# Differential Equations (MATH276) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Differential Equations MATH276 4 0 0 4 6
Pre-requisite Course(s)
Math 152 (Calculus II) or Math158 (Extended Calculus II)
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer. The course is specifically designed for engineering students as this material is applicable to many fields. The purpose of this course is to provide an understanding of ordinary differential equations (ODE's), systems of ODE’s and to give methods for solving them. This course provides also a preliminary information about partial differential equations (PDE's). The students who succeeded in this course; be able to determine the existence and uniqueness of a solution and select the appropriate method for finding the solution. use appropriate methods for solution of first, second and higher order ODE’s. solve differential equations using power series and Laplace transform methods. solve linear systems of ODE’s by using elimination and Laplace transform methods. find Fourier series expansions of periodic functions. solve some elementary PDE’s such as heat, wave and Laplace equations by the method of separation of variables technique. First-order, higher-order linear ordinary differential equations, series solutions of differential equations, Laplace transforms, linear systems of ordinary differential equations, Fourier analysis and partial differential equations.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 First Order Ordinary Differential Equations: Preliminaries, pp. 1-5 pp. 1-5
2 Solutions, Existence-Uniqueness Theorem, Separable Equations, Linear Equations. pp. 5-27
3 Bernoulli Equations, Homogeneous Equations, Exact Equations and Integrating Factors. pp. 27-49
4 Substitutions, Higher Order Linear Ordinary Differential Equations: Basic Theory of Higher Order Linear Equations pp. 49-98
5 Reduction of Order Method, Homogeneous Constant Coefficient Equations pp. 98-113
6 Undetermined Coefficients Method, Variation of Parameters Method pp. 113-125
7 Midterm
8 Cauchy-Euler Equations, Series Solutions of Ordinary Differential Equations: Power Series Solutions (Ordinary Point) pp. 125-191
9 Power Series Solutions (Ordinary Point) (continued), Power Series Solutions (Regular-Singular Point) pp. 191-221
10 Laplace Transforms: Basic Properties of the Laplace Transforms, Convolution pp. 223-244
11 Solution of Differential Equations by the Laplace Transforms pp. 244-255
12 Systems of Linear Ordinary Differential Equations: Solution of Systems of Linear ODE Using Elimination pp. 257-291
13 Solution of Systems of Linear ODE Using Laplace Transforms pp. 292-306
14 Fourier Analysis: Odd and Even Functions, Periodic Functions, Trigonometric Series, Fourier Series and Fourier Sine and Fourier Cosine Series for Functions of Any Period pp. 319-333
15 Partial Differential Equations: Separation of Variables, Solution of Heat, Wave and Laplace Equations pp. 307-319 and pp. 333-335
16 Final Exam

### Sources

Course Book 1. Lectures on Differential Equations, E. Akyıldız, Y. Akyıldız, Ş.Alpay, A. Erkip and A.Yazıcı,, Matematik Vakfı Yayın No:1 2. Differential Equations, 2nd Edition, Shepley L. Ross, John Wiley and Sons, 1984. 3. Advanced Engineering Mathematics, 8th Edition, Erwin Kreyszig, John Wiley and Sons, 1998. 4. Ordinary Differential Equations Problem Book with Solutions, Rajeh Eid, Atılım University Publications 16, Ankara, Atılım University, 2005.

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 60
Final Exam/Final Jury 1 40
Toplam 3 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 An ability to apply knowledge of mathematics, science and engineering to Industrial Engineering; an ability to apply theoretical and practical knowledge to model and solve engineering problems. X
2 An ability to identify, formulate and solve complex engineering problems; an ability to select and apply proper analysis and modeling methods. X
3 An ability to design a complex system, process, tool or component to meet desired needs within realistic constraints; an ability to apply modern design.
4 An ability to develop, select and put into practice techniques, skills and modern engineering tools necessary for engineering practice; an ability to use information technology effectively.
5 An ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or disciplinary research topics. X
6 An ability to work individually, on teams, and/or on multidisciplinary teams. X
7 Ability to communicate effectively in Turkish orally and in writing; knowledge of at least one foreign language; effective report writing and understand written reports, preparing design and production reports, making effective presentations, giving and receiving clear and understandable instruction.
8 A recognition of the need for, and an ability to engage in life-long learning; an ability to use information-seeking tools and to follow the improvements in science and technology.
9 An ability to behave according to the ethical principles, an understanding of professional and ethical responsibility. Information on standards used in industrial engineering applications.
10 Knowledge of business applications such as project management, risk management and change management. A recognition of entrepreneurship, innovativeness. Knowledge of sustainable improvement.
11 Information on the effects of industrial engineering practices on health, environment and security in universal and societal dimensions and the information on the problems of the in the field of engineering of the era. Awareness of the legal consequences of engineering solutions.
12 An ability to design, development, implementation and improvement of integrated systems that include human, materials, information, equipment and energy.
13 Knowlede on appropriate analytical, computational and experimental methods to provide system integration.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 4 56
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 10 10