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 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