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
Course Type N/A
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Question and Answer.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives 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).
Course Learning Outcomes 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.
Course Content 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
Other Sources 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
Percentage of Final Work 40
Total 100

Course Category

Core Courses X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Adequate knowledge in mathematics, science and subjects specific to the Materials Engineering; the ability to apply theoretical and practical knowledge of these areas to solve complex engineering problems and to model and solve of materials systems X
2 Understanding of science and engineering principles related to the structures, properties, processing and performance of Materials systems
3 Ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose X
4 Ability to design and choose proper materials for a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design and materials selection methods for this purpose X
5 Ability to develop, select and utilize modern techniques and tools essential for the analysis and solution of complex problems in Materails Engineering applications; the ability to utilize information technologies effectively X
6 Ability to design and conduct experiments, collect data, analyse and interpret results using statistical and computational methods for complex engineering problems or research topics specific to Materials Engineering X
7 Ability to work effectively in inter/inner disciplinary teams; ability to work individually
8 Effective oral and written communication skills in Turkish; knowlegde of at least one foreign language; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions
9 Recognition of the need for lifelong learning; the ability to access information; follow recent developments in science and technology with continuous self-development
10 Ability to behave according to ethical principles, awareness of professional and ethical responsibility; knowledge of standards used in engineering applications
11 Knowledge on business practices such as project management, risk management and change management; awareness in entrepreneurship and innovativeness; knowledge of sustainable development
12 Knowledge of the effects of Materials Engineering applications on the universal and social dimensions of health, environment and safety, knowledge of modern age problems reflected on engineering; awareness of legal consequences of engineering solutions

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