KERN COMMUNITY COLLEGE DISTRICT – CERRO COSO COLLEGE

MATH C152 COURSE OUTLINE OF RECORD

  1. DISCIPLINE AND COURSE NUMBER:
    MATH C152
  2. COURSE TITLE:
    Analytic Geometry and Calculus II
  3. SHORT BANWEB TITLE:
    Analytic Geom/Calc II
  4. COURSE AUTHOR:
    Bernsten, Dean
  5. COURSE SEATS:
    -
  6. COURSE TERMS:
    70 = Fall; 30 = Spring
  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 I, extending the skills of differentiation and integration by learning new techniques and working with the transcendental functions. Other major topics include sequences, series, polar coordinates and parameterization of plane curves.

  12. GRADING METHOD

    Default:
    S = Standard Letter Grade
    Optional:
    P = Pass/No Pass;A = Audit
  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 Education ()
    General Sciences (AA Degree Program)
    General Sciences AA (AA Degree Program)
    Liberal Arts: Mathematics & Science (AA Degree Program)

  21. GENERAL EDUCATION APPLICABILITY

    Local:
    CC GE Area IV: Language and Rationality = Analytical Thinking;
    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. Write the derivative of expres¬sions that contain the inverse trigonometric, logarithmic, exponential, hyperbolic, and inverse hyperbolic functions.
    2. Evaluate integrals (definite and indefinite)by using fundamental integral formulas, partial fractions, integration by parts, and substitutions, trigonometric substitutions.
    3. Expand skills with limits, including l’Hôpital’s Rule and improper integrals.
    4. Identify the conic section represented by a second degree equation and give the foci, vertices, and directricies.
    5. Use polar coordinates to graph equations and to find area, arc length, and intersection of curves.
    6. Use the tests for convergence and divergence of sequences and series.
    7. Write infinite series representations of various functions.
    8. Use the fundamental concepts of vectors including sums, dot product, and projection.

  23. REQUISITES

    Prerequisite:

    MATH C151

  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.    Transcendental Functions

    1.     Trigonometric Functions and their Inverses

            a.     Domain, range, graphs.

            b.     Derivatives and integrals.

    2.     Natural Logarithm

            a.     Definition and properties

            b.     Domain, range, and graphs.

            c.     Derivatives and integrals.

    3.     Exponential Function, base “e”

            a.     Definition and properties          

            b.     Domain, range, and graphs.

            c.     Derivatives and integrals.

    4.     Exponential and logarithmic functions of base “a”    

            a.     Definitions

            b.     Derivatives

            c.     Logarithmic differentiation

    5.     Hyperbolic and Inverse Hyperbolic Functions

            a.     Definitions and Identities

            b.     Domain, range, and graphs.

            c.     Derivatives and Integrals.

    6.     Applications

            a.     Rate of growth or decay (differential equations)

            b.     Area, volume, and arc length

            c.     The Hanging Cable

    B.    Methods of Integration

    1.     Fundamental Formulas and Substitutions

    2.     Powers of Trigonometric Functions

    3.     Trigonometric Substitution

    4.     Integrals involving Quadratic Polynomials

    5.     Partial Fractions

    6.     Integration by Parts

    7.     Improper Integrals

            a.     Two types

            b.     Convergent, divergent

    8.     Using Integral Tables

    9.     Applications of Integration

            a.     Work applications

            b.     Hydrostatic pressure and forces

    C.    Plane Analytic Geometry

    1.     Curves and Equations

            a.     Symmetry

            b.     Extent

            c.     Intercepts

    2.     Equations of Loci; Distance

    3.     The Circle

    4.     The Parabola

    5.     The Ellipse

    6.     The Hyperbola

    7.     Second Degree Curves

            a.     Rotation and Translation

            b.     Invariants and the disciminant

    8.     Parameterizations of Curves and Applications

                    D.    Polar Coordinates

                            1.     Relations between Polar and Rectangular Coordinates

                            2.     Graphs in Polar Coordinates

                            3.     Conic Sections

                            4.     Length of a curve in polar coordinates

                            5.     Plane Area

                    E.    Infinite Series

                            1.     Sequences and Series

                                    a.     Geometric series

                                    b.     Taylor series

                                    c.     Power series

                            2.     Convergence and Divergence

                                    a.     Integral test

                                    b.     Ratio test

                                    c.     Comparison test

                                    d.     nth root test

                                    e.     Limit Comparison test

                            3.     Limits using infinite series

                            4.     Absolute and Conditional convergence

                            5.     Power series: Taylor and Maclaurin, with applications

                    F.     Vectors in Two Dimensions

                            1.     Dot products, sums, components, projections

                            2.     Vector-valued functions

                            3.     Modeling projectile motion

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

    1. Discussion;
    2. Lecture;
    3. Other Methods: A. Textbook readings B. Lectures C. Online course management system D. Discussions

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

    A. Daily homework assignments (A – H) Example: Students work mathematics problems assigned from the text and from hand-outs to reinforce concepts and skills discussed in lecture. B. Online Course Management System (A – H) Example: Assignments on CourseCompass

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

    A. Daily in-class assignments (A – H)
    Example: Students work mathematics problems assigned from the text and from hand-outs to reinforce concepts and skills discussed in lecture.
    B. Weekly Quizzes (A – H)
    Weekly quizzes over the previous week’s lecture material, homework, and in-class assignments assess the student’s understanding.
    C. Chapter Exams (A – H)
    Chapter exams over the previous chapter’s lecture material, homework, and in-class assignments assess the student’s understanding.

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

    Textbooks
    Weir, M., Hass, J., Giordano, F.. (2010) Thomas’ CALCULUS, 12th , Addison-Wesley Publishing Company.
    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
    50 = Summer 2000
    IGETC Approval Status
    Approved
    CSU GE Approval
    50 = Summer 2000
    CSU GE Approval Status
    Approved