Faculty Of Engıneerıng
Industrıal Engıneerıng (Englısh)
Course Information
| DIFFERENTIAL EQUATIONS | |||||
|---|---|---|---|---|---|
| Code | Semester | Theoretical | Practice | National Credit | ECTS Credit |
| Hour / Week | |||||
| MAT203 | Spring | 4 | 0 | 4 | 6 |
| Prerequisites and co-requisites | |
|---|---|
| Language of instruction | English |
| Type | Required |
| Level of Course | Bachelor's |
| Lecturer | Assistant Professor Türker Ertem |
| Mode of Delivery | Face to Face |
| Suggested Subject | none |
| Professional practise ( internship ) | None |
| Objectives of the Course | The objectives of this course are to introduce the student with the concept of a differential equation, basic techniques for solving certain classes of differential equations, especially those which are linear, and making connections between the qualitative features of the equation and the solutions. Connections to problems from the physical world are emphasized. As well as ordinary differential equations, the course aims to introduce the students to certain partial differential equations. |
| Contents of the Course | First order equations and various applications. Higher order linear differential equations. Power series solutions. The Laplace transform. Solution of initial value problems. Systems of linear differential equations: Introduction Partial Differential Equations. |
Learning Outcomes of Course
| # | Learning Outcomes |
|---|---|
| 1 | To be able to classify differential equations and define their properties. |
| 2 | To be able to clearly solve and interpret some important types of differential equations. |
| 3 | To be able to apply the Laplace transform to solve differential equations. |
| 4 | To be able to use power series methods to solve differential equations. |
| 5 | To be able to solve linear differential equation systems with linear algebra information. |
| 6 | To be able to model some events such as oscillation of a spring, population dynamics using differential equations. |
Course Syllabus
| # | Subjects | Teaching Methods and Technics |
|---|---|---|
| 1 | I. Introduction 1.1 Some Basic Mathematical Models; Direction Fields 1.2 Solutions of Some Differential Equations 1.3 Classification of Differential Equations | lecturing, discussing, problem solving |
| 2 | II. First Order Differential Equations 2.1 Linear Equations; Methods of Integrating Factors 2.2 Separable Equations, Homogeneous Equations 2.6 Exact Equations and Integrating Factors 2.8 The Existence and Uniqueness Theorem | lecturing, discussing, problem solving |
| 3 | 2.4 Differences Between Linear and Nonlinear Equations 2.5 Autonomous Equations and Population Dynamics 2.7 Numerical Approximations: Euler’s Method | lecturing, discussing, problem solving |
| 4 | III. Second Order Linear Equations 3.1 Homogeneous Equations with Constant Coefficients 3.2 Fundamental Solutions of Linear Homogeneous Equations; the Wronskian 3.3 Complex Roots of the Characteristic Equation | lecturing, discussing, problem solving |
| 5 | 3.4 Repeated Roots; Reduction of Order 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients | lecturing, discussing, problem solving |
| 6 | 3.6 Variation of Parameters 3.7 Mechanical and Electrical Vibrations 3.8 Forced Vibrations | lecturing, discussing, problem solving |
| 7 | IV. Higher Order Linear Equations 4.1 General Theory of nth Order Linear Equations 4.2 Homogeneous Equations with Constant Coefficients 4.3 The Method of Undetermined Coefficients | lecturing, discussing, problem solving |
| 8 | V. Series Solutions of Differential Equations 5.2 Series Solution Near an Ordinary Point Part I 5.3 Series Solution Near an Ordinary Point Part II 5.4 Euler Equation, Regular Singular Points | lecturing, discussing, problem solving |
| 9 | 5.5 Series Solution Near a Regular Singular Point I 5.6 Series Solution Near a Regular Singular Point II | lecturing, discussing, problem solving |
| 10 | VI. The Laplace Transform 6.1 Definition of the Laplace Transform 6.2 Solution of Initial Value Problems 6.3 Step Functions | lecturing, discussing, problem solving |
| 11 | 6.4 Differential Equations with Discontinuous Forcing Functions 6.5 Impulse Functions 6.6 The Convolution Integral VII. Systems of Linear Equations 7.4 Basic Theory of Systems of First Order Linear Equations | lecturing, discussing, problem solving |
| 12 | 7.5 Homogeneous Linear Systems with Constant Coefficients 7.6 Complex Eigenvalues 7.7 Fundamental Matrices | lecturing, discussing, problem solving |
| 13 | 7.8 Repeated Eigenvalues 7.9 Nonhomogeneous Linear Systems X. Partial Differential Equations and Fourier Series 10.1 Two-point Boundary Value Problems | lecturing, discussing, problem solving |
| 14 | 10.2 Fourier series 10.3 The Fourier Convergence Theorem 10.4 Even and Odd Functions 10.5 Separation of Variables; Heat Conduction in a Rod | lecturing, discussing, problem solving |
| 15 | ||
| 16 | Final Exam |
Course Syllabus
| # | Material / Resources | Information About Resources | Reference / Recommended Resources |
|---|---|---|---|
| 1 | W. E. Boyce, R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems | John Wiley & Sons, Inc. | |
| 2 | W. F. Trench, A. G. Cowles, Elementary Differential Equations | Brooks Cole | |
| 3 | Wei-Chau Xie Differential Equations for Engineers | Cambridge University Press |
Method of Assessment
| # | Weight | Work Type | Work Title |
|---|---|---|---|
| 1 | 20% | Mid-Term Exam | Mid-Term Exam |
| 2 | 80% | Final Exam | Final Exam |
Relationship between Learning Outcomes of Course and Program Outcomes
| # | Learning Outcomes | Program Outcomes | Method of Assessment |
|---|---|---|---|
| 1 | To be able to classify differential equations and define their properties. | 1͵11 | 1͵2 |
| 2 | To be able to clearly solve and interpret some important types of differential equations. | 1͵11 | 1͵2 |
| 3 | To be able to apply the Laplace transform to solve differential equations. | 1͵11 | 1͵2 |
| 4 | To be able to use power series methods to solve differential equations. | 1͵11 | 1͵2 |
| 5 | To be able to solve linear differential equation systems with linear algebra information. | 1͵11 | 1͵2 |
| 6 | To be able to model some events such as oscillation of a spring, population dynamics using differential equations. | 1͵11 | 1͵2 |
Work Load Details
| # | Type of Work | Quantity | Time (Hour) | Work Load |
|---|---|---|---|---|
| 1 | Course Duration | 14 | 4 | 56 |
| 2 | Course Duration Except Class (Preliminary Study, Enhancement) | 14 | 5 | 70 |
| 3 | Presentation and Seminar Preparation | 0 | 0 | 0 |
| 4 | Web Research, Library and Archival Work | 0 | 0 | 0 |
| 5 | Document/Information Listing | 0 | 0 | 0 |
| 6 | Workshop | 0 | 0 | 0 |
| 7 | Preparation for Midterm Exam | 1 | 8 | 8 |
| 8 | Midterm Exam | 1 | 2 | 2 |
| 9 | Quiz | 0 | 0 | 0 |
| 10 | Homework | 0 | 0 | 0 |
| 11 | Midterm Project | 0 | 0 | 0 |
| 12 | Midterm Exercise | 0 | 0 | 0 |
| 13 | Final Project | 0 | 0 | 0 |
| 14 | Final Exercise | 0 | 0 | 0 |
| 15 | Preparation for Final Exam | 1 | 12 | 12 |
| 16 | Final Exam | 1 | 2 | 2 |
| 150 | ||||