DIFFERENTIAL EQUATIONS

Course Description

In this course, the ordinary differential equations and their applications will be considered. The course will demonstrate the usefulness of ordinary differential equations for modelling physical and engineering problems. Complementary mathematical approaches for their solution will be presented, including analytical methods. The basic content of the course includes first order ordinary differential equations and their types of exact, separable, Bernoulli, first order, homogeneous ordinary differential equations, linear independence of the solutions, higher order ordinary differential equations and their solutions. The undetermined coefficient methods, the variation of the parameter method, Cauchy-Euler equations. The definition of the Laplace transform and some important applications of the Laplace transform will be included in this lecture.

DIFFERENTIAL EQUATIONS

Evaluation Tools (Active Term)

Course outcomes

1. 01 Recognize the ordinary differential equations with their orders
2. 02 Classify the type of ordinary differential equations
3. 03 Apply solution methods for first order differential equations
4. 04 Solve the higher order constant coefficient differential equations
5. 05 Apply Laplace transform for solutions of initial value problems

Course Syllabus

Reference Books & Course Materials

1. 01 S.L. Ross, Introduction to Ordinary Differential Equations, Fourth edition, John Wiley & Sons, 1989.
2. 02 Differential Equations and Linear Algebra, 2nd edition, by Edwards Penney, Pearson Education.

Learning Outcomes

1. L01 Recognize the ordinary differential equations with their orders
2. L02 Classify the type of ordinary differential equations
3. L03 Apply solution methods for first order differential equations
4. L04 Solve the higher order constant coefficient differential equations
5. L05 Apply Laplace transform for solutions of initial value problems

Program Outcomes

1. Should be able to write effective reports, understand written reports, and prepare design and production reports.
2. Should have the ability to make effective presentations.
3. Should have the ability to give and have clear and understandable instructions.
4. Should gain consciousness (awareness) about the necessity of lifelong learning.
5. Should have the ability to access information.
6. Should have the ability to follow developments in science and technology and constantly renew himself/herself.
7. Should gain the awareness of professional and ethical responsibility and should act in accordance with ethical principles.
8. Should gain knowledge about the standards used in engineering applications.
9. Should gain knowledge about project management, risk management, and change management practices in business life.
10. Should gain awareness about entrepreneurship, and innovation.
11. Should gain knowledge about development in sustainability.
12. Should gain knowledge about the effects of engineering practices on health, environment, and security at universal and social dimensions and the problems of the age reflected in the field of engineering.
13. Awareness should be gained about the legal consequences of engineering solutions.
14. Should have sufficient knowledge in mathematics, science, and subjects specific to the relevant engineering discipline.
15. Should have the ability to use theoretical and applied knowledge in mathematics, science, and related engineering disciplines in complex engineering problems.
16. Should have the ability to detect, define, formulate, and solve complex engineering problems.
17. Should have the ability to select and apply appropriate analysis and modeling methods to solve complex engineering problems.
18. Should have the ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions.
19. Should have the ability to apply modern design methods.
20. Should have the ability to develop, select, and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications.
21. Should have the ability to use information technologies effectively.
22. Should have the ability to design experiments, for the study of complex problems or discipline-specific research topics.
23. Should have the ability to conduct experiments, collect data, analyze and interpret results for the study of complex problems or discipline-specific research topics.
24. Should have the ability to work in intradisciplinary teams.
25. Should have the ability to work in interdisciplinary teams.
26. Should have the skills to work individually.
27. Should have the ability to communicate effectively verbally and in writing.
28. Should have the knowledge of at least one foreign language.

Po-Lo Matrix