# Vector and Multivariable Calculus

## General

MATH

321

### College/School

College of Science and Engineering

### Description

Vectors, functions of several variables, gradients, multiple integrals, vector fields, Green's & Stokes' theorems, applications.

4

4

## Learning Outcomes

### Outcome

Analyze functions of several variables and interpret their properties in various contexts.

### Outcome

Perform vector operations and recognize their applications.

### Outcome

Describe and visualize 3D lines, curves, planes, and fundamental surfaces and analyze geometrical properties of each.

### Outcome

Determine extrema of functions of several variables.

### Outcome

Depict and interpret vector fields and compute curl, divergence, and flux.

### Outcome

Model a written description of a physical situation graphically, numerically, analytically, or verbally using vectors, curves, surfaces, derivatives, and integrals in rectangular, polar, cylindrical, and spherical coordinate systems in R^2 and R^3.

### Outcome

State the Fundamental Theorem of Line Integrals, Green's Theorem, Stoke's Theorem, and the Divergence Theorem in their own words.

### Outcome

Compare and contrast several generalizations of the Fundamental Theorem of Calculus.

### Outcome

Illustrate multivariable concepts by hand and with appropriate technology.

### Outcome

Use technology to help solve problems and illustrate solutions.

### Outcome

Communicate concepts both orally and in well-written sentences and explain solutions to problems.

## Dependencies

### Courses

MATH321 is a prerequisite for:

### Programs

MATH321 is a completion requirement for: