Industrial Engineering
Course Details
KTO KARATAY UNIVERSITY
Mühendislik ve Doğa Bilimleri Fakültesi
Programme of Industrial Engineering
Course Details
Mühendislik ve Doğa Bilimleri Fakültesi
Programme of Industrial Engineering
Course Details
| Course Code | Course Name | Year | Period | Semester | T+A+L | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| 88600007 | Differential Equations | 2 | Autumn | 3 | 4+0+0 | 4 | 5 |
| Course Type | Compulsory |
| Course Cycle | Bachelor's (First Cycle) (TQF-HE: Level 6 / QF-EHEA: Level 1 / EQF-LLL: Level 6) |
| Course Language | Turkish |
| Methods and Techniques | - |
| Mode of Delivery | Face to Face |
| Prerequisites | - |
| Coordinator | Prof. Murat DARÇIN |
| Instructor(s) | Asst. Prof. Sümeyye BAKIM |
| Instructor Assistant(s) | - |
Course Content
Differential Equations, The Definition and Classification, Order and Degree of Differential Equations, Solutions of Differential Equations: The Integral Curve, İmplicit-Explicit Solution, Particular Solution, The General Solution, Singular Solution, İnitial Value Problem. Derivation of Differential Equations. First Order Differantial equations
Objectives of the Course
Develop mathematical thinking. Mathematics, physics and engineering to solve problems encountered in.
Contribution of the Course to Field Teaching
| Basic Vocational Courses | |
| Specialization / Field Courses | |
| Support Courses | X |
| Transferable Skills Courses | |
| Humanities, Communication and Management Skills Courses |
Relationships between Course Learning Outcomes and Program Outcomes
| Relationship Levels | ||||
| Lowest | Low | Medium | High | Highest |
| 1 | 2 | 3 | 4 | 5 |
| # | Program Learning Outcomes | Level |
|---|---|---|
| P1 | Sufficient knowledge of mathematics, science and Industrial Engineering discipline-specific subjects; Ability to use theoretical and applied knowledge in these fields to solve complex Industrial Engineering problems | 5 |
Course Learning Outcomes
| Upon the successful completion of this course, students will be able to: | |||
|---|---|---|---|
| No | Learning Outcomes | Outcome Relationship | Measurement Method ** |
| O1 | Diferansiyel denklemleri sınıflandırabilir. | P.1.131 | 1 |
| O2 | Birinci mertebeden diferansiyel denklemleri çözümleyebilir. | P.1.132 | 1 |
| O3 | İntegrasyon çarpanını hesaplayabilir. | P.1.133 | 1 |
| O4 | Lineer diferansiyel denklemlerin mühendislik uygulamalarını çözümleyebilir. | P.1.134 | 1 |
| O5 | Diferansiyel denklemleri Laplace dönüşümleri kullanarak çözümleyebilir. | P.1.135 | 1 |
| ** Written Exam: 1, Oral Exam: 2, Homework: 3, Lab./Exam: 4, Seminar/Presentation: 5, Term Paper: 6, Application: 7 | |||
Weekly Detailed Course Contents
| Week | Topics |
|---|---|
| 1 | Differential Equations, The Definition and Classification, Order and Degree of Differential Equations,Solutions of Differential Equations |
| 2 | First order Differantial equations: Separable Differential Equations, Variables that can be converted Separable Differential Equations Differential Equations, Homogeneous Functions, Homogeneous Differential Equations, Becomes homogeneous differential equations that can be converted |
| 3 | Linear Equations, Method of Integrating Factors, Method of Variation Parameters |
| 4 | Bernoulli Equations, Exact Equtions,The Method of İntegrating Factors Based on a Single Variable. |
| 5 | Riccati Equations. First-Order Higher-Order Differential Equations: Clairaut and Lagrange's Equations. |
| 6 | Second Order Linear Equations: Homogeneous Equations with Constant Coefficients, Characteristic Equation, Fundamental Solutions of Linear Homogeneous Equations, Linear independence and Wronskian Determinant. |
| 7 | Complex Roots of The Characteristic Equation, Real Roots, Repeated Roots, Reduction of Order, Nonhomogeneous Equations |
| 8 | Ara Sınav |
| 9 | Method of Undetermined Coefficients, Method of Variation Parameters |
| 10 | Higher Order Linear Equations: General Theory of nth Order Linear Equations, The Homogeneous Equation and its solution. The Nonhomogeneous Equation, Particiluar Solutions, General Solutions, Linear İndependence and Wronskian Determinant, Homogeneous Equations with Constant Coefficients, Characteristic Polynomial, Characteristic Equation, Real and Unequal Roots, Complex Roots, Repeated Roots |
| 11 | Higher Order Linear Equations: General Theory of nth Order Linear Equations, The Homogeneous Equation and its solution. The Nonhomogeneous Equation, Particiluar Solutions, General Solutions, Linear İndependence and Wronskian Determinant, Homogeneous Equations with Constant Coefficients, Characteristic Polynomial, Characteristic Equation, Real and Unequal Roots, Complex Roots, Repeated Roots |
| 12 | Higher Order Linear Equations: General Theory of nth Order Linear Equations, The Homogeneous Equation and its solution. The Nonhomogeneous Equation, Particiluar Solutions, General Solutions, Linear İndependence and Wronskian Determinant, Homogeneous Equations with Constant Coefficients, Characteristic Polynomial, Characteristic Equation, Real and Unequal Roots, Complex Roots, Repeated Roots |
| 13 | Higher Order Linear Equations: General Theory of nth Order Linear Equations, The Homogeneous Equation and its solution. The Nonhomogeneous Equation, Particiluar Solutions, General Solutions, Linear İndependence and Wronskian Determinant, Homogeneous Equations with Constant Coefficients, Characteristic Polynomial, Characteristic Equation, Real and Unequal Roots, Complex Roots, Repeated Roots |
| 14 | Higher Order Linear Equations: General Theory of nth Order Linear Equations, The Homogeneous Equation and its solution. The Nonhomogeneous Equation, Particiluar Solutions, General Solutions, Linear İndependence and Wronskian Determinant, Homogeneous Equations with Constant Coefficients, Characteristic Polynomial, Characteristic Equation, Real and Unequal Roots, Complex Roots, Repeated Roots |
| 15 | Higher Order Linear Equations: General Theory of nth Order Linear Equations, The Homogeneous Equation and its solution. The Nonhomogeneous Equation, Particiluar Solutions, General Solutions, Linear İndependence and Wronskian Determinant, Homogeneous Equations with Constant Coefficients, Characteristic Polynomial, Characteristic Equation, Real and Unequal Roots, Complex Roots, Repeated Roots |
Textbook or Material
| Resources | Schaum's outline, Differential equation, McGraw-Hill Professional; 4. basım (16 Nisan 2014), Richard Bronson , Gabriel Costa |
Evaluation Method and Passing Criteria
| In-Term Studies | Quantity | Percentage |
|---|---|---|
| Attendance | - | - |
| Laboratory | - | - |
| Practice | - | - |
| Field Study | - | - |
| Course Specific Internship (If Any) | - | - |
| Homework | - | - |
| Presentation | - | - |
| Projects | - | - |
| Seminar | - | - |
| Quiz | - | - |
| Listening | - | - |
| Midterms | 1 | 40 (%) |
| Final Exam | 1 | 60 (%) |
| Total | 100 (%) | |
ECTS / Working Load Table
| Quantity | Duration | Total Work Load | |
|---|---|---|---|
| Course Week Number and Time | 14 | 4 | 56 |
| Out-of-Class Study Time (Pre-study, Library, Reinforcement) | 14 | 3 | 42 |
| Midterms | 1 | 20 | 20 |
| Quiz | 0 | 0 | 0 |
| Homework | 0 | 0 | 0 |
| Practice | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Workshop | 0 | 0 | 0 |
| Presentation/Seminar Preparation | 0 | 0 | 0 |
| Fieldwork | 0 | 0 | 0 |
| Final Exam | 1 | 32 | 32 |
| Other | 0 | 0 | 0 |
| Total Work Load: | 150 | ||
| Total Work Load / 30 | 5 | ||
| Course ECTS Credits: | 5 | ||
Course - Learning Outcomes Matrix
| Relationship Levels | ||||
| Lowest | Low | Medium | High | Highest |
| 1 | 2 | 3 | 4 | 5 |
| # | Learning Outcomes | P1 |
|---|---|---|
| O1 | Diferansiyel denklemleri sınıflandırabilir. | 5 |
| O2 | Birinci mertebeden diferansiyel denklemleri çözümleyebilir. | 5 |
| O3 | İntegrasyon çarpanını hesaplayabilir. | 5 |
| O4 | Lineer diferansiyel denklemlerin mühendislik uygulamalarını çözümleyebilir. | 5 |
| O5 | Diferansiyel denklemleri Laplace dönüşümleri kullanarak çözümleyebilir. | 5 |