7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of Math. 31 with a grade of "C" or better

7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)

7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)

9b. Catalog Description:

Continuation of Math. 31. Vectors and analytic geometry in the plane and space; functions of several variables; partial differentiation, multiple integrals, and application problems; vector functions and their derivatives; motion in space; and surface and line integrals, Stokes' and Green's Theorems, and the Divergence Theorem. (CAN MATH 22) (with Math 30 & 31, CAN MATH SEQ C)

10. Student Performance Outcomes: (Outcomes for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Outcomes must be related to items listed in Section 11.)

1. compute vector quantities such as the dot product and the magnitude of a vector;
2. write the equation of a line or a plane in space using vector methods;
3. solve problems dealing with the motion of a particle in the plane or in space using vectors methods;
4. calculate the length of a curve in 3-space;
5. graph and identify quadric surfaces;
6. sketch functions of two variables, level curves of functions of two variables, and level surfaces of functions of three variables;
7. find maximum and minimum values of functions of two variables and solve applied max/min problems;
8. compute partial derivatives of functions of more than one variable;
9. solve maximum and minimum problems using Lagrange multipliers;
10. evaluate double and triple integrals using rectangular, polar, cylindrical, or spherical coordinates;
11. compute area, volume, centers of mass, and moments of inertia using double and triple integration;
12. evaluate line integrals and solve related applied problems;
13. evaluate line integrals and areas using Green's Theorem;
14. compute the divergence and curve of a vector field;
15. compute the area of a parametric surface;
16. evaluate surface integrals using Stokes' Theorem and the Divergence Theorem; and
17. solve complex calculus problems using algebra and trigonometry skills.

11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I. Three Dimensional Analytic Geometry and Vectors
A. Three-Dimensional Coordinate Systems
B. Vectors
C. Dot Product
D. Cross Product
E. Equations of Lines and Planes
F. Quadric Surfaces
G. Vector Functions and Space Curves
H. Arc Length and Curvature
I. Motion in Space: Velocity and Acceleration
J. Cylindrical and Spherical Coordinates
II. Partial Derivatives
A. Functions of Several Variables
B. Limits and Continuity
C. Partial Derivatives
D. Tangent Planes and Differentials
E. The Chain Rule
F. Directional Derivatives and the Gradient Vector
G. Maximum and Minimum Values
H. Lagrange Multipliers
III. Multiple Integrals
A. Double Integrals over Rectangles
B. Iterated Integrals
C. Double Integrals over General Regions
D. Double Integrals in Polar Coordinates
E. Applications of Double Integrals
F. Surface Area
G. Triple Integrals
H. Triple Integrals in Cylindrical and Spherical Coordinates
I. Change of Variable in Multiple Integrals
IV. Vector Calculus
A. Vector Fields
B. Line Integrals
C. Fundamental Theorem for Line Integrals
D. Greens' Theorem
E. Curl and Divergence
F. Parametric Surfaces and Their Areas
G. Surface Integrals
H. Stokes' Theorem
I. The Divergence Theorem

12. Typical Assignments: (List types of assignments, including library assignments.)

a. Reading Assignments: (Submit at least 2 examples)

1. Read selected topics throughout the course from the textbook. For example, how vector valued functions and their properties can be used to prove Kepler's law of planetary motion.

2. Read supplementary handouts on topics such as Green's Theorem, Stokes' Theorem, the Divergence Theorem and their applications in the physical sciences.

b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Complete homework problems from the textbook on topics throughout the course. Such problems may involve computation, sketching curves in two and three dimensions, calculating areas and volumes of two and three dimensional regions, determining maximum and minimum values of functions of two or three variables, or explaining mathematical ideas.

2. Work in groups to set up double and triple integrals used to compute the volume of a three dimensional region. Determine the best choice of a coordinate system and order of integration for the given situation. Write a summary of your solution technique, comparing the evaluation required for each order of integration.

c. Other (Terms projects, research papers, portfolios, etc.)

SECTION D

SECTION E

SECTION F

SECTION G