COLLEGE OF ALAMEDA COURSE OUTLINE

COLLEGE: STATE APPROVAL DATE: 08/01/2015
ORIGINATOR: Michael J. Valdez STATE CONTROL NUMBER: CCC000350594
BOARD OF TRUSTEES APPROVAL DATE: 04/14/2015
CURRICULUM COMMITTEE APPROVAL DATE: 02/13/2015
CURRENT EFFECTIVE DATE: 08/01/2015
 
DIVISION/DEPARTMENT:

1. REQUESTED CREDIT CLASSIFICATION:
  Credit - Degree Applicable
Course is not a basic skills course.
Program Applicable
2. DEPT/COURSE NO: 3. COURSE TITLE:
  MATH 003F   Differential Equations
4. COURSE: COA Course Changes in Catalog Info   TOP NO. 1701.00
5. UNITS: 3.000   HRS/WK LEC: 3.00 Total: 52.50
  HRS/WK LAB:

6. NO. OF TIMES OFFERED AS SELETED TOPIC:       AVERAGE ENROLLMENT:
7. JUSTIFICATION FOR COURSE:
  Satisfies the General Education Analytical Thinking requirement for Associate Degrees. Provides foundation for more advanced study in mathematics and related fields, such as Physics. Satisfies the Quantitative Reasoning component required for transfer to UC, CSU, and some independent four-year institutions. Acceptable for credit: CSU, UC.
8. COURSE/CATALOG DESCRIPTION
  Ordinary differential equations: First-order, second-order, and higher-order equations; separable and exact equations, series solutions, LaPlace transformations, systems of differential equations. MATH 3E and 3F are equivalent to MATH 3D. Not open for credit to students who have completed or are currently enrolled in MATH 3D.
9. OTHER CATALOG INFORMATION
 
  1. Modular: No     If yes, how many modules:
  2. Open entry/open exit: No
  3. Grading Policy: Letter Grade Only
  4. Eligible for credit by Exam: No
  5. Repeatable according to state guidelines: No
  6. Required for degree/certificate (specify):
    New - Mathematics AS-T
  7. Meets GE/Transfer requirements (specify):
    Acceptable for credit: UC/CSU. AA/AS area 4b, 4e CSU area B4. IGETC area 2A.
  8. C-ID Number: Expiration Date:

  9. Are there prerequisites/corequisites/recommended preparation for this course? Yes
    Date of last prereq/coreq validation: 02/13/2015
  10. Acceptable for Credit: CSU/UC
10. LIST STUDENT PERFORMANCE OBJECTIVES (EXIT SKILLS): (Objectives must define the exit skills required of students and include criteria identified in Items 12, 14, and 15 - critical thinking, essay writing, problem solving, written/verbal communications, computational skills, working with others, workplace needs, SCANS competencies, all aspects of the industry, etc.)(See SCANS/All Aspects of Industry Worksheet.)

Students will be able to:
  1. classify a given first or higher order differential equation and select and apply an appropriate analytical technique for finding its solution
  2. use ordinary differential equations to create and analyze mathematical models of mechanical, electrical and biological phenomena
  3. apply the existence and uniqueness theorems for ordinary differential equations
  4. find power series solutions of ordinary differential equations
  5. determine and use the Laplace transform of a function to solve a linear differential equation
  6. solve systems of linear differential equations
11A. COURSE CONTENT: List major topics to be covered. This section must be more than listing chapter headings from a textbook. Outline the course content, including essential topics, major subdivisions, and supporting details. It should include enough information so that a faculty member from any institution will have a clear understanding of the material taught in the course and the approximate length of time devoted to each. There should be congruence among the catalog description, lecture and/or lab content, student performance objectives, and the student learning outcomes. List percent of time spent on each topic; ensure percentages total 100%.

LECTURE CONTENT:

1. Differential equations (6%)
a. Basic mathematical models, direction fields
b. Solutions of differential equations
c. Classification of differential equations

2. First order differential equations (14%)
a. Linear equations
b. Method of integrating factors
c. Separable equations
d. Distinguishing between linear and  non-linear equations
e. Method of substitution
f. Exact differential equations
g. Integrating factors, first-order linear equations
h. Numerical approximations, Euler’s method
i. The Existence and Uniqueness Theorem
j. First order difference equations
e. Applications of first order differential equations such as circuits, mixture problems, population modeling, orthogonal trajectories, and slope fields

3. Second order linear differential equations (16%)
a. Homogeneous linear equations with constant coefficients
b. Solutions of linear homogeneous equations, the Wronskian
c. Complex roots of the characteristic equation
d. Repeated roots, reduction of order
e. Nonhomogeneous equations, the method of undetermined coefficients
f.  Variation of parameters
g. Applications

4. Higher order linear differential equations (16%)
a. General theory of nth order linear equations
b. Homogeneous equations with constant coefficients
c. The method of undetermined coefficients
d. The method of variation of parameters
e. Applications of higher order differential equations such as the harmonic oscillator and circuits

5. Infinite series solutions of second order linear equations (16%)
a. Review of power series
b. Series solutions near an ordinary point
c. Euler equations
d. Series solutions near a regular singular point
e. Bessel’s equation

6. The Laplace transform (16%)
a. Definition of the Laplace transform
b. Solving initial-value problems
c. Step functions
d. Differential equations with discontinuous forcing functions
e. Impulse functions
f. The convolution integral

7.  Systems of first order linear differential equations (16%)
a. Matrices
b. Linear algebraic equations, linear independence, eigenvalues, eigenvectors
c. Basic theory of systems of first order linear differential equations
d. Homogeneous linear systems with constant coefficients
e. Complex eigenvalues
f. Fundamental matrices
g. Repeated eigenvalues
h. Nonhomogeneous linear systems

11B. LAB CONTENT:
N/A
12. METHODS OF INSTRUCTION (List methods used to present course content.)
  1. Discussion
  2. Lecture
  3. Other (Specify)

  4. Other Methods:
    Instructor-focused lecture on theory and the language of calculus and Differential Equations. Question and answer periods based on worksheets and in-class examples to encourage class discussion and demonstrations which emphasize alternative approaches to problem solving and their underlying rationales. Video demonstration of tools specific to this level of calculus. Distance Ed addendum for hybrid instruction use.
13. ASSIGNMENTS: 0.00 hours/week (List all assignments, including library assignments. Requires two (2) hours of independent work outside of class for each unit/weekly lecture hour. Outside assignments are not required for lab-only courses, although they can be given.)

Out-of-class Assignments:
Out-of-class Assignments: College-level textbook chapter readings that reinforce lecture material. Problem sets including computational problems equivalent in content and level of difficulty to those covered in the lectures. Additional problems that introduce supplemental concepts and formulas and require the synthesis and analysis of various concepts. Graphical representation and analysis specific to the study of calculus and differential equations.


ASSIGNMENTS ARE: (See definition of college level):
Primarily College Level
14. STUDENT ASSESSMENT: (Grades are based on):
ESSAY (Includes "blue book" exams and any written assignment of sufficient length and complexity to require students to select and organize ideas, to explain and support the ideas, and to demonstrate critical thinking skills.)
COMPUTATION SKILLS
SKILL DEMONSTRATION
OTHER (Describe):
Assess essay for understanding and application of concepts presented in classwork and supplemental material. Evaluate computation skills for accurate application of steps and correct answers. Evaluate students' ability to analyze given information and apply it in terms of the question.
15. TEXTS, READINGS, AND MATERIALS
  A. Textbooks:
 
  • Boyce & Diprima. 2012. Elementary Differential Equations 10th. John Wiley Publishing Company
    Rationale: -
  • Nagle, Saff, & Snider. 2012. Fundamentals of Differential Equations 8th. Addison-Wesley
 

*Date is required: Transfer institutions require current publication date(s) within 5 years of outline addition/update.

  B. Additional Resources:
 
  • Library/LRC Materials and Services:

    The instructor, in consultation with a librarian, has reviewed the materials and services of the College Library/LRC in the subject areas related to the proposed new course
  • Are print materials adequate?     Yes
  • Are nonprint materials adequate?     No
  • Are electronic/online resources available?     Yes
  • Are services adequate?     Yes
  • Specific materials and/or services needed have been identified and discussed. Librarian comments:
    Collection sufficient to support course. New book requests submitted as needed. Math Department to donate additional materials.
  C. Readings listed in A and B above are: (See definition of college level):
 

Primarily college level

16. DESIGNATE OCCUPATIONAL CODE:
E - Non-Occupational
17. LEVEL BELOW TRANSFER:
Y - Not Applicable
18. CALIFORNIA CLASSIFICATION CODE:
19. NON CREDIT COURSE CATEGORY:
Y - Not Applicable
20. FUNDING AGENCY CATEGORY:
Not Applicable - Not Applicable
SUPPLEMENTAL PAGE

Use only if additional space is needed. (Type the item number which is to be continued, followed by "continued." Show the page number in the blank at the bottom of the page. If the item being continued is on page 2 of the outline, the first supplemental page will be "2a." If additional supplemental pages are required for page 2, they are to be numbered as 2b, 2c, etc.)

1a. Prerequisites/Corequisites/Recommended Preparation:
    PREREQUISITE:
  • MATH 003E: Linear Algebra
  • PREREQUISITE:
  • MATH 003B: Calculus II
  • RECOMMENDED PREPARATION:
  • MATH 003C: Calculus III