# 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**

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 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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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 | |

In-service: | X | NOT IN-SERVICE |

Level below transfer: | X | NOT APPLICABLE |

Matric-requiring: | M | Requires Math assessment |

Maximum class size: | 0 | |

Maximum wait list: | 0 | |

Method of instruction: | 02 | LECTURE |

Non-credit 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 | Non-occupational |

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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