COURSE INFORMATION Course Title: DIFFERENTIAL EQUATIONS

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 201	A	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)	Dr. Marsed Leti mleti@epoka.edu.al
Main Course Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	M.Sc. Bredli Plaku bplaku@epoka.edu.al , 08:30-16:30
Second Course 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
Study program: (the study for which this course is offered)	Bachelor in Civil Engineering (3 years)
Classroom and Meeting Time:	A-129 / 8:40-11:30
Code of Ethics:	Code of Ethics of EPOKA University Regulation of EPOKA University "On Student Discipline"
Attendance Requirement:	75%
Course Description:	First-order differential equations, second-order linear equations, Wronskian, 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:	This course equips students with a strong grasp of ordinary differential equations (ODEs) while highlighting their significance in civil engineering. Students will learn to identify ODE types and apply solving techniques. Through practical applications in civil engineering, including structural analysis, fluid dynamics, and environmental modelling, students will see how ODEs play a pivotal role in addressing real-world challenges within the field.

BASIC CONCEPTS OF THE COURSE

1	Differential Equation
2	Ordinary Differential Equation (ODE)
3	Partial Differential Equation (PDE)
4	Order of a Differential Equation
5	Initial Value Problem (IVP)
6	Boundary Value Problem (BVP)
7	Linear Differential Equation
8	Homogeneous Differential Equation
9	Non-homogeneous Differential Equation
10	Solution of a Differential Equation

COURSE OUTLINE

Week	Topics
1	Introduction to Differential Equations
2	Basic concepts and classification of differential equations
3	First Order Differential Equations: Part 1
4	First Order Differential Equations: Part 2
5	Second Order Differential Equations: Part 1
6	Second Order Differential Equations: Part 2
7	Laplace Transforms
8	Midterm Exam
9	Systems of Differential Equations
10	Series Solutions
11	Higher Order Differential Equations
12	BVPs and Fourier Series
13	Partial Differential Equations: Part 1
14	Partial Differential Equations: Part 2

Prerequisite(s):	• Calculus I • Calculus II • General Physics I • General Physics II
Textbook(s):	Elementary Differential Equations and Boundary Value Problems, by William E. Boyce and Richard C. DiPrima (10th Edition) / ISBN 978-1118157381
Additional Literature:	Paul’s Online Math Notes
Laboratory Work:	-
Computer Usage:	Optional
Others:	No

COURSE LEARNING OUTCOMES

1	Solve first-order linear and separable differential equations.
2	Apply first-order differential equations to model exponential growth and decay.
3	Solve second-order homogeneous and nonhomogeneous linear differential equations.
4	Master the Laplace transform technique for solving differential equations.
5	Apply Laplace transforms to analyze transient responses and stability of systems.
6	Solve systems of first-order linear differential equations and gain proficiency in matrix methods.
7	Develop power series solutions for differential equations.
8	Utilize series solutions to tackle problems involving boundary value problems.
9	Solve and apply higher-order linear differential equations with constant coefficients.
10	Understand the basics of partial differential equations (PDEs) and their classifications.

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

No	Program Competencies	Cont.
Bachelor in Civil Engineering (3 years) Program
1	an ability to apply knowledge of mathematics, science, and engineering	5
2	an ability to design a system, component, or process to meet desired needs	5
3	an ability to function on multidisciplinary teams	5
4	an ability to identify, formulate, and solve engineering problems	5
5	an understanding of professional and ethical responsibility	5
6	an ability to communicate effectively	4
7	the broad education necessary to understand the impact of engineering solutions in a global and societal context	4
8	a recognition of the need for, and an ability to engage in life long learning	4
9	a knowledge of contemporary issues	3
10	an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice	3
11	skills in project management and recognition of international standards and methodologies	3

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	1	10
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

CONCLUDING REMARKS BY THE COURSE LECTURER

I extend my best wishes to all of you for a successful and productive experience in this course. I look forward to seeing your growth and achievements as we embark on this academic journey together.