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 Course Title:   Calculus IV

 Title Abbreviation:   CALCULUS IV

 Department:    MATH&

 Course #:    254

 Credits:    5

 Variable:     No

 IUs:    5

 CIP:    270101

 EPC:    n/a

 REV:    2014

 Course Description  

Topics include functions of several variables, tangent planes, partial differentiation, the chain rule, Lagrange multipliers, double and triple integrals, vector fields, line and surface integrals. Culminates in the theorems of Green and Stokes, along with the Divergence Theorem.


Prerequisite: MATH& 153.

Additional Course Details

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

Learning Outcomes

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

  1. Understand and use the chain rule properly.
  2. Understand and use Directional Derivatives and Gradient Vectors.
  3. Find Maximum and Minimum values of a multivariable equation.
  4. Properly use Lagrange Multipliers in applied problems.
  5. Work with double integrals over regions using both Rectangular and Polar coordinates.
  6. Finding applications of Double integrals, and find surface area.
  7. Work with Triple Integrals using both Cylindrical and Spherical Coordinates.
  8. Properly use the change of variables technique in Multiple Integrals.
  9. Understand Vector Fields and Line Integrals.
  10. Become comfortable with Green's Theorem and Stoke's Theorem and understand how to use them.
  11. Find the Curl and Divergence.
  12. Understand and use the Divergence Theorem.
  13. Work with functions of several variables.
  14. Find tangent planes.
  15. 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

  1. Partial Derivatives
  2. Multiple Integrals
  3. Vector Calculus
  4. Applications of all of the above.