KERN COMMUNITY COLLEGE DISTRICT – CERRO COSO COLLEGE

MATH C151 COURSE OUTLINE OF RECORD

  1. DISCIPLINE AND COURSE NUMBER:
    MATH C151
  2. COURSE TITLE:
    Analytic Geometry and Calculus I
  3. SHORT BANWEB TITLE:
    Analytical Geom/Calc
  4. COURSE AUTHOR:
    Bernsten, Dean
  5. COURSE SEATS:
    -
  6. COURSE TERMS:
    70 = Fall; 50 = Summer
  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 provides the student with a good foundation in differential and integral calculus with emphasis on both skills and applications. Topics covered include functions; limits; derivatives of polynomial, trigonometric, parametric, and implicit functions; applications of differentiation; the indefinite integral; the definite integral; applications of the definite integral.

  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 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. Differentiate and integrate rational functions and trigonometric functions.
    2. Apply the derivative in solving related rates problems.
    3. Apply the derivative in solving maximum/minimum problems.
    4. Apply the integral in solving area under the curve problems.
    5. Apply the integral in solving for the volume of a body of revolution.
    6. Apply the integral in finding the center of mass in one and two dimensions.
    7. Apply the derivative or integral in solving distance, velocity, and acceleration problems.
    8. Solve first order differential equations with initial conditions.

  23. REQUISITES

    Prerequisite:

    MATH C141

    MATH C142

  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.      Preliminary Concepts

    1.       Rectangular Coordinates

    a.       Slope of a Line

                                                             i.            Parallel Lines

                                                            ii.            Perpendicular Lines

    b.       Equations of Lines

    c.        Distance

    2.       Functions

    a.       Domain and Range

    b.       Graphs

    c.        Absolute Value

    d.       Composite Functions

    3.       Derivative of a Function

    a.       Definition - using the delta X process

    b.       Average and Instantaneous Rate of Change

    c.        Slope of a Curve

    d.       Velocity

    4.       Limits

    a.       Definition - epsilon and delta notation

    b.       Limit at a point

    c.        Limit as x

    d.       Continuity

    e.        Asymptotes of rational functions

    B.      Differentiation

    1.       Derivative of a Polynomial

    2.       Power Rule

    3.       Product Rule

    4.       Quotient Rule

    5.       Implicit Differentiation

    6.       Chain Rule

    7.       Differentials and Linear Approximations

    8.       Derivatives of the Trigonometric Functions

    9.       Higher Order Derivatives

    a.       Polynomial Functions

    b.       Implicit Functions

                                    Applications of Differentiation

    1.       Curve Sketching

    a.       Sign of first derivative – increasing and decreasing

    b.       Sign of second derivative - concavity

    c.        Relative maxima, minima

    d.       Points of inflection

    2.       Velocity and Acceleration

    3.       Related Rates

    4.       Maxima, Minima Problems

    5.       Newton's Method (Newton-Raphson)

    6.       Equations of Lines Tangent and Normal to a Curve

    7.       Mean Value Theorem

    8.       Rolle's Theorem

                    Integration

    1.       Indefinite Integral

    a.       Anti-differentiation

    b.       Of the form c du, u du, du+dv

    c.        Integrals of the Trigonometric Functions

    2.       Applications of the Indefinite Integral

    a.       Solutions to Simple Differential Equations with Initial Conditions

    b.       Velocity and Position

    c.        Equation of a Family of Curves

    3.       Numerical Methods for the Definite Integral

    a.       Circumscribed Rectangles

    b.       Inscribed Rectangles

    c.        Trapezoidal Method

    d.       Simpson's Method

    4.       The Fundamental Theorem of Integral Calculus

    a.       Evaluation of Definite Integrals

    b.       Substitution Method Applied to Definite Integrals

                    Applications of the Definite Integral

    1.       Area Under a Curve

    2.       Area Between two Curves

    3.       Volume of a Body of Revolution

    a.       Cylindrical Shell Method

    b.       Disk Method

    c.        Washer Method

    4.       Length of a Plane Curve

    5.       Moments and Center of Mass

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

    1. Demonstration;
    2. Discussion;
    3. Lecture;
    4. Other Methods: • Lecture and discussion of all course concepts. • Demonstration of developing proofs and solving application problems. • Reading textbooks and journals to see presentations different than those of the instructor. • Assignments and quizzes. • 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
    10/28/2011
    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