KERN COMMUNITY COLLEGE DISTRICT – CERRO COSO COLLEGE

MATH C255 COURSE OUTLINE OF RECORD

  1. DISCIPLINE AND COURSE NUMBER:
    MATH C255
  2. COURSE TITLE:
    Ordinary Differential Equations
  3. SHORT BANWEB TITLE:
    Ordinary Diff Equation
  4. COURSE AUTHOR:
    Bernsten, Dean
  5. COURSE SEATS:
    -
  6. COURSE TERMS:
    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 provides students with a foundation of differential equations of change, motion, and growth within chemical, physical, biological, and business systems with problem solving and applications. Students are introduced to modeling using mathematical software used in industry to solve complex problems. First, second, and higher order differential equations including Euler''s Method, Eigenvalues, Numerical Methods, Nonlinear Systems, and La Place Transforms are covered. Advisory: A computer algebra system or graphing calculator and basic computer skills are strongly recommended.

  12. GRADING METHOD

    Default:
    S = Standard Letter Grade
    Optional:
    A = Audit;P = Pass/No Pass
  13. TOTAL UNITS:
    4

  14. INSTRUCTIONAL METHODS / UNITS & HOURS:

    Method
    Min Units
    Min Hours
    Lecture
    4
    72
    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);CSU Transfer
  19. STAND-ALONE:
    No

  20. PROGRAM APPLICABILITY

    Required:
    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. Define and identify differential equations, distinguishing between forms and methods of solution (separable, exact, linear, substitution, and modeling).
    2. Demonstrate how to find the solution to an Ordinary Differential Equation (ODE) with and without initial values.
    3. Recognize homogeneous versus non-homogeneous differential equations.
    4. Demonstrate the interrelationships of real world situations to the ODE’s and modeling associated applications using formula development, direction fields, and phase lines.
    5. Recognize graphical representations of equations and demonstrate their properties algebraically and via computer methods.
    6. Perform basic reduction of order, the use of constant and undermined coefficients, and variation of parameters using the various methods.
    7. Demonstrate the use of series in determining the solution to differential equations.
    8. Apply numerical methods for ODE’s.
    9. Perform computations and graphical interpretations using computational and mathematical software.

  23. REQUISITES

    Prerequisite:

    MATH C251
    Advisory:

    A computer algebra system or graphing calculator and basic computer skills are strongly recommended.




  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.       Introduction

    1.        Description of Ordinary Differential Equations (ODE)

    2.       What constitutes a solution to an ODE 

    3.       Conceptualizing an Initial Value Problem 

    4.       Math modeling with ODE's 

    B.       Solving First Order ODE's

    1.       Separable 

    2.       Exact 

    3.       Linear 

    4.       Substitution methods

    5.       Modeling 

    C.       Higher Order ODE's

    1.       Linear Equations 

    a.        Homogeneous

    b.       Non?homogeneous

    2.       Reduction of order

    3.       Constant Coefficients 

    4.       Undetermined Coefficients 

    5.       Variation of Parameters

    6.       Cauchy?Euler Equation

    7.       Modeling

     

    D.       Series Solutions of Linear ODE's

    1.       Ordinary points

    2.       Singular points

    3.       Bessel's equation 

    4.       Legendre's equation

    E.        Numerical Methods for ODE's

    1.       Direction Fields 

    2.       Euler's method

    3.       Runge?Kutta  

    F.        Integration of Mathematical Software

    1.       Finding solutions to First, Second, and Higher Order ODE’s 

    2.       Graphing Vector/Direction fields

    3.       Finding and Identifying Phase Lines/Bifurcations

    4.       Using the software to model systems and both graph and solve these

    5.       Utilization of Maple, MuPad/Scientific Notebook, Textbook computational/graphing software

     

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

    1. Demonstration;
    2. Discussion;
    3. Lecture;
    4. 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

    This will be assessed by an exam, scored with a rubric.

    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
    Blanchard, Devany, & Hall. (2012) Differential Equations, 4th, Brooks/Cole
    -
    Manuals
    Periodicals
    Software
    Other
    Selected readings from mathematical journals (e.g., College Mathematics Journal), scientific journals (e.g., Scientific American, Science, and Nature), computer graphics/animation journals (e.g., Cadence) and books.
  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