MATH242 Calculus III

Department of Science, Technology, Engineering & Mathematics: Mathematics

I. Course Number and Title
MATH242 Calculus III
II. Number of Credits
4 credits
III. Number of Instructional Minutes
IV. Prerequisites
MATH141 (C or better)
V. Other Pertinent Information
At least 4 hours of testing are given.
VI. Catalog Course Description
This course is a continuation of Math 141. Topics for this course include: vectors and solid analytic geometry, surfaces, partial and directional derivatives, Lagrange multipliers, multiple integrals, cylindrical and spherical coordinates, line and surface integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.
VII. Required Course Content and Direction
  1. Course Learning Goals

    Students will:

    1. use vector-valued functions to parameterize curves and describe motion in space, find unit tangent and normal vectors, find tangential and normal components of acceleration, and find arc length and curvature;
    2. find partial derivatives of functions of several variables, find directional derivatives and gradients, find tangent planes, and use Lagrange multipliers to find extrema;
    3. evaluate multiple integrals in rectangular, polar, cylindrical and spherical coordinates, and use multiple integrals to find areas, volumes, centers of mass, and surface areas; and
    4. evaluate line and surface integrals, find work done in a vector field, use Green's Theorem, Stokes' Theorem, and the Divergence Theorem to evaluate integrals.
  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 of Vector-Valued Functions
    9. Velocity and Acceleration
    10. Tangent Vectors and Normal Vectors
    11. Arc Length and Curvature
    12. Functions of Several Variables
    13. Limits and Continuity
    14. Partial Derivatives
    15. Chain Rules
    16. Directional Derivatives and Gradients
    17. Differentials
    18. Tangent Planes
    19. Extrema of Functions of Several Variables
    20. Applications of Extrema of Functions 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 and Volume
    27. Triple Integrals in Cylindrical and Spherical Coordinates
    28. Center of Mass
    29. Vector Fields
    30. Line Integrals
    31. Conservative Vector Fields
    32. Green’s Theorem
    33. Divergence and Curl
    34. Surface Integrals
    35. Stokes’ Theorem
    36. Divergence Theorem
  3. Assessment Methods for Course Learning Goals

    The student applies 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 consists of open-ended questions reflecting theoretical and applied situations.
  4. Reference, Resource, or Learning Materials to be used by Student:

    Departmentally-selected textbook. Details provided by the instructor of each course section. See course syllabus.

Review/Approval Date - 1/99; Revised 4/06; Revised 09/2013; New Core 8/2015