Ordinary Differential Equations (MATH262) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Ordinary Differential Equations MATH262 4 0 0 4 6
Pre-requisite Course(s)
Course Language English N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer. This course is designed to enrich the knowledge of mathematics students in differential equations after calculus. As a replacement and enlargement of currently given Math 262 Differential Equations course, it is intended to present the subject being motivated from the basic mathematical concepts such as differentiation, integration, power series and to include further applications related to differential equations mostly used in mathematical problems. 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. express physical laws in the language of differential equations. solve these equations by modern techniques and interpret his results in terms of the original problem. solve differential equations using power series and Laplace transform methods. solve linear systems of differential equations by elimination and Laplace transform methods. First-order, higher-order linear ordinary differential equations, applications of first-order differential equations, series solutions of differential equations, Laplace transforms, linear systems of ordinary differential equations.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Introduction: Preliminaries, Solutions and Existence-Uniqueness Theorem pp. 1-12
2 First Order Equations: Separable, Linear and Homogeneous Equations pp. 13-40
3 Exact Equations and Integrating Factors, Substitutions. pp. 40-55
4 The Method of Isoclines. Further Applications: Geometrical Problems, Orthogonal and Oblique Trajectories. pp. 65-75
5 Higher Order Linear Ordinary Differential Equations : Basic Theory of Higher Order Linear Equations. pp. 87-98
6 Midterm
7 Reduction of Order Method, Homogeneous Constant Coefficient Equations. pp. 98-113
8 The Method of Undetermined Coefficients, Variation of Parameters Method, Cauchy-Euler Equations. pp. 113-128
9 Series Solutions of Ordinary Differential Equations : Power Series Solutions (Ordinary Point) pp. 169-197
10 Power Series Solutions (Regular-Singular Point) pp. 197-210
11 Power Series Solutions (Regular-Singular Point) (continued) pp. 210-221
12 Laplace Transforms : Basic Properties of the Laplace Transforms, Solution of Initial Value Problems. pp. 223-238
13 The Convolution Integral, Solutions of various Equations. pp. 238-255
14 System of Linear Ordinary Differential Equations : Solution of Systems of Linear Ordinary Differential Equations Using Simple Elimination pp. 257-286
15 Solution of Systems of Linear Ordinary Differential Equations Using Laplace Transform. pp. 292-301
16 Final Exam

Sources

Course Book 1. Lectures on Differential Equations, Yılmaz Akyıldız and Ali Yazıcı, ODTÜ, Matematik Vakfı 2. Differential Equations, Second Edition, by Shepley L. Ross, John Wiley and Sons, 1984 3. Advanced Engineering Mathematics, 8th Edition, by Erwin Kreyszig, John Wiley and Sons, 1998.

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 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

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 16 4 64
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 16 32
Prepration of Final Exams/Final Jury 1 20 20