Math 253: an obsolete account

Taken from the service courses page of the math department on 2003 September 22:

MATH 253 Ordinary Differential Equations

Prerequisites: Math 152, Math 156 or Math 158

Frequency: Fall/Spring Terms

Credit: (3-0)3

Content: First order equations and applications. Higher order linear differential equations: Constant coefficient equations, method of undetermined coefficients, variation of parameters. Power series solutions. The Laplace Transform. Solution of initial value problems, convolution integral. Solution of systems of linear differential equations by Laplace Transform.

Goals: The main objective of the course is to present the main concepts in the theory of (ordinary) differential equations and to show how (ordinary) differential equations are used in mathematical models describing meal-live situations.

Course Outline:

(1 Week) Preliminaries. Solutions. Existence-Uniqueness Theorem. ~

(1 Week) Separable Equations. Linear Equations. Homogeneous Equations.

(1 Week) Exact Equations and Integrating Factors.

(1 Week) Applications (2.7.2,2.7.3).

(1 Week) Basic Theory of Higher Order Linear Equations.

(1 Week) Reduction of Order. Homogeneous Constant Coefficient Equations..

(1 Week) Undetermined Coefficients.

(1 Week) Variation of Parameters. The Cauchy-Euler Equations.

(1 Week) Power Series Solutions (ordinary points).

(1 Week) Power Series Solutions (regular singular points).

(1 Week) Power Series Solutions (regular singular points), The Laplace Transform (basic properties.)

(1 Week) Basic Properties (continued). Convolution.

(1 Week) Solutions of Differential Equations by the Laplace Transform.

(1 Week) Solutions of Systems of Linear Differential Equations by the Laplace Transform.

(1 Week) Solutions of Systems of Linear Differential Equations by Elimination: simple elimination.

Suggested textbooks:

Şafak Alpay, Ersan Akyıldız, Albert Erkip; Lectures on Differential Equations. Matematik Vakfı yayını, 1995.

J.A.Tierrey; Differential equations. Allyn and Bacon, Inc. 1979

 

Notes:

1. Grading: For the total sum. Letter grades will be given according to the usual catalog.
2. Make-up Exams: they will be given after each exam, ONLY for students who have an official medical report. Consult your section instructors.
3. Inspection of Exam Papers: It must be done ONLY at the time which will be announced after each exam.
4. Section Change: If the schedule of your section does not fit into your program, you may switch to another section without informing your instructor.

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