Foothill CollegeApproved Course Outlines

Physical Sciences, Mathematics & Engineering Division
5 hours lecture.5 Units

Total Quarter Learning Hours: 60 (Total of All Lecture, Lecture/Lab, and Lab hours X 12)
 Lecture Hours: 5 Lab Hours: Lecture/Lab:
 Note: If Lab hours are specified, see item 10. Lab Content below.

Repeatability -
Statement: Not Repeatable.

Status -
 Course Status: ActiveGrading: Letter Grade with P/NP option
 Degree Status: ApplicableCredit Status: Credit
 Degree or Certificate Requirement: AS Degree
 GE Status: Non-GE

Articulation Office Information -
 Transferability: BothValidation: 07/4; 11/27/12; 11/16/13

1. Description -
Differential equations and selected topics of mathematical analysis.
Prerequisite: MATH 1C.
Co-requisite: None
Advisory: Demonstrated proficiency in English by placement into ENGL 1A as determined by score on the English placement test or through an equivalent placement process; not open to students with credit in MATH 12A.

2. Course Objectives -
The student will be able to:
  1. Classify differential equations by order, linearity, separability, exactness, coefficient fuctions, homogeneity, type of any nonhomogeneities, and other qualities.
  2. Identify appropriate analytic, numerical, and graphical techniques for solving or approximating solutions to differential equations of the particular classes specified in the expanded description of course content.
  3. Solve differential equations with appropriate analytic techniques.
  4. Approximate solutions to differential equations with appropriate numeric techniques.
  5. Investigate solutions to differential equations with appropriate graphical techniques.
  6. Verify solutions to differential equations analytically, numerically, graphically, and qualitatively.
  7. Write differential equations and initial value problems to model phenomena in the physical, life, and social sciences.
  8. Interpret solutions to differential equations and initial value problems in context.
  9. Discuss differential equations and their solutions in accurate mathematical language and notation.
  10. Investigate solutions to differential equations using at least one numerical or graphing utility.
3. Special Facilities and/or Equipment -
  1. Graphing calculator
  2. When taught hybrid: Four lecture hours per week in face-to-face contact and one hour per week using CCC Confer. Students need internet access.

4. Course Content (Body of knowledge) -
  1. Classes of Differential Equations
    1. First Order
      1. Linear
      2. Separable
      3. Exact
    2. Second Order
      1. Linear
      2. Constant Coefficient
      3. Polynomial Coefficient
    3. Higher-Order Linear
    4. Autonomous
    5. Homogeneous
    6. Nonhomogeneous
      1. Polynomial
      2. Exponential
      3. Sinusoid
      4. Other continuous functions
      5. Discontinuous functions
      6. Impulses
  2. Initial Value Problems
    1. Existence and Uniqueness Theorem
      1. Applications
  3. Systems of Linear Differential Equations
  4. Techniques for Solving Differential Equations
    1. Separation of variables
    2. Integrating factors
    3. Characteristic Equations
      1. Distinct real roots
      2. Repeated real roots
      3. Complex roots
    4. Fundamental solutions
    5. Superposition principle
    6. Undetermined coefficients
    7. Variation of parameters
    8. Annihilator method
    9. Reduction of order
    10. Laplace transforms
    11. Power series
    12. Method of Frobenius
    13. Matrix methods
    14. Euler's method
    15. Improved Euler's method (predictor-corrector)
    16. Graphical analysis
  5. Applications selected from the following topics
    1. Population models
      1. Predator-prey models
      2. Thresholds and carrying capacities
    2. Growth and decay
    3. Mixing problems
    4. Spring-mass systems
      1. Undamped
      2. Damped
    5. Electrical circuits
      1. Inductor-capacitor
      2. Resistor-inductor-capacitor
    6. Newton's Laws
      1. Falling bodies
      2. Pendulums
      3. Cooling
    7. Torricelli's Law
    8. Financial applications
      1. Compound interest
      2. Time value of money
      3. Annuities
    9. Communication models
      1. Spread of a rumor
      2. Mass marketing
    10. Public health models
      1. Epidemics
      2. Health care utilization
5. Repeatability - Moved to header area.
6. Methods of Evaluation -
  1. Homework
  2. Class Participation
  3. Term Paper(s)
  4. Presentation(s)
  5. Computer Lab Assignment(s)
  6. Term Project
  7. Quizzes
  8. Unit Exam(s)
  9. Proctored Comprehensive Final Examination
7. Representative Text(s) -
Boyce,W. and R. DiPrima. Elementary Differential Equations. 9th ed. New York: John Wiley and Sons, Inc., 2009.

8. Disciplines -
9. Method of Instruction -
  1. Lecture
  2. Discussion
  3. Cooperative learning exercises
10. Lab Content -
Not applicable.
11. Honors Description - No longer used. Integrated into main description section.
12. Types and/or Examples of Required Reading, Writing and Outside of Class Assignments -
  1. Homework Problems: Homework problems covering subject matter from text and related material ranging from 15 - 30 problems per week
  2. Students will need to employ critical thinking in order to complete assignments
  3. Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes
  4. Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB
  5. Worksheets: Problems and activities covering the subject matter. Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class
13. Need/Justification -
This course is a required core course for the A.S. degree in Mathematics.

Course status: Active
Last updated: 2014-03-21 20:22:35

Foothill CollegeApproved Course Outlines