Course Code:
MATH 246
Semester:
Spring
Course Type:
Core
P:
3
Lab:
0
Laboratuvar Saati:
0
Credits:
3
ECTS:
6
Course Language:
English
Course Objectives:
Main goals are to provide the properties of the systems of linear and nonlinear equations, the development of their general solutions, the linearization of nonlinear systems, adjoint equations, Green’s functions and Sturm-Liouville equations.
Course Content:

Self-adjoint second order equations, general theorems. Green's function. Spectral theory. Sturm-Liouville systems, Liouville normal forms. Orthogonal functions and their completeness. Stability of first order systems of equations. Autonomous systems, matrix exponential functions and general solutions of systems of equations with constant coefficients Autonomous,gradient and Hamiltonian systems, Lyapunov functions.. Linearization. Periodic solutions, Poincare-Bendixon theorem.

Course Methodology:
1: Lecture, 2: Problem Solving
Course Evaluation Methods:
A: Written examination, B: Homework

## Vertical Tabs

### Course Learning Outcomes

 Learning Outcomes Teaching Methods Assessment Methods 1) Knows the stability of systems of equations 1, 2 A, B 2) Knows matrix exponential functions 1, 2 A, B 3) Knows the general solutions of systems of equations with constant coefficents 1, 2 A, B 4) Has some information on Hamilton systems and Lyapunov functions 1, 2 A, B 5) Uses Poincare-Bendixon theorem 1, 2 A, B 6) Knows Green’s functions and orthogonal functions 1, 2 A, B

### Course Flow

 Week Topics Study Materials 1 Main results, linear phase diagram 1.1, 1.2, 1.3 2 Bifurcation, linear systems 1.4, 2.1 3 Linear systems, vectorial equations 2.1, 2.2 4 Matrix exponential systems, continuous systems 2.3, 3.1 5 Autonomous systems, plane phase diagrams 3.1, 3.2 6 Plane phase diagrams for linear systems 3.3 7 Plane phase diagrams for linear systems, stability of nonlinear systems 3.3, 3.4 8 Stability of nonlinear systems 3.4 9 Midterm Linearizations of nonlinear systems 3.5 10 Linearizations of nonlinear systems 3.5 11 Self-adjoint second order equations 5.1, 5.2 12 Sturm-Liouville problems 5.4 13 Green’s functions 5.9 14 Green’s functions 5.9

### Recommended Sources

 Textbook Theory of Differential Equations Kelley-Peterson, Pearson Additional Resources

### Material Sharing

 Documents Assignments Exams

### Assessment

 IN-TERM STUDIES NUMBER PERCENTAGE Mid-terms 1 100 Quizzes Assignments Total 100 CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE 50 CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE 50 Total 100

 COURSE CATEGORY Expertise/Field Courses

### Course’s Contribution to Program

 No Program Learning Outcomes Contribution 1 2 3 4 5 1 The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) x 2 Acquiring fundamental knowledge on fundamental research fields in mathematics x 3 Ability form and interpret the relations between research topics in mathematics x 4 Ability to define, formulate and solve mathematical problems x 5 Consciousness of professional ethics and responsibilty x 6 Ability to communicate actively x 7 Ability of self-development in fields of interest x 8 Ability to learn, choose and use necessary information technologies x 9 Lifelong education x

### ECTS

 Activities Quantity Duration (Hour) Total Workload (Hour) Course Duration (14x Total course hours) 14 3 42 Hours for off-the-classroom study (Pre-study, practice) 14 4 56 Mid-terms (Including self study) 2 15 30 Quizzes - - - Assignments - - - Final examination (Including self study) 1 20 20 Total Work Load 148 Total Work Load / 25 (h) 5.92 ECTS Credit of the Course 6