Prerequisites: Math 152 or Math 154
Frequency: Fall/Spring Terms
Credit: (4-0)4
Content: First order equations and various applications. Higher
order linear differential equations. Power series solutions: ordinary
and regular singular points. The Laplace transform: solution of initial
value problems. Systems of linear differential equations: solutions
by operator method, by Laplace transform. Introduction to partial differential
equations; Separation of variables.
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:
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(1 Week) Preliminaries. Solutions. Existence-Uniqueness Theorem.
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(1 Week) Separable Equations. Linear Equations. Homogeneous Equations.
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(1 Week) Exact Equations and Integrating Factors.Substitutions.
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Approximate solutions (2.6.1 and 2.6.2). Applications (2.7.2).
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(1 Week) Basic Theory of Higher Order Linear Equations.
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(1 Week) Reduction of Order. Homogeneous Constant Coefficient Equations..
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(1 Week) Undetermined Coefficients. Variation of Parameters.
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(1 Week) The Cauchy-Euler Equations. Operator Method
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(1 Week) Operator Method (continued) Power Series Solutions
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(ordinary points).
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(1 Week) Power Series Solutions (ordinary and regular singular points).
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(1 Week) Power Series Solutions (regular singular points), The Laplace
Transform (basic properties.)
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(1 Week) Convolution. Solutions of Differential Equations by the
Laplace Transform.
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(1 Week) Solutions of Systems of Linear Differential Equations by
the Laplace Transform.
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(1 Week) Solutions of Systems of Linear Differential Equations by
Elimination: simple elimination and operator method.
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(1 Week) Partial Differential Equations: Seperation of Variables
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(1 Week) Partial Differential Equations: Seperation of Variables
Suggested textbook: Şafak Alpay, Ersan Akyıldız, Albert Erkip;
Lectures on Differential Equations. Matematik Vakfı, 1995.
Reference books:
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B.Kolman; Introductory Linear Algebra with applications. Macmillan
Publish Co, 1976.
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H.Anton; Elementary Linear Algebra. John Wiley and Sons. 1994
Notes:
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Grading: For the total sum. Letter grades will be given according
to the usual catalog.
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Make-up Exams: they will be given after each exam, ONLY for
students who have an official medical report. Consult your section instructors.
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Inspection of Exam Papers: It must be done ONLY at the time
which will be announced after each exam.
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Section Change: If the schedule of your section does not
fit into your program, you may switch to another section without
informing your instructor.
Courrent
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