KERN COMMUNITY COLLEGE DISTRICT – CERRO COSO COLLEGE

MATH C251 COURSE OUTLINE OF RECORD

  1. DISCIPLINE AND COURSE NUMBER:
    MATH C251
  2. COURSE TITLE:
    Analytic Geometry and Calculus III
  3. SHORT BANWEB TITLE:
    Analytical Geom/Calc III
  4. COURSE AUTHOR:
    Bernsten, Dean
  5. COURSE SEATS:
    -
  6. COURSE TERMS:
    30 = Spring; 70 = Fall
  7. CROSS-LISTED COURSES:
  8. PROPOSAL TYPE:
    CC Course Revision
  9. START TERM:
    30 = Spring, 2012
  10. C-ID:
  11. CATALOG COURSE DESCRIPTION:
    This course is a continuation of Analytic Geometry and Calculus II, extending the skills of differentiation and integration by learning new techniques and working with partial derivatives and double and triple integrals. Other major topics include cylindrical and spherical coordinates, quadric surfaces, vector functions, vector analysis, Green''s theorem and Stoke''s theorem.

  12. GRADING METHOD

    Default:
    S = Standard Letter Grade
    Optional:
    A = Audit;P = Pass/No Pass
  13. TOTAL UNITS:
    5

  14. INSTRUCTIONAL METHODS / UNITS & HOURS:

    Method
    Min Units
    Min Hours
    Lecture
    5
    90
    Lab
    0
    0
    Activity
    0
    0
    Open Entry/Open Exit
    0
    0
    Volunteer Work Experience
    0
    0
    Paid Work Experience
    0
    0
    Non Standard
    0
    0
    Non-Standard Hours Justification:

  15. REPEATABILITY

    Type:
    Non-Repeatable Credit
  16. MATERIALS FEE:
    No
  17. CREDIT BY EXAM:
    No
  18. CORE MISSION APPLICABILITY:
    UC Transfer;Associate Degree Applicable (AA/AS);Certificate of Achievement (COA);CSU Transfer;Career Technical Education (CTE)
  19. STAND-ALONE:
    No

  20. PROGRAM APPLICABILITY

    Required:
    Computer Science (AS Degree Program)
    Computer Technology Cert (Certificate)
    Computer Technology- (Certificate of Achievement)
    Mathematics AA (AA Degree Program)
    Elective:
    General Sciences (AA Degree Program)
    General Sciences AA (AA Degree Program)
    Liberal Arts: Mathematics & Science (AA Degree Program)

  21. GENERAL EDUCATION APPLICABILITY

    Local:
    IGETC:
    IGETC Area 2: Math Concepts and Quantitative Reasoning = 2A: Mathematic;
    CSU:
    CSU GE Area B: Physical and its Life Forms(mark all that apply) = B4 - Mathematics/Quantitative Thinking;
    UC Transfer Course:
    CSU Transfer Course:

  22. STUDENT LEARNING OUTCOMES Upon completion of the course, the student will be able to

    1. Use the Cartesian, polar, cylindrical, and spherical coordinate systems effectively.
    2. Use scalar and vector products in applications.
    3. Use vector-valued functions to describe motion in space.
    4. Extend the concepts of derivatives, differentials, and integrals to include multiple independent variables.
    5. Solve simple differential equations of the first and second order.

  23. REQUISITES

    Prerequisite:

    MATH C152

  24. DETAILED TOPICAL OUTLINE:

    Lecture:

    The Mathematics Department has adopted the following best practices for teaching this course:  offering or awarding extra-credit is forbidden, the allowance of multiple attempts at exams is forbidden, and an approved on-site proctor for online course exams is required.

                     A.      Partial Differentiation

    1.       Functions of two or more variables

    a.       Limits

    b.       Continuity

    c.        Geometric interpretation

    d.       Derivatives

    2.       Tangent planes and normal lines

    3.       The directional derivative

    4.       The gradient

    5.       The chain rule

    6.       Linearization and differentials

    7.       Maximum-Minimum problems

    a.       Use of derivatives for extreme values

    b.       Lagrange multipliers

    c.        Methods of least squares

    8.       Higher order derivatives

    B.      Multiple Integrals

    1.       Functions of two or more variables

    a.       Plane area

    b.       Volume

    c.        Center of mass

    d.       Moments of inertia

    e.        Polar coordinates

    f.        Surface area

    2.       Triple Integrals

    a.       Volume

    b.       Center of mass

    c.        Moments of inertia

    d.       Cylindrical coordinates

    e.        Spherical coordinates

    C.      Vectors and Parametric Equations

    1.       Parametric Equations in Kinematics

    2.       Parametric Equations in Analytic Geometry

    3.       Vectors in two dimensions

    a.       The i and j components

    b.       Vector algebra

    c.        Unit and Zero Vectors                               

    4.       Space Coordinates

    a.       Cartesian

    b.       Cylindrical

    c.        Spherical

    5.       Vectors in Space

    6.       Scalar Product of Two Vectors

    a.       Algebraic properties

    b.       Orthogonal vectors

    c.        Vector projection

    7.       Vector Product of Two Vectors

    a.       Algebraic properties

    b.       Area

    8.       Equations of Lines and Planes

    9.       Product of Three or More Vectors

    10.    Cylinders

    11.    Quadric Surfaces

    D.      Vector Functions and Their Derivatives

    1.       Derivative of a Vector Function

    2.       Velocity and Acceleration

    3.       Tangential Vectors

    4.       Curvature and Normal Vectors

    5.       Differentiation of Products of Vectors

    6.       Polar and Cylindrical Coordinates

    E.       Multi-Dimensional Vector Analysis

    1.       Vector fields

    2.       Surface integrals

    3.       Line integrals

    4.       Green's Theorem

    5.       Stokes' Theorem

  25. METHODS OF INSTRUCTION--Course instructional methods may include but are not limited to

    1. Discussion;
    2. Lecture;
    3. Other Methods: A. lecture and discussion of all course concepts. B. demonstration of developing proofs and solving application problems. C. reading textbooks and journals to see presentations different than those of the instructor. D. assignments and quizzes E. the use of computational and other types of mathematical software

  26. OUT OF CLASS ASSIGNMENTS: Out of class assignments may include but are not limited to

    A. Reading assignments. B. Bi-weekly homework assignments.

  27. METHODS OF EVALUATION: Assessment of student performance may include but is not limited to

    A. tests on course content, to include solving equations as well as demonstration of specific skills
    B. quizzes (in-class and take-home) to include solving equations as well as demonstration of specific skills
    C. group work to analyze and solve application problems

  28. TEXTS, READINGS, AND MATERIALS: Instructional materials may include but are not limited to

    Textbooks
    Thomas, Weir, Hass & Giordano. (2010) Thomas' Calculus, Media Upgrade, with MyMathLab , 12th , Addison-Wesley
    Manuals
    Periodicals
    Software
    Other
  29. METHOD OF DELIVERY:
    Online with some required face-to-face meetings (“Hybrid”);iTV – Interactive video = Face to face course with significant required activities in a distance modality ;Online course with on ground testing;Face to face;
  30. MINIMUM QUALIFICATIONS:
    Chemistry (Masters Required);Engineering (Masters Required);Mathematics (Masters Required);Physics/Astronomy (Masters Required);

  31. APPROVALS:

    Origination Date
    08/18/2010
    Last Outline Revision
    02/24/2012
    Curriculum Committee Approval
    02/24/2012
    Board of Trustees
    05/03/2012
    State Approval
    UC Approval
    50 = Summer 2000
    UC Approval Status
    Approved
    CSU Approval
    50 = Summer 2000
    CSU Approval Status
    Approved
    IGETC Approval
    30 = Spring 2010
    IGETC Approval Status
    Approved
    CSU GE Approval
    30 = Spring 2000
    CSU GE Approval Status
    Approved