MAT-273 Calculus III
The calculus of multivariable functions and vectors. Topics include partial differentiation, multiple integrals, optimization, multiple integration, line integrals and vector fields. Graphing calculator required; see department chair for specific model.
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Course Outline
Course Description
The calculus of multivariable functions and vectors. Topics include partial differentiation, multiple integrals, optimization, multiple integration, line integrals and vector fields. Graphing calculator required; see department chair for specific model.
Credit Hours
4Semester(s) Course Will Be Offered
Fall, Spring, Summer
Course Learning Outcomes
- Use multivariable functions and analyze them algebraically and graphically
- Perform operations with vectors
- Find the partial derivatives of multivariable functions
- Find local and global extrema of multivariable functions
- Solve applied problems using multivariable functions and vectors
- Integrate multivariable functions
- Evaluate line integrals
- Apply Green's, divergence and Stokes' theorems
- Evaluate their results for reasonableness
Topic Outline
- 1. Functions of several variables
- a. Functions of two variables
- b. Three-dimensional space
- c. Graphs of functions of two variables
- d. Contour diagrams
- e. Linear functions
- f. Functions of more than two variables
- g. Limits and continuity
- 2. Vectors
- a. Displacement vectors
- b. Vectors in general
- c. The dot product
- d. The cross product
- 3. Differentiating functions of many variables
- a. Partial derivatives
- b. Computing partial derivatives algebraically
- c. Local linearity and the differential
- d. Gradients and directional derivatives in the plane
- e. Gradients and directional derivatives in space
- 4. Optimization: local and global extrema
- a. Local extrema
- b. Global extrema: unconstrained optimization
- 5. Integrating functions of many variables
- a. The definite integral of a function of two variables
- b. Iterated integrals
- c. Triple integrals
- d. Double integrals in polar coordinates
- e. Integrals in cylindrical and spherical coordinates
- 6. Line integrals
- a. The idea of a line integral
- b. Computing line integrals over parameterized curves
- c. Gradient fields and path-independent fields
- d. Green's theorem
- 7. Calculus of vector fields
- a. The divergence of a vector field
- b. The divergence theorem
- c. The curl of a vector field
- d. Stokes' theorem