ENERGY SYSTEMS ENGINEERING | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT2062 | Differential Equations | Spring | 3 | 0 | 3 | 6 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | English |
Type of course: | Non-Departmental Elective |
Course Level: | Bachelor’s Degree (First Cycle) |
Mode of Delivery: | Face to face |
Course Coordinator : | Dr. Öğr. Üyesi GÜLSEMAY YİĞİT |
Course Lecturer(s): |
Prof. Dr. NAFİZ ARICA |
Recommended Optional Program Components: | None |
Course Objectives: | This course covers the fundamental concepts of an introductory level of elementary differential equations with basic concepts, theory, solution methods and applications. Main goal is to develop the basics of modeling at an introductory level and connect this step to the theoretical and methodological resource of mathematics. |
The students who have succeeded in this course; 1. Classify differential equations and determine the existence and uniqueness of solutions of Initial Value Problems 2. Solve first order separable and linear differential equations 3. Use substitution methods to solve homogeneous and Bernoulli equations 4. Solve exact differential equations 5. Solve the higher order linear homogeneous and nonhomogeneous differential equations 6. Solve the systems of linear differential equations 7. Solve differential equations by using Laplace transform method |
In this course basic concepts of elementary differential equations will be covered. The solution techniques for the different types of first order differential equations will be given and the solution methods will be taught. The higher order linear differential equations and solution methods will be discussed. The systems of linear equations will be covered with different techniques. Finally, the Laplace Transform method will be taught to solve linear differential equations. |
Week | Subject | Related Preparation |
1) | Classification of differential equations, Explicit solution, implicit solution, Initial Value Problems, Integrals as General and Particular Solutions. | |
2) | Existence and Uniqueness of Solution. Separable Differential Equations. | |
3) | First Order Linear Differential Equations. | |
4) | Substitutions methods. Homogeneous Differential Equations. Bernoulli Differential Equations. | |
5) | Exact Differential Equations. | |
6) | Population models. Reducible second order equations. | |
7) | Theory of Higher Order Linear Differential Equations, Existence and Uniqueness Theorem, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Cases. | |
8) | Homogeneous Linear Equations with Constant Coefficients. Euler Equations. | |
9) | Solution of Nonhomogeneous Linear Differential Equations. Method of Undetermined Coefficients. | |
10) | Solution of Nonhomogeneous Linear Differential Equations. Method of Variation of Parameters. | |
11) | Theory of Systems of Linear Differential Equations. | |
12) | The Eigenvalue Method for Systems of Linear Differential Equations. | |
13) | Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform. Inverse Laplace Transform. | |
14) | Solution of Differential Equations by using Laplace Transform. |
Course Notes / Textbooks: | Differential Equations with Boundary Value Problems by C. Henry Edwards & D. E.Penney, sixth edition |
References: | Introduction to Ordinary Differential Equations” by Shepley L. Ross. Fourth Edition, John Wiley and Sons. |
Semester Requirements | Number of Activities | Level of Contribution |
Quizzes | 2 | % 20 |
Midterms | 1 | % 35 |
Final | 1 | % 45 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 55 | |
PERCENTAGE OF FINAL WORK | % 45 | |
Total | % 100 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Build up a body of knowledge in mathematics, science and Energy Systems Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. | |
2) | Ability to identify, formulate, and solve complex Energy Systems Engineering problems; select and apply proper modeling and analysis methods for this purpose. | |
3) | Ability to design complex Energy systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. | |
4) | Ability to devise, select, and use modern techniques and tools needed for solving complex problems in Energy Systems Engineering practice; employ information technologies effectively. | |
5) | Ability to design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Energy Systems Engineering. | |
6) | Ability to cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Energy Systems-related problems | |
7) | Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions. | |
8) | Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself. | |
9) | Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Energy Systems Engineering applications. | |
10) | Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development. | |
11) | Acquire knowledge about the effects of practices of Energys Systems Engineering on health, environment, security in universal and social scope, and the contemporary problems of Energys Systems engineering; is aware of the legal consequences of Energys Systems engineering solutions. |