COURSE INFORMATION Course Title: DIFFERENTIAL EQUATIONS

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 201	C	3	3	0	0	3	5

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Shkëlqim Hajrulla
Second Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Classroom and Meeting Time:
Course Description:	First-order differential equations, second-order linear equations, change of parameters, homogeneous and non-homogeneous equations, series solutions, Laplace transform, systems of first-order linear equations, boundary value problems, Fourier series.
Course Objectives:	The students will demonstrate an understanding of the ordinary differential equations, will be able to determine their types and apply the appropriate solving techniques. To illustrate several of the many applications of differential equations.

COURSE OUTLINE

Week	Topics
1	Basic concepts and classification of differential equations: ordinary and partial differential equations.
2	Application of ordinary and partial differential equations.
3	First order linear equations: Separable and homogeneous types. Exact linear and Bernoulli types.
4	Applications of first order differential equations. Exercises
5	Linear homogeneous second order differential equations with constant coefficients.
6	Linear non-homogeneous second order differential equations with constant coefficients. The undetermined coefficient method.
7	Application. The Wronskian, the variation of parameters method.
8	Midterm exam.
9	Linear non-homogeneous differential equations. The variation of parameters method.
10	Applications of second order differential equations. Mechanical and electrical vibrations.
11	Higher order linear differential equations.
12	Introduction to Laplace transforms and inverse Laplace transforms.
13	Solving Initial value problems using Laplace and inverse Laplace transforms.
14	General review.

Prerequisite(s):	Calculus I, II
Textbook:	“Elementary Differential Equations” (10-th ed.) W. Boyce R. DiPrima
Other References:
Laboratory Work:
Computer Usage:
Others:	No

COURSE LEARNING OUTCOMES

1	To create and analyze mathematical models based on ordinary differential equations.
2	To be able to determine the type of a given differential equation, determine the existence of a solution and if a solution can be obtained, select the appropriate analytical technique for finding the solution.
3	In general to develop skills in modeling real-life problems using differential equations.
4	Solve initial value problems using Laplace transforms.

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Bachelor in Computer Engineering (3 years) Program
1	Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice.	5
2	Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations.	5
3	Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects.	5
4	Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies.	4
5	Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions.	4
6	Ability of identifying the potential resources for information or knowledge regarding a given engineering issue.	4
7	The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence.	4
8	Ability for effective oral and official communication skills in foreign language.	3
9	Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology.	5
10	Engineering graduates with well-structured responsibilities in profession and ethics.	3
11	Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues.	2
12	Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity.	2

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	2	5
Midterm Exam(s)	1	35
Quiz	2	5
Final Exam	1	45
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	3	48
Hours for off-the-classroom study (Pre-study, practice)	16	1	16
Mid-terms	1	16	16
Assignments	1	5	5
Final examination	1	25	25
Other	3	5	15
Total Work Load:			125
Total Work Load/25(h):			5
ECTS Credit of the Course:			5