Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
4MATH212Differential Equations3+0+03629.07.2024
Course Details
Language of Instruction English
Level of Course Unit Bachelor's Degree
Department / Program Civil Engineering
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course To create the necessary infrastructure for the solution of differential equations in engineering courses and applications.
Course Content Classification of differential equations, solutions, initial value and boundary value problems, existence of solutions, First-Order Equations for which exact solutions are obtainable, Solution methods of high order linear differential equations, Electric circuit problems, Laplace Transform;definitions, theorems, examples, solution of linear, constant-coefficient initial-value problems, theorems, convolution integral and theorem, Impulse function and response, system function. Systems of Linear Differential Equations, Solutions of systems of linear differential equations.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator Associate Prof.Dr. Ece Yetkin Çelikel
Name of Lecturers None
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Lecture notes
Course Notes Fundamentals of Differential Equations, Global Edition, 9/E, Nagle, Saff, Snider, Pearson.

Course Category
Mathematics and Basic Sciences %60
Engineering %40

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Mid-terms 1 % 40
Final examination 1 % 60
Total
2
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Course Duration 13 3 39
Hours for off-the-c.r.stud 14 7 98
Mid-terms 1 2 2
Final examination 1 2 2
Total Work Load   Number of ECTS Credits 4,5 141

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Recognizes basic DE types and grasps basic definitions, the meaning of solution functions, the initial-value problem concept.
2 Recognize 1st order equation types for which exact solutions are available, and should be able to solve them; separable, linear, exact and those reducible to them.
3 Understands solution character of homogeneous and nonhomogeneous linear DE’s, the relation between them, and solves linear DE’s with constant coefficients by two methods; (i) applying the method of undetermined coefficients, and (ii) using the method of variation of parameters.
4 Analyzes electrical circuits by solving linear DE’s with constant coefficients.
5 Grasps definitions of Laplace and inverse Laplace transforms, their basic properties, performs simple transform calculations and solves linear DE’s with constant coefficients by means of Laplace transform.
6 Understands the concepts of impulse function and response, system function, convolution integral and convolution t heorem of Laplace transform.
7 Solves systems of linear DE’s with constant coefficients in Laplace domain and by means of the matrix exponential and understands the equivalance of the two.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Classification of differential equations, solutions, initial value and boundary value problems, existence of solutions.
2 Separable differential equations and solution methods
3 Finding Integrating factor
4 Homogeneous differential equations and solution methods
5 Linear differential equations and solution methods.
6 Bernoulli differential equations and solution methods.
7 Riccatti differential equations and solution methods.
8 Midterm exam
9 Solution methods of high order linear differential equations.
10 Laplace Transform; solution of linear, constant-coefficient initial-value problems.
11 Laplace Tansform; theorems, convolution integral and theorem.
12 Nonhomogeneous Equations, Method of Undetermined Coefficients
13 Method of Variation of Parameters, Cauchy-Euler Equation
14 Review

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11
All 5 5
C1 5 5
C2 5 5
C3 5 5
C4 5 5
C5 5 5
C6 5 5
C7 5 5

  Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant