Course Detail
Course Description
Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|
DIFFERENTIAL EQUATIONS | COE2114258 | Fall Semester | 2+0 | 2 | 4 |
Prerequisites Courses | |
Recommended Elective Courses | |
Language of Course | English |
Course Level | First Cycle (Bachelor's Degree) |
Course Type | Required |
Course Coordinator | Assist.Prof. Cihan Bilge KAYASANDIK |
Name of Lecturer(s) | Assist.Prof. Cihan Bilge KAYASANDIK, Assist.Prof. Seçil TUNALI ÇIRAK |
Assistant(s) | |
Aim | To provide the recognition of differential equations and to give solution techniques and to give also its applications for the study of Engineering. To provide supports on studies and researches in the area of Engineering. |
Course Content | This course contains; Preliminaries/Differential Equations,Definitions and Terminology, Initial-Value Problems ,Methods of Solving First Order Differential Equations: Separable Differential Equations,Linear Differential Equations,Exact Differential Equations, Making non-exact Differential Equations to Exact,Solutions by Substitutions ,Differential Equations as Mathematical Models, Linear Models ,Preliminaries: Higher Order Linear Differential Equations,Methods of Solving Higher Order Linear Differential Equations: Reduction of Order,Homogeneous Linear Equations with Constant Coefficients,Undetermined Coefficients—Superposition and Annihilator Approaches,Variation of Parameters and Cauchy-Euler Differential Equations,Definition of the Laplace Transform, Inverse Transforms,Transforms of Derivatives and Solving Initial Value Problems from Laplace Transform. |
Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
2.Apply the methods for solving first-order differential equations. | 12, 14, 6, 9 | A |
1. Recognize the classification of differential equations, solutions of differential equations, systems of differential equations, initial value problems and apply Existence and Uniqueness Theorem for first-order differential equations. | 12, 14, 6, 9 | A |
3. Recognize and solve differential equations as mathematical models and higher-order linear differential equations and apply Existence and Uniqueness Theorem for higher-order equations. | 12, 14, 6, 9 | A |
4. Recognize linearly dependent and independent solutions and Wronskian and apply the methods for solving higher-order linear differential equations. | 12, 14, 6, 9 | A |
5. Solve Cauchy-Euler differential equations and calculate initial value problems by Laplace transforms. | 12, 14, 6, 9 | A |
Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 6: Experiential Learning, 9: Lecture Method |
Assessment Methods: | A: Traditional Written Exam |
Course Outline
Order | Subjects | Preliminary Work |
---|
1 | Preliminaries/Differential Equations | Book Chapter 1.1 |
2 | Definitions and Terminology, Initial-Value Problems | Book Chapters 1.1, 1.2 |
3 | Methods of Solving First Order Differential Equations: Separable Differential Equations | Book Chapter 2.2 |
4 | Linear Differential Equations | Book Chapter 2.3 |
5 | Exact Differential Equations, Making non-exact Differential Equations to Exact | Book Chapter 2.4 |
6 | Solutions by Substitutions | Book Chapter 2.5 |
7 | Differential Equations as Mathematical Models, Linear Models | Book Chapters 1.3, 3.1 |
8 | Preliminaries: Higher Order Linear Differential Equations | Book Chapter 4.1 |
9 | Methods of Solving Higher Order Linear Differential Equations: Reduction of Order | Book Chapter 4.2 |
10 | Homogeneous Linear Equations with Constant Coefficients | Book Chapter 4.3 |
11 | Undetermined Coefficients—Superposition and Annihilator Approaches | Book Chapters 4.4, 4.5 |
12 | Variation of Parameters and Cauchy-Euler Differential Equations | Book Chapters 4.6, 4.7 |
13 | Definition of the Laplace Transform, Inverse Transforms | Book Chapters 7.1, 7.2 |
14 | Transforms of Derivatives and Solving Initial Value Problems from Laplace Transform | Book Chapter 7.2 |
Resources |
Dennis G. Zill - A First Course in Differential Equations with Modeling Applications 11th Edition. |
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications |
No | Program Qualification | Contribution Level |
1 | 2 | 3 | 4 | 5 |
1 | 1. An ability to apply knowledge of mathematics, science, and engineering | | | | X | |
2 | 2. An ability to identify, formulate, and solve engineering problems | | | X | | |
3 | 3. An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability | | | | | |
4 | 4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | | | X | | |
5 | 5. An ability to design and conduct experiments, as well as to analyze and interpret data | | | X | | |
6 | 6. An ability to function on multidisciplinary teams | | | | X | |
7 | 7. An ability to communicate effectively | | | | | |
8 | 8. A recognition of the need for, and an ability to engage in life-long learning | | | | | |
9 | 9. An understanding of professional and ethical responsibility | | | | | |
10 | 10. A knowledge of contemporary issues | | | | | |
11 | 11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context | | | | | |
Assessment Methods
Contribution Level | Absolute Evaluation |
Rate of Midterm Exam to Success | | 30 |
Rate of Final Exam to Success | | 70 |
Total | | 100 |
ECTS / Workload Table |
Activities | Number of | Duration(Hour) | Total Workload(Hour) |
Course Hours | 14 | 3 | 42 |
Guided Problem Solving | 14 | 1 | 14 |
Resolution of Homework Problems and Submission as a Report | 14 | 3 | 42 |
Term Project | 0 | 0 | 0 |
Presentation of Project / Seminar | 0 | 0 | 0 |
Quiz | 0 | 0 | 0 |
Midterm Exam | 6 | 2 | 12 |
General Exam | 6 | 2 | 12 |
Performance Task, Maintenance Plan | 0 | 0 | 0 |
Total Workload(Hour) | 122 |
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(122/30) | 4 |
ECTS of the course: 30 hours of work is counted as 1 ECTS credit. |
Detail Informations of the Course
Course Description
Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|
DIFFERENTIAL EQUATIONS | COE2114258 | Fall Semester | 2+0 | 2 | 4 |
Prerequisites Courses | |
Recommended Elective Courses | |
Language of Course | English |
Course Level | First Cycle (Bachelor's Degree) |
Course Type | Required |
Course Coordinator | Assist.Prof. Cihan Bilge KAYASANDIK |
Name of Lecturer(s) | Assist.Prof. Cihan Bilge KAYASANDIK, Assist.Prof. Seçil TUNALI ÇIRAK |
Assistant(s) | |
Aim | To provide the recognition of differential equations and to give solution techniques and to give also its applications for the study of Engineering. To provide supports on studies and researches in the area of Engineering. |
Course Content | This course contains; Preliminaries/Differential Equations,Definitions and Terminology, Initial-Value Problems ,Methods of Solving First Order Differential Equations: Separable Differential Equations,Linear Differential Equations,Exact Differential Equations, Making non-exact Differential Equations to Exact,Solutions by Substitutions ,Differential Equations as Mathematical Models, Linear Models ,Preliminaries: Higher Order Linear Differential Equations,Methods of Solving Higher Order Linear Differential Equations: Reduction of Order,Homogeneous Linear Equations with Constant Coefficients,Undetermined Coefficients—Superposition and Annihilator Approaches,Variation of Parameters and Cauchy-Euler Differential Equations,Definition of the Laplace Transform, Inverse Transforms,Transforms of Derivatives and Solving Initial Value Problems from Laplace Transform. |
Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
2.Apply the methods for solving first-order differential equations. | 12, 14, 6, 9 | A |
1. Recognize the classification of differential equations, solutions of differential equations, systems of differential equations, initial value problems and apply Existence and Uniqueness Theorem for first-order differential equations. | 12, 14, 6, 9 | A |
3. Recognize and solve differential equations as mathematical models and higher-order linear differential equations and apply Existence and Uniqueness Theorem for higher-order equations. | 12, 14, 6, 9 | A |
4. Recognize linearly dependent and independent solutions and Wronskian and apply the methods for solving higher-order linear differential equations. | 12, 14, 6, 9 | A |
5. Solve Cauchy-Euler differential equations and calculate initial value problems by Laplace transforms. | 12, 14, 6, 9 | A |
Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 6: Experiential Learning, 9: Lecture Method |
Assessment Methods: | A: Traditional Written Exam |
Course Outline
Order | Subjects | Preliminary Work |
---|
1 | Preliminaries/Differential Equations | Book Chapter 1.1 |
2 | Definitions and Terminology, Initial-Value Problems | Book Chapters 1.1, 1.2 |
3 | Methods of Solving First Order Differential Equations: Separable Differential Equations | Book Chapter 2.2 |
4 | Linear Differential Equations | Book Chapter 2.3 |
5 | Exact Differential Equations, Making non-exact Differential Equations to Exact | Book Chapter 2.4 |
6 | Solutions by Substitutions | Book Chapter 2.5 |
7 | Differential Equations as Mathematical Models, Linear Models | Book Chapters 1.3, 3.1 |
8 | Preliminaries: Higher Order Linear Differential Equations | Book Chapter 4.1 |
9 | Methods of Solving Higher Order Linear Differential Equations: Reduction of Order | Book Chapter 4.2 |
10 | Homogeneous Linear Equations with Constant Coefficients | Book Chapter 4.3 |
11 | Undetermined Coefficients—Superposition and Annihilator Approaches | Book Chapters 4.4, 4.5 |
12 | Variation of Parameters and Cauchy-Euler Differential Equations | Book Chapters 4.6, 4.7 |
13 | Definition of the Laplace Transform, Inverse Transforms | Book Chapters 7.1, 7.2 |
14 | Transforms of Derivatives and Solving Initial Value Problems from Laplace Transform | Book Chapter 7.2 |
Resources |
Dennis G. Zill - A First Course in Differential Equations with Modeling Applications 11th Edition. |
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications |
No | Program Qualification | Contribution Level |
1 | 2 | 3 | 4 | 5 |
1 | 1. An ability to apply knowledge of mathematics, science, and engineering | | | | X | |
2 | 2. An ability to identify, formulate, and solve engineering problems | | | X | | |
3 | 3. An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability | | | | | |
4 | 4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | | | X | | |
5 | 5. An ability to design and conduct experiments, as well as to analyze and interpret data | | | X | | |
6 | 6. An ability to function on multidisciplinary teams | | | | X | |
7 | 7. An ability to communicate effectively | | | | | |
8 | 8. A recognition of the need for, and an ability to engage in life-long learning | | | | | |
9 | 9. An understanding of professional and ethical responsibility | | | | | |
10 | 10. A knowledge of contemporary issues | | | | | |
11 | 11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context | | | | | |
Assessment Methods
Contribution Level | Absolute Evaluation |
Rate of Midterm Exam to Success | | 30 |
Rate of Final Exam to Success | | 70 |
Total | | 100 |
Numerical Data
Ekleme Tarihi: 09/10/2023 - 10:50Son Güncelleme Tarihi: 09/10/2023 - 10:51
×- A-Z Programs
- Undergraduate
- Graduate
- Academic Calendar
- Double Major & Minor Programs
- Erasmus
- Prospective Students
- Registration
- Re-Enrolment
- Fees
- Directorate of Registrar’s Office
- FAQ
- Accommodation
- Scholarships
- Lateral and Vertical Transfer
- Summer School
- Preparation
- Transportation