2
13.4 Motion in Space: Velocity and Acceleration---------------------------1
Chapter 14.................................................................14
14.1 Functions of Several Variables---------------------------------------1
14.2 Limits and Continuity------------------------------------------------1
14.3 Partial Derivatives--------------------------------------------------1
14.4 Tangent Planes and Linear Approximations-----------------------------2
14.5 The Chain Rule-------------------------------------------------------2
14.6 Directional Derivatives and the Gradient Vector----------------------2
14.7 Maximum and Minimum Values-------------------------------------------3
14.8 Lagrange Multipliers-------------------------------------------------2
Chapter 15.................................................................12
15.1 Double Integrals over Rectangles-------------------------------------2
15.2 Iterated Integrals---------------------------------------------------1
15.3 Double Integrals over General Regions--------------------------------2
15.4 Double Integrals in Polar Coordinates--------------------------------2
15.7 Triple Integrals-----------------------------------------------------2
15.9 Change of Variables in Multiple Integrals----------------------------3
Chapter 16.................................................................16
16.1 Vector Fields--------------------------------------------------------1
16.2 Line Integrals (with Review of Section 6.4, Work)--------------------2
16.3 The Fundamental Theorem for Line Integrals---------------------------2
16.4 Green's Theorem------------------------------------------------------2
16.5 Curl and Divergence--------------------------------------------------1
16.6 Parametric Surfaces and Their Areas----------------------------------2
16.7 Surface Integrals----------------------------------------------------2
16.8 Stokes's Theorem-----------------------------------------------------2
16.9 The Divergence Theorem-----------------------------------------------2
TOTAL......................................................................53
Comment. The topics on the syllabus, including the entire Chapter 16 (except
for the Divergence Theorem), are mandated by State Articulation Requirements.
However, there is obviously not enough time for a thorough treatment of the
Integral Theorems of Vector Calculus. Students who need a strong background in
Vector Calculus should be encouraged to take MATH-6010.