Faculty of Engineering and Natural Sciences · Food Engineering (English 30%) · Undergraduate
ECTS: 5 T+P+L: 3+0+0 Compulsory
Coordinator: Doç. Dr. Sinem GÜLER
Prerequisites: MAT 115 - Mathematics I, MAT 116 - Mathematics II
Course Objective
To comprehend the mathematical formulation of ordinary differential equations and to find solutions of the first order and second order differential equations.
Course Content
Covers mathematical formulation of ordinary differential equations, methods of solution and applications of first order and second order differential equations, power series solutions, solutions by Laplace transforms and solutions of first order linear systems.
Course Learning Outcomes
- Classify a given differential equation as ordinary or partial, and determine its order and whether or not it is linear.
- Solve first-order linear ordinary differential equations.
- Apply reduction of order to find a second linearly independent solution for a homogenous differential equation, given one solution.
- Compute real valued linearly dependent solutions to homogenous ordinary differential equations with constant coefficients.
- Apply variation of parameters and method of undetermined coefficients to find a particular solution.
- Formulate and solve appropriately applied engineering.
- Compute power-series solutions to certain differential equations with variable coefficients.
- Apply the Laplace transform to solve a given Initial-Value problem and solve systems of linear differential equations
Core Area Distribution
(46) Mathematics and Statistics%60 (52) Engineering and Engineering Trades%40
Teaching Methods
ExpressionQuestion-AnswerExercise and PracticePresentationGuided PracticeSelf studyProblem Solving
Assessment & Evaluation
HomeworkTesting (Essay / Tests: True-Falls, multiple-choice, short answer, matching)
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 16 | 3 | 48 |
| Out of Class Study Period | 16 | 3 | 48 |
| Midterm | 1 | 2 | 2 |
| Quiz | 10 | 1 | 10 |
| Assignment | 3 | 5 | 15 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 2 | 2 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | Introduction to the course. Classification of Differetial equation. First order ordinary differential equations. | |
| 2 | Zero order homogeneous differential equations. | |
| 3 | Reducible homogenous equations. Linear differential equations. | |
| 4 | Linear differential equations. | |
| 5 | Bernoulli and Riccati differential equations. | |
| 6 | Exact differential equations. | |
| 7 | Integration multipliers. Solvability, existence and uniqueness. | |
| 8 | Midterm | Midterm |
| 9 | Higher order differential equations. Constant coefficients linear homogeneous second order differntial equations. | |
| 10 | Linear dependence and independence. Wronskien determinant. Constant coefficient linear non-homogeneous second order differential equations. | |
| 11 | Constant coefficient linear non-homogeneous second order differential equations. | |
| 12 | Lagrange method. n.th order linear constant coefficient differential equations. | |
| 13 | n.th order linear constant coefficient differential equations. | |
| 14 | Lagrange method for n.th order linear constant coefficient differential equations. | |
| 15 | Euler-Cauchy differential equations. | |
| 16 | Final Exam | Final Exam |