### Prerequisites

Upon successful completion of the course, students should be able to demonstrate the following knowledge or skills:

- Visualize three dimensional mathematical objects.
- Find the limits of multidimensional functions.
- Differentiate and integrate multidimensional functions.
- Find extreme of multidimensional functions.
- Find the surface area and volume of multidimensional objects.
- Solve applied problems in physics and engineering using the calculus of several dimensions.

**Quantitative Reasoning:**Students will be able to reason mathematically.

Introduction to functions of several variables

Limits and continuity

Partial derivatives

Differentials

Chain rule for functions of several variables

Directions derivatives and gradients

Tangent planes and normal lines

Extrema of functions of two variables

Multiple Integration

Terated integrals and area in the deplane

Double integrals and volume

Change of variables: Polar Coordinates

Center of mass and moments of inertia

Surface area

Triple integrals and applications

Triple integrals in cylindrical and spherical coordinates

Change of variables: Jacobians

Vector Analysis

Vector Fields

Line integrals

Conservative vector fields and independence of path

Green’s theorem

Surface integrals

Divergence theorem

Stoke’s theorem

In order to give the instructor the greatest flexibility in assigning a grade for the course, grades will be based on various instruments at the instructor’s discretion. However, to maintain instructional integrity there must be four class exams or three class exams and a project. A final exam will be given if there are less than four exams or a project may be substituted for the final exam if there are four in-class exams. At least 60% of the grade will be based on quantifiable work (exams, homework, quizzes, etc.). The remaining portion of the grade may be based on quantifiable work, attendance, projects, journal work, etc., at the instructor’s discretion.

The following is a compilation of acceptable grading instruments: in class exams and a final, attendance, homework or quizzes, research paper, modeling projects on the calculator or computer. Other projects or assignments may be assigned as deemed appropriate at the instructor’s discretion.

PO5 should be assessed: Students will be able to solve problems by gathering, interpreting, combining and/or applying information from multiple sources.