Ders Planı

CLASS 4

Lesson plan / DIFFERENTIAL EQUATIONS -II

Lesson Information

Course Credit	3.0
Course ECTS Credit	5.0
Teaching Language of Instruction	Türkçe
Level of Course	Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course	Compulsory
Mode of Delivery	Face-to-face
Does the course require compulsory or optional work experience?	Z
Course Coordinator
Instructor (s)
Course Assistant

Purpose and Content

The aim of the course	The aim of this course is to give the general solutions of linear and non-linear equation systems ,linearization of non-linear equation systems , information about the Green's functions and Sturm-Liouville equations.
Course Content	This course covers the first order equations system stability, autonomous systems, exponential matrix functions and general solutions of equations with constant coefficients, autonomous, gradient and Hamiltonian systems, Lyapunov functions. Linearization. Periodic solutions, Poincare-Bendixon theorem. Self-adjoint second-order equations, general theorems. Green's function. Spectral theory. Sturm-Liouville systems, Liouville normal form. Orthogonal functions and their completeness.

The aim of the course

The aim of this course is to give the general solutions of linear and non-linear equation systems ,linearization of non-linear equation systems , information about the Green's functions and Sturm-Liouville equations.

Course Content

This course covers the first order equations system stability, autonomous systems, exponential matrix functions and general solutions of equations with constant coefficients, autonomous, gradient and Hamiltonian systems, Lyapunov functions. Linearization. Periodic solutions, Poincare-Bendixon theorem. Self-adjoint second-order equations, general theorems. Green's function. Spectral theory. Sturm-Liouville systems, Liouville normal form. Orthogonal functions and their completeness.

Learning Outcomes

Have advanced theoretical and practical knowledge in mathematics and computer science.
Gain an in-depth knowledge on Computer Science including computer programming, word processing, database functions, accessing the internet and softwares.
Possess the knowledge of advanced research methods in mathematics-computer field.
Possess theoretical and practical knowledge in mathematics, computation and computer science.
Define computer programming, word processing, data functions, internete access and software programs.
Describe advanced research methods in the field of Mathematics-Computer Science.
Evaluate and interpret data using the knowledge and skills gained in the fields of mathematics and computer science.
Identify, define and analyze problems in the fields of mathematics and computer science; develop solutions based on research and evidence.
Identify, define and model mathematics, computation and computer science problems; select and apply appropriate analysis and modeling methods for this purpose.
Design and apply interactive experimental environments to get the definitions and first solutions of the problems of computer science and computer science and evaluate these environments.
Having the discipline of mathematics, understand the operating logic of the computer and gain the ability to think based on account.
Perform all phases of life cycle in computer based systems.
Work effectively as an individual and as a team member to solve problems in the areas of mathematics and computer science.
Have the ability to act independently, use initiative and creativity.
Work effectively either individually or in multidisciplinary teams.
Evaluate advanced knowledge and skills in the field with a critical approach.
Follow current developments about the awareness of the necessity of continuous professional development and information and communication technologies.
Have the consciousness of the necessity of lifelong learning and continuously develop professional knowledge and skills.
Use the time effectively in the process of getting the conclusion with analytical thinking ability.
Have at least one foreign language knowledge and the ability to communicate effectively in Turkish, verbally and in writing.
Be aware of the effects of information applications on individual, institutional, social and universal dimensions and have the awareness about entrepreneurship, innovation.
Have the awareness of professional and ethical responsibility and legal consequences of information applications
Use the knowledge about the field for the benefit to society.

Weekly Course Subjects

1	first order equations system stability.
2	autonomous systems, exponential matrix functions.
3	General solutions of equations with constant coefficients.
4	autonomous, gradient and Hamiltonian systems.
5	Lyapunov functions.
6	Linearization.
7	Periodic solutions.
8	Poincare-Bendixon theorem.
9	Self-adjoint second-order equations.Midterm Exam.
10	General theorems. Green's function.
11	Spectral theory.
12	Sturm-Liouville systems.
13	Liouville normal forms.
14	Orthogonal functions and their completeness.

Resources

1.William E. Boyce, Richard C.DiPrima, Elementary Differential Equations and Boundary Value Problems : International Student Version, Boyce & Dprima, John Wiley & Sons, 2010.
2. Richard Bronson, Erin J. Bredensteiner , Differential Equations,Schaum’s Outlines, McGraw-Hill, 2003.
3. Shepley L. Ross, Differential Equations, 3. Edition
4 Edward B. Saff and Arthur David Snider, Fundementals of Differential Equations and Boundary Value Problems, R. Kent Nagle, Addison,New York, 2004.

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Lesson Information

Purpose and Content

Learning Outcomes

Weekly Course Subjects

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