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. P01 Knowledge of mathematics, natural sciences, basic engineering, computer-based computation, and topics specific to the relevant engineering discipline.
2. P02 Ability to apply knowledge of mathematics, natural sciences, basic engineering, computer-based computation, and topics specific to the relevant engineering discipline to the solution of complex engineering problems.
3. P03 Ability to define complex engineering problems by using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) related to the problem addressed.
4. P04 Ability to formulate complex engineering problems using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) associated with the problem addressed.
5. P05 Ability to analyse and solve complex engineering problems using knowledge of basic sciences, mathematics, and engineering, while considering the relevant United Nations Sustainable Development Goals (SDGs) associated with the problem addressed.
6. P06 Ability to design creative solutions to complex engineering problems.
7. P07 Ability to design complex systems, processes, devices, or products in a way that meets present and future needs while considering realistic constraints and conditions.
8. P08 Ability to select and use appropriate techniques and resources—including estimation and modelling—for the analysis and solution of complex engineering problems, while being aware of their limitations.
9. P09 Ability to select and use modern engineering and computational tools—including estimation and modelling—for the analysis and solution of complex engineering problems, while being aware of their limitations.
10. P10 Ability to conduct literature research and use appropriate research methods for the investigation of complex engineering problems.
11. P11 Ability to design experiments for the investigation of complex engineering problems.
12. P12 Ability to conduct experiments, collect data, analyse results, and interpret findings for the investigation of complex engineering problems.
13. P13 Knowledge of the impacts of engineering practices on society, health and safety, the economy, sustainability, and the environment within the framework of the United Nations Sustainable Development Goals (SDGs).
14. P14 Awareness of the legal implications of engineering solutions within the framework of the United Nations Sustainable Development Goals (SDGs).
15. P15 Knowledge of ethical responsibility and adherence to the principles of professional engineering conduct.
16. P16 Awareness of acting impartially without discrimination in any matter and of being inclusive of diversity.
17. P17 Ability to work effectively as an individual.
18. P18 Ability to work effectively as a team member or leader in intra-disciplinary teams (face-to-face, remote, or hybrid).
19. P19 Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote, or hybrid).
20. P20 Ability to communicate effectively in spoken form on technical matters, taking into account the diverse characteristics of the target audience (such as education, language, and profession).
21. P21 Ability to communicate effectively in written form on technical matters, taking into account the diverse characteristics of the target audience (such as education, language, and profession).
22. P22 Knowledge of professional practices such as project management and economic feasibility analysis.
23. P23 Awareness of entrepreneurship and innovation.
24. P24 Ability for independent and lifelong learning.
25. P25 Ability to adapt to new and emerging technologies.
26. P26 Lifelong learning ability that includes the capacity to think critically about technological changes.

Po-Lo Matrix