MATH242 Calculus III

Department of Science, Technology, Engineering & Mathematics: Mathematics

  1. Course Number and Title

    MATH242 Calculus III

  2. Number of Credits

    4 credits

  3. Minimum Number of Instructional Minutes Per Semester

    3000 minutes

  4. Prerequisites

    MATH141 (C or better)

    Corequisites

    None

  5. Other Pertinent Information

    At least 4 hours of testing will be given.

  6. Catalog Course Description

    Topics for this course include vectors and solid analytic geometry, surfaces, partial differentiation, directional derivatives, Lagrange multipliers, multiple integrals, cylindrical coordinates, spherical coordinates, Jacobians.

  7. Required Course Content and Direction

    1. Learning Goals:

      Course Specific:
      The student will be able to:

      1. apply vector techniques to solid analytic geometry problems, find curvature, find tangential and normal components of acceleration.
      2. find moments, centroid and moments of inertia of three dimensional figures.
      3. find partial derivatives for functions, of several variables, find directional derivatives, find extrema of functions, and use Lagrange multipliers to find extrema.
      4. evaluate iterated integrals.
      5. convert between rectangular, cylindrical, and spherical coordinates. Use change of variables and Jacobians.
      6. use multiple integration to solve area, volume, surface, and moment problems.

    2. Planned Sequence of Topics and/or Learning Activities:

      1. Vectors in the Plane
      2. Vectors in three Dimensions
      3. The Dot Product
      4. The Cross Product
      5. Lines and Planes in Space
      6. Surfaces
      7. Vector Valued Functions and Limits
      8. Derivatives and Integrals
      9. Velocity and Acceleration
      10. Tangent and Vectors and Normal Vectors
      11. Arc Length and Curvature
      12. Functions of Several Variables
      13. Limits and Continuity
      14. Partial Derivatives
      15. Differentials
      16. Chain Rules
      17. Directional Derivatives
      18. Tangent Planes and Normal
      19. Extrema of Functions of Several Variables
      20. Applications of Extrema of Function of Two Variables
      21. Lagrange Multipliers
      22. Iterated Integrals and Area
      23. Double Integrals and Volume
      24. Double Integrals in Polar Coordinates
      25. Surface Area
      26. Triple Integrals
      27. Moments and Center of Mass
      28. Cylindrical Spherical Coordinates
      29. Cylindrical and Spherical Coordinates in Space
      30. Change of Variables: Jacobians

    3. Assessment Methods for Core Learning Goals:

      All Core Discipline-Specific Course Objectives will be assessed as follows:

      The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment will consist of open-ended questions reflecting theoretical and applied situations.

    4. Reference, Resource, or Learning Materials to be used by Students:

      Departmental selected textbook. Details provided by the instructor of each course section. See Course Format.

  8. Teaching Methods Employed

    Primary teaching methods are lecture, recitation, problem solving, and class discussion as appropriate.

Review/Approval Date - 1/99; Revised 4/06