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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
|
Spring
|
2
|
2
|
3
|
5
|
| Prerequisites |
|
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| Course Language |
English
|
|||||||||
| Course Type |
Required
|
|||||||||
| Course Level |
First Cycle
|
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| Mode of Delivery | - | |||||||||
| Teaching Methods and Techniques of the Course | Problem SolvingCase StudyQ&A | |||||||||
| National Occupation Classification | - | |||||||||
| 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. |
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| Learning Outcomes |
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| 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. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Related Sustainable Development Goals |
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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 | Learning Outcome |
| 1 | Introduction, classification of differential equations, Mathematical Modelling. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 1.1 | |
| 2 | 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: 2.2, 2.3 | |
| 3 | Exact Differential Equations. Non- Exact 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 | Bernoulli Differential Equations. Existence and uniqueness theorem. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 2.6, 13.2 | |
| 5 | Homogeneous, Non-homogeneous Constant Coefficient Second Order Differential Equations. The Method of Undetermined Coefficients. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.2, 4.4 | |
| 6 | Non-homogeneous Constant Coefficient Second Order Differential Equations. The Method of Undetermined Coefficients. 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, 4.6 | |
| 7 | Homogeneous, Non-homogeneous Variable 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 4.7 | |
| 8 | Higher order linear equations: General theory, Systems of Linear Differential Equations, Distinct eigenvalues. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.6 | |
| 9 | Midterm Exam | - | |
| 10 | Systems of Linear Differential Equations, Distinct eigenvalues and Complex eigenvalues. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.6 | |
| 11 | Systems of Linear Differential Equations, Complex and repeated eigenvalues. | R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.6 | |
| 12 | 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. | |
| 13 | 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. | |
| 14 | 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 | |
| 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 | LO 1 | LO 2 | LO 3 | LO 4 | LO 5 | LO 6 |
| Participation | ||||||||
| Laboratory / Application | ||||||||
| Field Work | ||||||||
| Quizzes / Studio Critiques |
2
|
20
|
||||||
| Portfolio | ||||||||
| Homework / Assignments | ||||||||
| Presentation / Jury | ||||||||
| Project | ||||||||
| Seminar / Workshop | ||||||||
| Oral Exams | ||||||||
| Midterm |
1
|
30
|
||||||
| Final Exam |
1
|
50
|
||||||
| Total |
| Weighting of Semester Activities on the Final Grade |
3
|
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 |
2
|
4
|
8
|
| Portfolio |
0
|
||
| Homework / Assignments |
0
|
||
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
16
|
16
|
| Final Exam |
1
|
20
|
20
|
| Total |
150
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
PC Sub | Program Competencies/Outcomes |
* Contribution Level
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||||
|
1
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2
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3
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4
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5
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| 1 |
To have adequate knowledge in Mathematics, Mathematics based physics, statistics and linear algebra and Mechanical Engineering; to be able to use theoretical and applied information in these areas on complex engineering problems. |
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| 2 |
To be able to identify, define, formulate, and solve complex Mechanical Engineering problems; to be able to select and apply proper analysis and modeling methods for this purpose. |
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-
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| 3 |
To be able to design a thermal and mechanical system, process, device or product under realistic constraints and conditions, in such a way as to meet the requirements; to be able to apply modern design methods for this purpose. |
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| 4 |
To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in engineering applications. |
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| 5 |
To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or Mechanical Engineering research topics. |
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| 6 |
To be able to work efficiently in Mechanical Engineering disciplinary and multi-disciplinary teams; to be able to work individually. |
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| 7 |
To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions. |
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| 8 |
To have knowledge about global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of engineering solutions. |
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| 9 |
To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in engineering applications. |
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| 10 |
To have knowledge about industrial practices such as project management, risk management, and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development. |
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| 11 |
To be able to collect data in the area of Mechanical Engineering, and to be able to communicate with colleagues in a foreign language. |
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| 12 |
To be able to speak a second foreign language at a medium level of fluency efficiently. |
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| 13 |
To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Mechanical Engineering. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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