FACULTY OF ARTS AND SCIENCES

Department of Physics

MATH 207 | Course Introduction and Application Information

Course Name
Introduction to Differential Equations I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 207
Fall
2
2
3
5

Prerequisites
  MATH 154 To get a grade of at least FD
or MATH 110 To get a grade of at least FD
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Case Study
Q&A
Course Coordinator
Course Lecturer(s)
Assistant(s)
Course Objectives This course is an introduction to the basic concepts, theory, methods and applications of ordinary differential equations. The aim of this course is to solve differential equations and to
develop the basics of modeling of real life problems.
Learning Outcomes The students who succeeded in this course;
  • will be able to classify the differential equations.
  • will be able to use solution methods of first order ordinary differential equations.
  • will be able to solve higher order linear differential equations with constant coefficients.
  • will be able to use the Laplace transform method of linear differential equations.
  • will be able to analyze series solutions of linear differential equations.
  • will be able to solve systems of linear differential equations.
  • will be able to analyze approximate methods of solving first-order equations by using the method of succesive approximations and the Euler method.
Course Description In this course basic concepts of differential equations will be discussed.The types of first order ordinary differential equations will be given and the solution methods will be taught. Also, solution methods for higherorder ordinary differential equations will be analyzed.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Description and Classification of differential equations. Separable Differential Equations. First - Order Linear Differential Equations. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 1.1, 2.2, 2.3
2 Description and Classification of differential equations. Separable Differential Equations. First - Order Linear Differential Equations. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section: 1.1, 2.2, 2.3
3 Exact Differential Equations. Non- Exact Differential Equations. Bernoulli Differential Equations. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 2.4, 2.5
4 Systems of Linear Differential Equations R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5
5 Systems of Linear Differential Equations/ Matrix Exponential R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.8
6 Midterm I
7 Homogeneous Constant Coefficient Second Order Differential Equations. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.2
8 Non-homogeneous Constant Coefficient Second Order Differential Equations. Variation of parameters. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.4
9 Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform, Inverse Laplace Transforms. Solving Initial Value Problems by Laplace Transforms. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 7.2, 7.3.,7.4, 7.5.
10 Midterm II
11 Laplace Transform: Systems of Linear Differential Equations (Including Non-homogeneous Case)Series Solutions of Differential Equations. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 7.9
12 Power Series Solutions: Series Solutions around an Ordinary Point. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 8.3
13 Series Solutions around a Singular Point. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 8.3
14 Review
15 Semester review
16 Final exam

 

Course Notes/Textbooks

Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), ISBN-13: 978-0321747747.

Suggested Readings/Materials

Shepley L. Ross, ''Introduction to Ordinary Differential Equations'', Fourth Edition, (John Wiley and Sons,1989), ISBN-13: 978-0471032953.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
2
50
Final Exam
1
50
Total

Weighting of Semester Activities on the Final Grade
2
50
Weighting of End-of-Semester Activities on the Final Grade
1
50
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
2
32
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
2
32
Study Hours Out of Class
14
3
42
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
2
12
24
Final Exam
1
20
20
    Total
150

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To be able master and use fundamental phenomenological and applied physical laws and applications,

X
2

To be able to identify the problems, analyze them and produce solutions based on scientific method,

X
3

To be able to collect necessary knowledge, able to model and self-improve in almost any area where physics is applicable and able to criticize and reestablish his/her developed models and solutions,

X
4

To be able to communicate his/her theoretical and technical knowledge both in detail to the experts and in a simple and understandable manner to the non-experts comfortably,

5

To be familiar with software used in area of physics extensively and able to actively use at least one of the advanced level programs in European Computer Usage License,

6

To be able to develop and apply projects in accordance with sensitivities of society and behave according to societies, scientific and ethical values in every stage of the project that he/she is part in,

7

To be able to evaluate every all stages effectively bestowed with universal knowledge and consciousness and has the necessary consciousness in the subject of quality governance,

8

To be able to master abstract ideas, to be able to connect with concreate events and carry out solutions, devising experiments and collecting data, to be able to analyze and comment the results,

9

To be able to refresh his/her gained knowledge and capabilities lifelong, have the consciousness to learn in his/her whole life,

10

To be able to conduct a study both solo and in a group, to be effective actively in every all stages of independent study, join in decision making stage, able to plan and conduct using time effectively.

11

To be able to collect data in the areas of Physics and communicate with colleagues in a foreign language ("European Language Portfolio Global Scale", Level B1).

12

To be able to speak a second foreign at a medium level of fluency efficiently

13

To be able to relate the knowledge accumulated throughout the human history to their field of expertise.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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