El Camino College - Division of Mathematical Sciences

Math 220
Multi-Variable Calculus
4 units; 4 hours lecture

Catalog Description Course Objectives and Methods of Evaluation
Outline of Subject Matter Planned Instructional Activities

Grading Method: Letter

Associate Degree Credit --- Transfers to CSU and Transfers to UC

Prerequisite: Mathematics 191 with a minimum grade of C.

Catalog Description:
Solid analytic geometry, vector algebra, partial derivatives, line surface and volume integrals, multiple integrals, vector field theory, Green's Theorem, Stoke's Theorem and Gauss' Theorem are topics included in this course.
Note: Mathematics 220 was formerly numbered Mathematics 6A.

Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1.  Use vector algebra (addition, scalar multiplication, magnitude, dot-product and cross-product) in a variety of problems.
    2. Determine equations of lines (parametric, symmetric and vector), planes and quadrics.
    3. Find tangent, normal and binormal vectors, curvature, velocity and acceleration.
    4. Convert between rectangular, cylindrical and spherical coordinates.
    5. Determine limits and the continuity of functions of several variables, and prove the existence or non-existence of limits.
    6. Calculate partial derivatives, and use the chain rule to find partial or total derivatives of functions of several variables.
    7. Find tangent planes and differentials and use in applications.
    8. Calculate directional derivatives and gradients and use in applications.
    9. Determine extrema of functions of several variables with and without Lagrange multipliers and use in applications.
    10. Find potential functions of conservative vector fields.
    11. Evaluate multiple integrals directly and by converting to cylindrical or spherical coordinates.
    12. Use multiple integrals to find plane areas, surface areas and volumes.
    13. Evaluate line integrals, surface integrals and find flux.
    14. Calculate the curl and divergence of vector fields and use these to solve problems.
    15. Use Green's Theorem, Stoke's Theorem and Gauss' Theorem to solve a variety of problems.
  1. Methods of Evaluation - Associate Degree Credit Course
    1. Substantial writing assignments are inappropriate for this degree applicable course because:
      1. The course is primarily computational in nature.
    2. Computational or non-computational problem-solving demonstrations, including:
      1. Exam

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Outline of Subject Matter
 

Approximate Time

Major Topic

16 hours

I. Three Dimensional Analytic Geometry and Vectors

  1. Vectors, dot-product and cross-product
  2. Equations of lines, planes and quadric surfaces
  3. Applications of vectors (distances, volumes, etc.)
  4. Vector functions and space curves
  5. Arclength and curvature
  6. Velocity and acceleration
  7. Cylindrical and spherical coordinates

16 hours

II. Functions of Several Variables

  1. Limits and continuity
  2. Partial derivatives
  3. Tangent planes and differentials
  4. Chain rule
  5. Directional derivatives and gradient
  6. Extrema, Lagrange multipliers
  7. Applications

12 hours

III. Multiple Integrals

  1. Double integrals in rectangular and polar coordinates
  2. Surface area
  3. Triple integrals in rectangular, cylindrical and spherical coordinates
  4. Change of variables and Jacobian

20 hours

IV.  Vector Calculus

  1. Vector fields
  2. Line integrals and the Fundamental Theorem for Line Integrals
  3. Green's Theorem
  4. Curl and divergence
  5. Surface integrals
  6. Stoke's and Gauss' Theorems

  8 hours

Examinations

Total:

72 Hours

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Planned Instructional Activities:

Lecture, individual work, group work and computer aided instruction, inter alia.

Entrance Skills and Knowledge:

List the required skills and/or knowledge without which a student would be highly unlikely to receive a grade of A, B, C, or Credit (or for Health and Safety, would endanger self or others) in the Target Course.

  1. Integrate using a variety of techniques and use integration in applications.
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Source of information: Course Outline of Record dated November, 1999



 Last Updated On: 4/20/06