Code |
Name of the Course Unit |
Semester |
In-Class Hours (T+P) |
Credit |
ECTS Credit |
MAT203 |
DIFFERENTIAL EQUATIONS |
3 |
4 |
3 |
5 |
GENERAL INFORMATION |
Language of Instruction : |
Turkish |
Level of the Course Unit : |
BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle |
Type of the Course : |
Compulsory |
Mode of Delivery of the Course Unit |
- |
Coordinator of the Course Unit |
Assist.Prof. SERKAN GÖNEN |
Instructor(s) of the Course Unit |
Assist.Prof. MELİS BOLAT-Assist.Prof. MELTEM UZUN |
Course Prerequisite |
MAT105 - MATHEMATICS I |
OBJECTIVES AND CONTENTS |
Objectives of the Course Unit: |
This is one of the basic calculus course of the sequence which serves as the foundation of all advanced subjects in applied and theoretical mathematics. |
Contents of the Course Unit: |
First order equations: separable, linear, homogeneous exact equations, orthogonal and oblique trajectories, applications. Higher order linear differential equations: Reduction of order, method of undetermine coefficients, method of variation of parameters, Cauchy-Euler equations, operator methods, applications. Power series solutions: ordinary points, regular singular points. The Laplace Transform: basic properties, solution of initial value problems, convolution integral, solution of various equations. Systems of linear differential epuations: Brief discussion of theory of linear systems, solving linear systems; by operator method, by Laplace transform. Introduction to Partial Differential equations: Separation of variables. |
KEY LEARNING OUTCOMES OF THE COURSE UNIT (On successful completion of this course unit, students/learners will or will be able to) |
WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY |
Week |
Preparatory |
Topics(Subjects) |
Method |
1 |
- |
Preliminaries. Solutions. Existence-Uniqueness Theorem. Separable Equations. Linear Equations. Homogeneous Equations. |
- |
2 |
- |
Exact Equations and Integrating Factors.Substitutions. Approximate solutions (2.6.1 and 2.6.2). Application |
- |
3 |
- |
Basic Theory of Higher Order Linear Equations. |
- |
4 |
- |
Reduction of Order. Homogeneous Constant Coefficient Equations. |
- |
5 |
- |
Undetermined Coefficients. Variation of Parameters. |
- |
6 |
- |
The Cauchy-Euler equation. Operator Method. |
- |
7 |
- |
Power Series Solutions (ordinary points). |
- |
8 |
- |
MID-TERM EXAM |
- |
9 |
- |
Power Series Solutions (regular singular points) |
- |
10 |
- |
The Laplace Transform. Basic Properties. Convolution. |
- |
11 |
- |
Solution of Differential Equations by the Laplace Transform. |
- |
12 |
- |
Solutions of Systems of Linear Differential Equations by the Laplace Transform. |
- |
13 |
- |
Solutions of Systems of Linear Differential Equations by Elimination: simple elimination and operator method. |
- |
14 |
- |
Introduction to Partial Differential Equations |
- |
15 |
- |
Introduction to Partial Differential Equations |
- |
16 |
- |
FINAL EXAM |
- |
17 |
- |
FINAL EXAM |
- |
SOURCE MATERIALS & RECOMMENDED READING |
ASSESSMENT |
Assessment & Grading of In-Term Activities |
Number of Activities |
Degree of Contribution (%) |
Description |
Level of Contribution |
0 |
1 |
2 |
3 |
4 |
5 |
CONTRIBUTION OF THE COURSE UNIT TO THE PROGRAMME LEARNING OUTCOMES
KNOWLEDGE |
Theoretical |
|
Programme Learning Outcomes |
Level of Contribution |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to identify, analyze, design, model and solve complex engineering problems based on engineering, science and mathematics fundamentals
|
|
|
|
|
|
|
KNOWLEDGE |
Factual |
|
Programme Learning Outcomes |
Level of Contribution |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to apply engineering design to produce solutions that meet specific needs, taking into account global, cultural, social, environmental and economic factors as well as public health, safety and well-being
|
|
|
|
|
|
|
SKILLS |
Cognitive |
|
Programme Learning Outcomes |
Level of Contribution |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to communicate effectively with various stakeholders
|
|
|
|
|
|
|
SKILLS |
Practical |
|
Programme Learning Outcomes |
Level of Contribution |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
The ability to recognize ethical and professional responsibilities in engineering and make informed decisions considering the impact of engineering solutions in their global, economic, environmental and social contexts
|
|
|
|
|
|
|
OCCUPATIONAL |
Autonomy & Responsibility |
|
Programme Learning Outcomes |
Level of Contribution |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
The ability to recognize ethical and professional responsibilities in engineering and make informed decisions considering the impact of engineering solutions in their global, economic, environmental and social contexts
|
|
|
|
|
|
|
OCCUPATIONAL |
Learning to Learn |
|
Programme Learning Outcomes |
Level of Contribution |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to acquire new knowledge and find ways to apply it when necessary, using appropriate learning strategies
|
|
|
|
|
|
|
OCCUPATIONAL |
Communication & Social |
|
Programme Learning Outcomes |
Level of Contribution |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to work effectively in a team where its members lead together, create a collaborative and inclusive environment, set goals, plan tasks, and meet goals
|
|
|
|
|
|
|
OCCUPATIONAL |
Occupational and/or Vocational |
|
Programme Learning Outcomes |
Level of Contribution |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to design and conduct appropriate experiments, analyze and interpret data, and apply engineering principles to draw conclusions
|
|
|
|
|
|
|
WORKLOAD & ECTS CREDITS OF THE COURSE UNIT |
Workload for Learning & Teaching Activities |
Type of the Learning Activites |
Learning Activities (# of week) |
Duration (hours, h) |
Workload (h) |
Lecture & In-Class Activities |
14 |
3 |
42 |
Preliminary & Further Study |
14 |
3 |
42 |
Land Surveying |
0 |
0 |
0 |
Group Work |
0 |
0 |
0 |
Laboratory |
0 |
0 |
0 |
Reading |
3 |
4 |
12 |
Assignment (Homework) |
6 |
5 |
30 |
Project Work |
0 |
0 |
0 |
Seminar |
0 |
0 |
0 |
Internship |
0 |
0 |
0 |
Technical Visit |
0 |
0 |
0 |
Web Based Learning |
0 |
0 |
0 |
Implementation/Application/Practice |
0 |
0 |
0 |
Practice at a workplace |
0 |
0 |
0 |
Occupational Activity |
0 |
0 |
0 |
Social Activity |
0 |
0 |
0 |
Thesis Work |
0 |
0 |
0 |
Field Study |
0 |
0 |
0 |
Report Writing |
0 |
0 |
0 |
Final Exam |
1 |
1 |
1 |
Preparation for the Final Exam |
0 |
0 |
0 |
Mid-Term Exam |
1 |
1 |
1 |
Preparation for the Mid-Term Exam |
0 |
0 |
0 |
Short Exam |
0 |
0 |
0 |
Preparation for the Short Exam |
0 |
0 |
0 |
TOTAL |
39 |
0 |
128 |
|
Total Workload of the Course Unit |
128 |
|
|
Workload (h) / 25.5 |
5 |
|
|
ECTS Credits allocated for the Course Unit |
5,0 |
|