MATHEMATICAL MODELLING

Course Code:

MATH 348

Course Type:

Area Elective

P:

3

Lab:

0

Laboratuvar Saati:

0

Credits:

3

ECTS:

6

Course Language:

English

Course Objectives:

Determining suitable mathematical models for problemles in some areas. advancing closest solutions to the models and evoluating results

Course Content:

Modeling of systems with one independent, one dependent variable and with several variables, Modelling of systems with difference equations, Applications to some examples; population, finance, epidemic problems. Analytical and numerical solutions of the model equations. Linear, Nonlinear, Periodic Models, Continuous modelling with differential equations, Applications to some problems.

Course Methodology:

1: Lecture, 2: Problem Solving 4: Homework

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) Determines variables and parameters of problem.	1,4	1,2,4	A
2) Analyzes the problem which is modelled.	2,3,4	1,2,4	A
3) Associates the solution of the model with the solution of the problem.	2,3,4	1,2,4	A
4) Writes a discrete model equation of a problem.	1,4	1,2,4	A
5) Writes a continous model equation of a problem.	1,4	1,2,4	A
6) Interests in modelling of some industrial, financial, social, health problems.	2,3,4,6,7,9	1,2,4	A

Course Flow

Week	Topics	Study Materials
1	Variables, parameters, setting up modelling materials.
2	Setting up model with difference equations
3	Examples in finance, population problems
4	Fixed points and stability
5	Systems of difference equations
6	Examples in epidemic problems and some industrial problems
7	Linear, nonlinear, periodic models
8	Midterm, Markov chain
9	Markov Chain, Continous modelling, differential equations
10	Continous modelling, basic models of paticle dynamics
11	Midterm, dimensionless equations
12	Perturbation techniques for nonlinear models
13	Examples in various areas.
14	Examples in various areas

Recommended Sources

Textbook

Additional Resources

Principles of Mathematical Modelling, C. Dym.

 Mathematical Modelling, J. N. Kapur

Material Sharing

Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	2	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
No	Program Learning Outcomes	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	2	28
Mid-terms (Including self study)	2	13	26
Quizzes
Assignments	10	3	30
Final examination (Including self study)	1	15	15
Total Work Load			141
Total Work Load / 25 (h)			5,64
ECTS Credit of the Course			6

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