Math 215 Differential Equations

CATALOG DESCRIPTION:
Covers the theory and applications of the solutions of ordinary differential
equations. Students will be introduced to various topics useful in solving
first- and second-order differential equations including power series,
Laplace transforms, matrices, eigenvalues and eigenvectors, and numerical
methods. Math 215 is primarily for majors in mathematics and engineering.
Use of graphing calculators will be essential for the course.

PREREQUISITES:
MTH 212 and MTH 214.

COREQUISITES:

RECOMMENDED PREPARATION:
No advisories.

LIMITS ON ENROLLMENT:

SCHEDULE OF CLASSES INFORMATION:
Prerequisites: MTH 212 and MTH 214.
Covers the theory and applications of the solutions of ordinary differential
equations. Students will be introduced to various topics useful in solving
first- and second-order differential equations including power series,
Laplace transforms, matrices, eigenvalues and eigenvectors, and numerical
methods. Math 215 is primarily for majors in mathematics and engineering.
Use of graphing calculators will be essential for the course. (Grade or
CR/NC)
Transfer Credit: CSU; UC. (CAN MATH 24)

ARTICULATION and CERTIFICATE INFORMATION

APPROVAL AND DATES

COURSE CONTENT

OUTCOME AND OBJECTIVES:
1. Distinguish ordinary differential equations by order and type.
2. Select appropriate techniques to solve single differential equations
and systems of linear differential equations.
3. Perform appropriate techniques to solve separable, exact, and linear
differential equations.
4. Use numerical techniques to approximate solutions to differential
equations.
5. Solve initial value problems using Laplace transforms.
6. Use power series to solve differential equations around both singular
and nonsingular points.
7. Apply matrix techniques and Laplace transforms to solve systems of
differential equations.
8. Analyze, model, and solve applied science problems with ordinary
differential equations.
9. Use traditional manual techniques and newer technological methods
(graphing calculator and/or CAS such as Mathematica@ and TI-92@) in
establishing the skills above.

TOPICS AND SCOPE:
1. First-order differential equations and their applications:
 a. Definitions and theory
 b. Separable and exact equations
 c. Linear equations
 d. Numerical solutions: Euler and Runge-Katta methods
 e. Applications
 2. Higher-order differential equations:
 a. Definitions and theory
 b. Homogeneous linear equations with constant coefficients
 c. Non-homogeneous linear equations with constant coefficients
 d. Cauchy-Euler equations
 e. Variation of parameters
 f. Applications
3. Power series solutions
 a. (Optional; review of power series)
 b. Solutions around ordinary points
 c. Solutions around singular points using the method of Frobenius
4. Laplace transforms:
 a. Definitions and properties
 b. Use of Laplace transforms and inverse transforms in solving initial value problems
 c. (Optional: transforms of periodic, discontinuous and impulse functions)
5. Systems of linear differential equations:
 a. (Optional: review of matrices, eigenvalues and eigenvectors)
 b. Introduction and definitions
 c. Homogeneous linear systems
 d. Non-homogeneous linear systems
 e. Numerical solutions: Euler and Runge-Katta methods
 f. Applications

ASSIGNMENTS:
READING ASSIGNMENTS:
Students will have daily reading assignments on each instructional
unit from required text(s), or instructor-chosen supplementary
materials.
WRITING ASSIGNMENTS:
1. Daily homework problem assignments for each instructional unit.
2. Student-developed projects using appropriate course techniques to
solve applications problems.
OUTSIDE ASSIGNMENTS:
1. Completion of reading and writing assignments as detailed above.
2. Preparing for in-class presentation of project.
3. Preparing for course examinations.

METHOD OF INSTRUCTION:
METHODS OF EVALUATION:

1. Evaluation of homework problem assignments for understanding of
terminology, knowledge of subject matter, and ability to perform
manual or technological methods of solution. 2. Evaluation of
student-developed projects for ability to choose an
appropriate method of solutions, and for ability to correctly interpret
solutions in a physical situation. 3. Evaluation of occasional tests and
a final examination for understanding of terminology, knowledge of subject matter, ability to
choose an appropriate method of solution, and ability to perform
manual or technological methods of solution.

BASIS FOR GRADING:
The assignment of a grade is based on the level of achievement
of the outcomes and objectives of the course outline and is
reflected in quantifiable terms in the course syllabus.

REPRESENTATIVE TEXTBOOKS:
1. Modern Differential Equations, latest ed., Abel and Braselton, Brooks/Cole, 2001.
2. A First Course in Differential Equations with Modeling Applications,
latest ed., D. Zill, Brooks/Cole, 2001.

RATIONALE
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RESOURCES REQUIRED
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MISCELLANEOUS
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