# MTH 255 : Vector Calculus II

## Transcript title

Vector Calculus II

## Credits

4

## Grade mode

Standard letter grades

## Contact hours total

60

## Lecture hours

30

## Lab hours

30

## Recommended preparation

## Description

Continuation of the study of vector analysis for science and engineering students. Includes double and triple integrals with applications to area, volume and center of mass; introduction to vector analysis including divergence, curl, line integrals and work, surface integrals; conservative fields and the theorems of Green and Stokes. A graphing calculator is required. TI-83 or TI-84 recommended. Basic computer skills required.

## Learning outcomes

1. Students will set up and evaluate double and triple integrals.

2. Students will apply double and triple integrals in applications such as area, volume, surface area, and center of mass.

3. Students will use polar coordinates to set up a double integral.

4. Students will evaluate triple integrals in cylindrical and spherical coordinates.

5. Students will use the Jacobian to calculate double and triple integrals.

6. Students will find the curl and divergence of a vector field.

7. Students will set up and evaluate line integrals of scalar valued and vector valued functions.

8. Students will find the equations of and be able to graph parametric surfaces.

9. Students will find the equations of tangent planes of parametric surfaces.

10. Students will determine whether a vector field is conservative or not.

11. Students will use Green's Theorem to evaluate line integrals.

12. Students will set up and evaluate surface and flux integrals.

13. Students will use Stoke's Theorem to evaluate a line integral as a surface integral.

14. Students will use a computer algebra or graphing system (such as Mathematica or Maple) to deepen understanding of vector calculus.

## General education/Related instruction lists

- Science not Lab
- Mathematics