(Revised: May, 2005)
Description
Continuation of Math 211. Vector calculus, functions of several real variables, partial differentiation, implicit functions, multiple integrals, line and surface integrals, and applications. (4 credits)
Prequisites
A grade of C- or better in Math 211.
Objectives
The student will:
· Understand the algebra and geometry of vectors in 2 and 3 dimensions.
· Understand the calculus of curves in R2, the unit tangent and unit normals vectors, curvature, and motion along a trajectory.
· Learn the three-dimensional vector algebra required by linear algebra courses: Dot and cross products, projections, and equations of line and planes in R3.
· Understand spherical coordinates and cylindrical coordinates.
· Understand partial differentiation, and will apply partial derivatives to the computation of gradients, directional derivatives, tangent planes, and differentials.
· Understand differentiable functions of several variables.
· Locate and classify critical points of functions of several variables, and will solve applied optimization problems.
· Understand definite integrals in higher dimensions. The student will set up and evaluate multiple integrals, and will be able to interchange the order of integration.
· Understand line and surface integrals, potential functions, and path independence. The student will apply Green's theorem in the plane, and Gauss's and Stokes' theorems in R3.
Texts
· Calculus, 2nd edition, Robert T. Smith and Roland B. Minton, McGraw-Hill, New York, 2002.
· Students are required to purchase a graphing calculator (TI-82, TI-83, TI-84, TI-85, TI-86, or TI-92).
Course Outline
Note: The course outline refers to the text by Smith and Minton.
|
Topic |
Section (Smith/Minton) |
|
Vectors in the plane |
10.1 |
|
Vectors in space |
10.2 |
|
Dot Product and Projections |
10.3 |
|
Cross Product |
10.4 |
|
Lines and Planes in space |
10.5 |
|
Surfaces in space |
10.6 |
|
Vector-Valued Functions and Space Curves |
11.1 |
|
The calculus of vector-valued functions |
11.2 |
|
Motion in space |
11.3 |
|
Curvature |
11.4 |
|
Tangent and normal vectors |
11.5 |
|
Functions of Several Variables |
12.1 |
|
Limits and continuity |
12.2 |
|
Partial Derivatives |
12.3 |
|
Tangent planes and linear approximation |
12.4 |
|
The chain rule |
12.5 |
|
Directional Derivatives and Gradients |
12.6 |
|
Extrema of functions of several variables |
12.7 |
|
Lagrange multipliers |
12.8 |
|
Double Integrals in Rectangular Coordinates |
13.1 |
|
Area and volume |
13.2 |
|
Double integrals in polar coordinates |
13.3 |
|
Surface Area |
13.4 |
|
Triple Integrals |
13.5 |
|
Cylindrical Coordinates |
13.6 |
|
Spherical Coordinates |
13.7 |
|
Vector Fields |
14.1 |
|
Line Integrals |
14.2 |
|
Independence of path and conservative vector fields |
14.3 |
|
Green's Theorem |
14.4 |
|
Curl and divergence |
14.5 |
|
Surface integrals |
14.6 |
|
The Divergence Theorem |
14.7 |
|
Stokes' Theorem |
14.8 |
General Education Credit
This course may be taken for general education credit (G2).
Mathematics
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Page maintained by: Bob
Buchanan
jbuchana@marauder.millersv.edu
Last
updated: October 7, 2004