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 and by elimination. 

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 real-life 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.  

  Notes: 

Grading: Letter grades will be awarded according to the catalogue. 
Make-up Exams:There will only be one make-up examination for the midterms missed which will be given before the final examination. Please note that make-up examinations can only be taken if one has an official/medical report.
Inspection of Exam Papers: It must be done ONLY at the time which will be announced after each exam. 
Section Change: If the schedule of your section does not fit your program, you may attend another section without informing your instructor. 
 

  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 
• Di. Prima, W.E. Boyce, Elementary Differential Equations and Boundary Value Problems, Wiley International Edititon.

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