Course Objectives

By the end of the semester, students should be able to:  

1. Use three-dimensional Cartesian coordinates (including vectors and vector operations) to classify and distinguish between common equations and graphs of surfaces and curves. 
2. Evaluate first and second partial derivatives of a multivariable function and relate these functions and their values to the behavior of a surface. 
3. Use partial derivatives to determine equations of tangent planes, to locate and to classify critical points, and to calculate a rate of change of a surface in any direction. 
4. Identify points in two-dimensional (Cartesian and polar) and three-dimensional (Cartesian, cylindrical, and spherical) coordinate systems and express common equations of surfaces and boundaries of regions in each system. 
5. Write, reorder, evaluate, and interpret double and triple integrals of regions in the plane and space, respectively. 
6. Set up, evaluate, and interpret line integrals of a scalar function or vector field over a given curve, applying famous results like the Fundamental Theorem for Line Integrals and Green’s Theorem when appropriate. 
7. Set up, evaluate, and interpret surface integrals of a scalar function or vector field over a given surface, applying famous results like Stokes’ Theorem and the Divergence Theorem when appropriate. 

 

Course Calendar

Week	Sections Covered	Topic	Additional Practice Worksheets
1	12.1 12.2 12.3 12.4	Three-Dimensional Coordinate Systems Vectors The Dot Product The Cross Product	Calculus I and II Review 12.2 Vectors Notes (12.2 solutions) Practice with Vectors (solutions)
2	12.5 12.6	Equations of Lines & Planes Cylinders and Quadric Surfaces	Understanding Surfaces
3	14.1 14.3 14.4 14.5	Functions of Several Variables Partial Derivatives Tangent Planes and Linear Approximation The Chain Rule	Lines and Planes 14.5 The Chain Rule Notes (14.5 solutions)
4	14.6 14.7 14.8	Directional Derivatives & the Gradient Vector Maximum and Minimum Values Lagrange Multipliers	Tangent Planes and Directional Derivatives Classifying Critical Points 14.8 Lagrange Multipliers Notes (14.8 Solutions)
5	EXAM 1 15.1 15.2	Covers Ch 12 and 14, (during discussion) Double Integrals over Rectangles Double Integrals over General Regions	Double Integrals and Volume
6	15.3 15.6	Double Integrals in Polar Coordinates Triple Integrals in Cartesian Coordinates	Double Integrals in Polar Coordinates (solutions) Cartesian Triple Integrals
7	15.7 15.8	Triple Integrals in Cylindrical Coordinates Triple Integrals in Spherical Coordinates	Cylindrical Triple Integrals Spherical Triple Integrals
8	15.9	Change of Variables in Multiple Integrals	15.9 Change of Variables Notes (15.9 solutions)
9	EXAM 2 13.1 13.2 13.3	Covers Ch 14 and 15 (during discussion) Vector Functions Derivatives & Integrals of Vector Functions Arc Length	Vector Functions and Parameterized Curves
10	16.2 16.1 16.2	Line Integrals (Scalar Functions) Vector Fields Line Integrals (Vector Fields)	Line Integrals
11	16.3 16.4	The Fundamental Thm for Line Integrals Green’s Theorem	Line Integral Theorems
12	16.5 16.6	Curl and Divergence Parametric Surfaces and Their Areas	Curl and Divergence Common Parametric Surfaces
13	EXAM 3 16.7 16.8	Covers Ch 15, 13 and 16.1-6 (during discussion) Surface Integrals (Scalar and Vector Functions) Stokes’ Theorem	Line Integrals vs. Surface Integrals.pdf
—		THANKSGIVING BREAK, NO CLASSES
14	16.9	Divergence Theorem	Using the Divergence Theorem
		Finals Week	Final Portfolio Due Monday 12/9