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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 secondorder 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 secondorder 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
ASSOCIATE DEGREE:  Effective: FALL 2004 Inactive:  
Area:  D2  COMMUNICATIONS & ANALYTICAL THINKING 
CSU GE:  Effective: FALL 2004 Inactive:  
Transfer area:  B4  MATHEMATICS/QUANTITATIVE REASONING 
IGETC:  Effective: FALL 2004 Inactive:  
Transfer area:  2A  MATHEMATICS 
CSU TRANSFER: TRANSFERABLE  Effective: FALL 2003 Inactive:  
UC TRANSFER: TRANSFERABLE  Effective: FALL 2007 Inactive:  
CAN:  
MATH 24 Grp Nbr:  01  Effective: FALL 2003 Inactive: 
CERTIFICATE APPLICABLE:  N  NOT CERTIFICATE/MAJOR APPLICABLE 
APPROVAL AND DATES
Version 01 Submitted by:  ROGER AHDERS  Date: 11/15/2002 
Department approved:  Date:  
Curriculum approved:  02/05/2003  Version approved: 02/05/2003 
Prerequisites approved :  02/05/2003  Last reviewed: 02/05/2003 
Term effective : FALL 2003  Last taught:  SPRING 2008 Inactive: 
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 TI92@) in
establishing the skills above.
TOPICS AND SCOPE:
1. Firstorder differential equations and their applications:
a. Definitions and theory
b. Separable and exact equations
c. Linear equations
d. Numerical solutions: Euler and RungeKatta methods
e. Applications
2. Higherorder differential equations:
a. Definitions and theory
b. Homogeneous linear equations with constant coefficients
c. Nonhomogeneous linear equations with constant coefficients
d. CauchyEuler 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. Nonhomogeneous linear systems
e. Numerical solutions: Euler and RungeKatta methods
f. Applications
ASSIGNMENTS:
READING ASSIGNMENTS:
Students will have daily reading assignments on each instructional
unit from required text(s), or instructorchosen supplementary
materials.
WRITING ASSIGNMENTS:
1. Daily homework problem assignments for each instructional unit.
2. Studentdeveloped projects using appropriate course techniques to
solve applications problems.
OUTSIDE ASSIGNMENTS:
1. Completion of reading and writing assignments as detailed above.
2. Preparing for inclass 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
studentdeveloped 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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Advisory generate desc:  N  NO 
Area department:  MTH  MATHEMATICS 
Audit flag:  N  NOT AUDITABLE 
Basic skills:  X  NOT BASIC SKILLS 
Classification:  A  Liberal Arts and Sciences 
Cost level:  00  VALUE NOT FOUND 
Disciplines:  MATHEMATICS  
Division :  00  VALUE NOT FOUND 
Faculty service areas:  MATHEMATICS  
Fee:  $0.00  
Inservice:  X  NOT INSERVICE 
Level below transfer:  X  NOT APPLICABLE 
Matricrequiring:  M  Requires Math assessment 
Maximum class size:  0  
Maximum wait list:  0  
Method of instruction:  02  LECTURE 
Noncredit category:  X  NOT APPLICABLE, CREDIT COURSE 
Open entry/exit:  N  Not open entry/exit 
Pacs activity:  1701  MATHEMATICS GENERAL 
Pacs program project:  0000  
Preq/coreq generate desc:  N  NO 
Preq/coreq provisional:  N  NO 
Preq/coreq reg check:  Y  PREREQUISITE RULES EXIST 
Repeat group id :  
Requires instructor sig:  N  INSTRUCTOR'S SIGNATURE NOT REQUIRED 
SAM classification:  E  Nonoccupational 
Selected/special topic:  N  NOT A SELECTED TOPIC COURSE 
Special class:  X  NOT A SPECIAL COURSE 
TOP code:  1701.00  MATHEMATICS ,GENERAL 
Workload:  0.0000 
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