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.