COURSE UNIT TITLE

: DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 2301 DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA COMPULSORY 3 2 0 4

Offered By

Faculty of Engineering

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR SEVAL ÇATAL

Offered to

Mechanical Engineering (Evening)
Geophysical Engineering
Civil Engineering
Mechanical Engineering
Environmental Engineering
Mining Engineering
Geological Engineering
Metallurgical and Materials Engineering
Civil Engineering (Evening)
Industrial Engineering

Course Objective

The goal of this course is to establish the mathematical background about the fundamental concepts, solution methodologies and technical applications of differential equations and linear algebra.

Learning Outcomes of the Course Unit

1   To classify and solve first-order ordinary differential equations.
2   To classify and solve higher-order ordinary differential equations.
3   To understand matrix algebra and solve systems of linear equations.
4   To compute the eigenvalues and eigenvectors of a matrix.
5   To apply the Laplace transform and solve differential equations and systems of equations.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Matrix algebra: matrix operations, transpose, symmetric, skew-symmetric, triangular and orthogonal matrices.
2 Linear systems, solutions of linear systems by Gaussian elimination. Invertibility of matrices.
3 Determinant and its properties. Cramer s rule.
4 Vector spaces. Linear combination and linear independence of vectors. Basis and dimension.Linear transformations. Geometric transformations.
5 Eigenvalues, eigenvectors, diagonalization.
6 Differential equations, types of solutions and mathematical models. Initial value problems and existence-uniqueness theorem. Separable equations.
7 Linear equations, Bernoulli equations and exact equations.
8 Exact and Non-exact differential equations.
9 Singular Solutions and Applications of First-Order First-Degree and First-Order Higher-Degree Differential Equations
10 Higher order differential equations, linear independency of their solutions and Wronskian. Second order linear homogeneous equations with constant coefficients.
11 Higher order non-homogeneous differential equations and their solutions: Method of variation of parameters.
12 Laplace transformation and its properties.
13 Solutions of differential equations by Laplace transformation.
14 Systems of differential equations and their solutions.

Recomended or Required Reading

1. Differential equations and linear algebra, Calvis, David T; Edwards, Charles Henry; Penney, David E, Pearson Education Canada, Fourth edition, Boston (2018).
2. Diferensiyel denklemler ve sınır değer problemleri, Edwards, Charles Henry; Penney, David E, Çeviri editörü: Prof. Dr. Ömer Akın, Palme Yayınevi.
3. Uygulamalı lineer cebir, Kolman, Bernard; Hill, David R, Çeviri editörü: Prof. Dr. Ömer Akın, Palme Yayınevi.
4. Ileri mühendislik matematiği, O Neil, Peter V, Çeviri editörü: Prof. Dr. Yaşar Pala, Nobel Akademik Yayıncılık.

Planned Learning Activities and Teaching Methods

Lecture presentations, problem solving and applications.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

The performance of students will be evaluated by final exam and midterm exam grades.

Language of Instruction

Turkish

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

To be announced.

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Tutorials 14 2 28
Preparations before/after weekly lectures 14 1 14
Preparation for midterm exam 1 10 10
Preparation for final exam 1 12 12
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 110

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.12
LO.22
LO.32
LO.42
LO.52

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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