MATH 254 Multivariable Calculus

Presents multivariable calculus with emphasis on the calculus of vector-valued functions and space curves. Topics include partial derivatives, double and triple integrals, directional derivatives, gradient vectors, vector fields, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem. Real world applications are emphasized.  (QS)

Credits

5

Prerequisite

MATH 126

Distribution

Quantitative Skills (QS)

Outcomes

1. Find the domain and range of a multivariable function, and sketch its typical level curve or level surface.
2. Identify key features of multivariable functions.
3. Find both first-order and second-order partial derivatives of a multivariable function.
4. Compute the gradient and apply it to finding equations of tangent lines and planes, as well as to computing directional derivatives of multivariable functions.
5. Evaluate double and triple integrals; apply these multiple integration principles to solving area, volume, and average-value applications.
6. Compute line and surface integrals, and use them to solve relevant applications.
7. Use alternative coordinate systems to simplify multiple integration problems.
8. Compute gradient, curl, and divergence. Use vector and scalar fields appropriately.
9. Apply Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.
10. Solve first-order differential equations, including initial value problems.
11. Communicate mathematical ideas.
12. Use appropriate technology strategically.