**Contact Hours (based on 11 week quarter)**

Lecture: 55

Lab: 0

Other: 0

Systems: 0

Clinical: 0

**Intent:**
**Distribution Requirement(s) Status:**

Academic
Elective

**Equivalencies At Other Institutions**

Other Institution Equivalencies Table
Institution |
Course # |
Remarks |

N/A |

**Learning Outcomes**

**After completing this course, the student will be able to:**

- Understand and use the chain rule properly.
- Understand and use Directional Derivatives and Gradient Vectors.
- Find Maximum and Minimum values of a multivariable equation.
- Properly use Lagrange Multipliers in applied problems.
- Work with double integrals over regions using both Rectangular and Polar coordinates.
- Finding applications of Double integrals, and find surface area.
- Work with Triple Integrals using both Cylindrical and Spherical Coordinates.
- Properly use the change of variables technique in Multiple Integrals.
- Understand Vector Fields and Line Integrals.
- Become comfortable with Green's Theorem and Stoke's Theorem and understand how to use them.
- Find the Curl and Divergence.
- Understand and use the Divergence Theorem.
- Work with functions of several variables.
- Find tangent planes.
- Work with partial derivatives.

**General Education Learning Values & Outcomes**

Revised August 2008 and affects outlines for 2008 year 1 and later.

1. Information Literacy

*Definition:*
Recognizing when information is needed and have the ability to locate, evaluate, and use effectively the needed information.

*Outcomes:* Students will be able to . . .

1.1 Determine the extent of information needed.

2. Critical Thinking

*Definition:*
The ability to think critically about the nature of knowledge within a discipline and about the
ways in which that knowledge is constructed and validated and to be sensitive to the ways these
processes often vary among disciplines.

*Outcomes:* Students will be able to . . .

2.1 Identify and express concepts, terms, and facts related to a specific discipline.

2.3 Identify, interpret, and evaluate pertinent data and previous experience to reach conclusions.

2.7 Identify and evaluate connections and relationships among disciplines.

2.9 Apply and/or create problem-solving strategies to successfully adapt to unpredictable and/or changing environments.

8. Mathematical Reasoning

*Definition:*
Understanding and applying concepts of mathematics and logical reasoning in a variety of contexts, both academic and non-academic.

*Outcomes:* Students will be able to . . .

8.1 Analyze problems to determine what mathematical principles apply.

8.2 Correctly apply logical reasoning and mathematical principles to solve problems.

8.3 Interpret information and reasoning expressed mathematically (for example in spreadsheets,
diagrams, charts, formulas, etc.).

8.4 Communicate mathematical information effectively.

10. Technology

*Definition:*
Understanding the role of technology in society and using technology appropriately and effectively.

*Outcomes: *Students will be able to . . .

10.3 Use technology appropriate to the context and task to effectively retrieve
and manage information, solve problems, and facilitate communication.

**Course Contents**

- Partial Derivatives
- Multiple Integrals
- Vector Calculus
- Applications of all of the above.