# Differential Equations (MATH276) Ders Detayları

Course Name Corse Code Dönemi Lecture Hours Uygulama Saati Lab Hours Credit ECTS
Differential Equations MATH276 4. Semester 4 0 0 4 6
Pre-requisite Course(s)
Math 152 (Calculus II) or Math158 (Extended Calculus II)
Course Language İngilizce Service Courses Taken From Other Departments Lisans 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

Requirements Number Percentage of Grade
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

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

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Accumulated knowledge on mathematics, science and mechatronics engineering; an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. X
2 An ability to differentiate, identify, formulate, and solve complex engineering problems; an ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. X
3 An ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; an ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions may include economics, environment, sustainability, producibility, ethics, human health, social and political problems.)
4 An ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; an ability to use information and communications technologies effectively.
5 An ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies.
6 An ability to work effectively on single disciplinary and multi-disciplinary teams; an ability for individual work; ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines. X
7 An ability to express creative and original concepts and ideas effectively in Turkish and English language, oral and written, and technical drawings.
8 An ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; consciousness on the necessity of improvement and sustainability as a result of life-long learning; monitoring the developments on science and technology; awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation.
9 Consciousness on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself.
10 A knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project.
11 Knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; consciousness on these issues; awareness of legal results of engineering solutions.
12 Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions. X
13 Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planing, improving or changing the norms with a criticism.

### ECTS/Workload Table

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
Total Workload 86