Course Detail
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| DIFFERENTIAL EQUATIONS | - | Fall Semester | 2+0 | 2 | 4 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Özge BİÇER ÖDEMİŞ |
| 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 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||
| 2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||
| 3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | ||||||
| 4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | X | |||||
| 5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | X | |||||
| 6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | X | |||||
| 7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | ||||||
| 8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | ||||||
| 9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||
| 10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||
| 11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | ||||||
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 | - | Fall Semester | 2+0 | 2 | 4 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Özge BİÇER ÖDEMİŞ |
| 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 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||
| 2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||
| 3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | ||||||
| 4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | X | |||||
| 5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | X | |||||
| 6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | X | |||||
| 7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | ||||||
| 8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | ||||||
| 9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||
| 10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||
| 11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 30 | |
| Rate of Final Exam to Success | 70 | |
| Total | 100 | |