Palomar Logo Effective Term: Fall 2003
Status: Historical
 
PALOMAR COLLEGE
 COURSE OUTLINE FOR CREDIT COURSE
 
  • Courses numbered 1 - 49 are remedial or college preparatory courses which do not apply toward an A. A. Degree and are not intended for transfer.
  • Courses numbered 50-99 apply toward an AA Degree, but are not intended for transfer.
  • Courses numbered 100 and higher apply toward an AA Degree and/or are intended for transfer to a four-year college or university.
 
Course Number and Title: MATH 206 Calculus with Differential Equations
 

Unit Value: 4  

Lecture Hours Per Week: 4  

Lab Hours Per Week:  

Lecture/Lab Hours Per Week:  

 

Grading Basis: Grade/Pass/No Pass
 
Basic Skills Requirements: Appropriate Language and/or Computational Skills.
 
Requisite(s)
To satisfy a prerequisite, the student must have earned a letter grade of A, B, C or P(Pass) in the prerequisite course, unless otherwise stated.
Prerequisite:
A minimum grade of 'C' in MATH 205
Corequisite:
None
Prerequisite: Completion of, or concurrent enrollment in
None
Recommended Preparation:
None
Limitation on Enrollment:
None
Catalog Description:
A first course in ordinary differential equations from analytic, geometric, numeric and applied perspectives (including the use of modern computational technology as appropriate). Topics include exact, separable, and linear equations; initial value and boundary-value problems; systems of first-order equations; reduction of order; undetermined coefficients; variation of parameters; series solutions; and Laplace transforms.
 
Specific Course Objectives:
Upon successful completion of the course the student will be able to:
  1. Classify and solve first- and second-order differential equations using analytic, geometric, and numeric methods.
  2. Model application problems with first- and second-order differential equations.
  3. Construct series solutions to differential equations.
  4. Solve linear systems of differential equations.
  5. Solve second-order differential equations using Laplace transforms.
  6. Apply critical thinking and quantitative reasoning skills to advanced mathematical problem solving.
 
Methods of Instruction:
Methods of Instruction may include, but are not limited to, the following:
  1. Lecture
 
Content in Terms of Specific Body of Knowledge:

At least the following topics will be covered:

  1. Classification of differential equations.
  2. 1st-order differential equations: exact equations, integrating factors, separable equations, linear equations, Bernoulli equations, homogeneous equations.
  3. Applications of 1st-order differential equations.
  4. Linear differential equations: linear independence and dependence, Wronskian, existence of solutions, reduction of order, homogeneous equations, undetermined coefficients, variation of parameters.
  5. Applications of 2nd-order linear differential equations.
  6. Series solutions of linear differential equations: ordinary points, singular points, solutions about ordinary points.
  7. The Laplace transform: definition of Laplace transform, basic properties, step functions, translated functions, the inverse transform, the convolution, Laplace transform solution of linear differential equations with constant coefficients, Laplace transform solution of linear systems.
  8. Linear systems of differential equations. Solving Linear systems using eigenvectors and eigenvalues.
  9. Additional topics may be included at instructor's discretion.
Textbooks/Resources:
May Include Textbooks, Manuals, Periodicals, Software, and Other Resources
  1. Boyce, William E., DiPrima, Richard C. Elementary Differential Equations. 7th Edition. New York: John Wiley & Sons, Inc., 2001. or
  2. Zill, Dennis G., Cullen, Michael R. Differential Equations with Boundary-Value Problems. 5th Edition. Pacific Grove: Brooks/Cole, 2001.
Required Reading:
Boyce, William E., DiPrima, Richard C. Elementary Differential Equations. 7th Edition. New York: John Wiley & Sons, Inc., 2001.
or
Zill, Dennis G., Cullen, Michael R. Differential Equations with Boundary-Value Problems. 5th Edition. Pacific Grove: Brooks/Cole, 2001.
 
Suggested Reading:
 
Critical Thinking:
 
Required Writing:
Problem-solving exercises on homework assignments and written tests are more appropriate. In addition, students may be required to write reports from one paragraph to several pages explaining concepts or explaining and interpreting solutions to non-routine or applied problems.
 
Outside Assignments:
Students are expected to spend a minimum of three hours per unit per week in class and on outside assignments, prorated for short-term classes.

Students are expected to read the text, study lecture notes, and complete daily homework assignments. Homework assignments may include practice solving routine problems, explaining concepts, and solving application or non-routine problems. Other outside assignments may include computer laboratory assignments, problem-solving reports or journals.
 
Methods of Assessment:
Methods of Assessment may include, but are not limited to, the following:
  • Homework
  • Exams/Tests
 
Open Entry/Open Exit:
No, course is not offered as open entry/open exit.
 
Is Course Repeatable for Reason(s) Other Than Deficient Grade? No
 
Contact Person: Jorge I. Saavedra Guzman