ECTS - Ordinary Differential Equations
Ordinary Differential Equations (MATH262) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Ordinary Differential Equations | MATH262 | 4. Semester | 4 | 0 | 0 | 4 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH251 |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | 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. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | 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 |
|---|---|
| Other Sources | 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
| 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 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and 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 | ||||
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 | 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 |
| Total Workload | 116 | ||