Mathematical Modeling (MATH486) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Mathematical Modeling	MATH486	Area Elective	3	0	0	3	6

Pre-requisite Course(s)
N/A

Course Language	English
Course Type	Elective Courses
Course Level	Natural & Applied Sciences Master's Degree
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Question and Answer, Team/Group.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	Differential equations constitute main tools that scientists and engineers use to make mathematical models of important practical problems. This course discusses three major issues: 1) Formulating a model, using differential equations; 2) Analyzing the model, both by solving the differential equation and by extracting qualitative information about the solution from the equation; 3) Interpreting the analysis in light of the physical (practical) setting modeled in step 1).
Course Learning Outcomes	The students who succeeded in this course; make mathematical models of practical problems by mens of differential equations gain skill with solution techniques in order to understand complex physical phenomena
Course Content	Differetial equations and solutions, models of vertical motion, single-species population models, multiple-species population models, mechanical oscillators, modeling electric circuits, diffusion models.

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	Some terminology, Examples, Separation of variables.	pp. 1-8
2	The Euler method, Linear differential equations with constant coefficients.	p. 23, Exercise 8
3	Vertical motion without air resistence.	pp. 29-37, 41-46
4	Vertical motion with air resistence.	pp. 47-51
5	Simple population model, Population with emigration.	pp. 65-71
6	Population with competition (The logistic equation).	pp. 72-75
7	Midterm
8	Predator-prey (Fox-rabbit) population model, Epidemics (SIR).	pp. 203-215
9	Two-species competition.	pp. 219-222
10	Spring-mass without damping or forcing, Spring-mass with damping and forcing.	p. 77, Exercises 3 and 4, pp. 223-227
11	Pendulum without damping, Approximate pendulum without damping.	pp. 227-230
12	Series RC charge, Series RLC charge and current (First-order system).	pp. 428-435
13	Parallel RLC voltage (Second-order scalar equation).	pp. 465-468
14	Diffusion without convection or source, Diffusion with convection and source.	pp. 1-6
15	Heat flow without heat source, Time-dependent diffusion.	p. 23, Exercise 8
16	Final Exam

Sources

Course Book	1. P. W. Davis, Differential Equations: Modeling with matlab, Prentice Hall, Upper Saddle River, New Jersey, 1999.
	3. S. L. Ross, Differential Equations, 3rd ed.,Wiley, New York, 1984.
Other Sources	2. E. Kreyszig, Advanced Engineering Mathematics, 8th ed., Wiley, New York, 1999.

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	5	10
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	2	50
Final Exam/Final Jury	1	40
Toplam	8	100

Percentage of Semester Work	60
Percentage of Final Work	40
Total	100

Course Category

Core Courses	X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area.
2	Has the ability to obtain, to evaluate, to interpret and to apply information by doing scientific research.
3	Can apply gained knowledge and problem solving abilities in inter-disciplinary research.
4	Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary.
5	Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study.
6	Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework.
7	Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility.
8	Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation.
9	Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields.
10	Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge.
11	Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications.

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)	16	3	48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	14	3	42
Presentation/Seminar Prepration
Project
Report
Homework Assignments	5	4	20
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	10	20
Prepration of Final Exams/Final Jury	1	20	20
Total Workload			150