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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MTE 2116 DIFFERANTIAL EQUATIONS COMPULSORY 2 2 0 4

Offered By

Marine Transportation Engineering

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR EMIN DENIZ ÖZKAN

Offered to

Marine Transportation Engineering

Course Objective

1. To form a sound basis for advanced mathematics, 2. To develop skills for solving problems.

Learning Outcomes of the Course Unit

1   Definitions, 1st order linear differential equations, existence and uniqueness, 2   Separable equations, change of variables, characteristic, higher order linear 3   Method of change of parameters, reduction of order, equations with constant 4   Euler-Cauchy equation, Legecndre and Bessel s equations 5   Power series method, solutions around regular-singular points, Laplace 6   Laplace transformations; definitions and fundamental theorems 7   Initial value problems, convolution integral and transfer function 8   Linear system of differential equations, physical and engineering applications

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Classification of differential equations and their solutions 2 Initial-value problems, boundary-value problems, existence of solutions 3 Exact differential equations and integrating factors 4 Separable differential equations and homogeneous differential equations 5 Linear differential equations 6 Bernoulli equations 7 Special integrating factors and transformations 8 Theory of higher order linear differential equations 9 Linear dependence and linear independence, representation of solutions for homogeneous and nonhomogeneous cases, reduction of order 10 Homogeneous linear differential equations with constant coefficients 11 The method of undetermined coefficients 12 The method of variation of parameters 13 Cauchy-Euler differential equations 14 Review

Recomended or Required Reading

Introduction to Ordinary Differential Equations; by Shepley L. Ross. Fourth Edition, John Wiley and Sons.

Planned Learning Activities and Teaching Methods

Solving problems, homework, presentation

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FINS FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.40 + FINS * 0.60 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

In relation to Differential Equations topics at undergraduate level, skills and competencies in having knowledge, research interpretation, verbal and written expression, solving problems will be evaluated.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

Asst. Prof. Dr. Emin Deniz Özkan deniz.ozkan@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 2 28 Tutorials 14 2 28 Preparations before/after weekly lectures 14 2 28 Preparation for midterm exam 1 4 4 Preparation for final exam 1 4 4 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 98

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 PO.14 PO.15 PO.16 PO.17 LO.1 5 3 5 5 5 5 LO.2 5 3 5 5 3 5 3 5 LO.3 5 5 5 3 5 LO.4 5 5 5 5 3 3 3 5 LO.5 5 3 3 3 3 5 LO.6 3 3 5 5 LO.7 3 5 5 5 LO.8 3 5