| Prerequisites: Math 156 and Math 260
Frequency: Fall Term
Credit: (4-0)4
Content: Existence and uniqueness theorems. First order equations.
Trajectories. Higher order linear equations; undetermined coefficients,
variation of parameters and operator methods. Power series solutions. Laplace
transform solutions of IVP’s. Theory of linear systems. Solutions
by operator, Laplace and linear algebra methods. Partial differential equations,
seperation of variables and Fourier series.
Course Outline:
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(1 Week) Introduction: Existence and uniqueness; seperable, linear
equations.
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(1 Week) Bernoulli, homogeneous, exact equations, integrationg factors,
substitutions.
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(1 Week) Riccati, Clairaut, higher order equations (reduction of
order); successive approximations, geometric problems, oblique and
orthogonal trajactories.
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(1 Week) Basic theory of higher order linear equations.
Wronskian, discussions of linearly independent solutions
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(1 Week) Definition of general solutions; reduction of order, homogeneous
constant coefficient equations, undetermined coefficients.
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(1 Week) Undetermined coefficients (continued) variation of parameters,
Cauchy- Euler equation, operator techniques.
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(1 Week) Operator techniques (continued), Power series solutions.
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(1 Week) Solution around ordinary and regular singular points.
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(1 Week) Solutions around regular singular points (continued), Laplace
transforms.
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(1 Week) Laplace transforms (continued)
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(1 Week) Systems; matrix notation, basic properties, solution by
elimination (use of operators included).
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(1 Week) Use of Laplace transform techniques and matrix exponential
functions.
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(1 Week) Use of matrix exponential functions (continued) Introduction
to PDE, general solutions, seperation of variables.
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(1 Week) Initial and boundary value problems (together with Fourier
series expansion) for wave and heat equations; boundary value problems
for Laplace equation.
Suggested textbook: Þafak Alpay, Ersan Akyýldýz, Albert Erkip;
Lectures on Differential Equations. Matematik Vakfý, 1995.
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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