COURSE UNIT TITLE

: APPLIED MATHEMATICS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
ELECTIVE

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR GÜLTER BUDAKÇI

Offered to

M.Sc. in Biochemistry
Ph.D. in Biotechnology
Nanoscience and Nanoengineering
Nanoscience and Nanoengineering
Mechanics
Computer Engineering Non-Thesis
MARINE CHEMISTRY
COASTAL ENGINEERING
CONSTRUCTION MATERIALS
HYDRAULIC ENGINEERING AND WATER RESOURCES
TRANSPORTATION ENGINEERING
PHYSICS
COMPUTER ENGINEERING
Biomedical Tehnologies (English)
GEOGRAPHICAL INFORMATION SYSTEMS
Environmental Engineering
Computer Science
Industrial Ph.D. Program In Advanced Biomedical Technologies
Mechatronics Engineering
Industrial Ph.D. Program In Advanced Biomedical Technologies
PHYSICAL OCEANOGRAPHY
GEOGRAPHICAL INFORMATION SYSTEMS - NON THESIS (EVENING PROGRAM)
NATURAL BUILDING STONES AND GEMSTONES
MARINE GEOLOGY AND GEOPHYSICS
ENVIRONMENTAL EARTH SCIENCES
PHYSICS
Logistics Engineering (Non-Thesis-Evening)
DESIGN AND PRODUCTION
Machine Theory and Dynamics
TRANSPORTATION ENGINEERING
CONSTRUCTION MATERIALS
THERMODYNAMICS
Computer Engineering
MARINE LIVING RESOURCES
NAVAL ARCHITECTURE
MARINE LIVING RESOURCES
Structural Engineering
Marine Transportation Systems Engineering
Geothermal Energy
Mechanics
MARINE CHEMISTRY
ENVIRONMENTAL EARTH SCIENCES-NON THESIS
Mechanics
THERMODYNAMICS
Chemistry
GEOTECHNICAL ENGINEERING
ENVIRONMENTAL ENGINEERING
Ph.D. in Computer Science
Industrial Engineering - Thesis (Evening Program)
Ph.D. in Biotechnology
Machine Theory and Dynamics
EARTHQUAKE MANAGEMENT - NON THESIS
M.Sc. Metallurgical and Material Engineering
UNDERWATER ARCHAELOGY
INDUSTRIAL ENGINEERING - NON THESIS
Machine Theory and Dynamics
Mathematics
GEOTECHNICAL ENGINEERING
TRANSPORTATION ENGINEERING
STRUCTURAL ENGINEERING
Mathematics
Geophysical Engineering
GEOGRAPHIC INFORMATION SYSTEMS
MARINE TRANSPORTATION SYSTEMS ENGINEERING
Chemistry
DESIGN AND PRODUCTION
HYDRAULIC ENGINEERING AND WATER RESOURCES
Design and Production
COASTAL ENGINEERING
Geographical Information Systems (Non-Thesis)
Metallurgical and Material Engineering
NAVAL ARCHITECTURE
M.Sc. Geothermal Energy (Non-Thesis-Evening)
EARTHQUAKE MANAGEMENT
HYDRAULIC ENGINEERING AND WATER RESOURCES
INDUSTRIAL ENGINEERING - NON THESIS (EVENING PROGRAM)
Mechatronics Engineering
Ph.D in Biochemistry
STRUCTURAL ENGINEERING
Ph.D. in Occupational Health and Safety
Geotechnicel Engineering
Marine Transportation Systems Engineering
Energy
ENGINEERING MANAGEMENT- NON THESIS (EVENING PROGRAM)
INDUSTRIAL ENGINEERING
Computer Engineering
GEOPHYSICAL ENGINEERING
BIOTECHNOLOGY
Occupational Healty and Safety
Metallurgical and Material Engineering
Nanoscience and Nanoengineering
Computer Engineering (Non-Thesis-Evening)
THERMODYNAMICS
Energy
COASTAL ZONE MANAGEMENT
Energy
MARINE GEOLOGY AND GEOPHYSICS
Logistics Engineering
M.Sc. Mechatronics Engineering
CONSTRUCTION MATERIALS
Chemistry
INDUSTRIAL ENGINEERING

Course Objective

This course will give the students basic concepts in linear analysis where the entities are the elements of finite dimensional linear spaces or the elements of infinite dimensional function spaces. Students will learn the analytical solution methods to obtain the exact solutions of the problems encountered in applications

Learning Outcomes of the Course Unit

1   will be able to understand the basic theory and techniques in linear algebra
2   will be able to understand the existence and uniquness theorem for sytem of linear equations
3   will be able to understand the basic theory and techniques in differential equations
4   will be able to understand Fourier s method for solving initial and boundary value problems of wave, heat, Laplace equations
5   will be able to understand Fourier integral methods for solving heat and wave equations in unbounded domains

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Matrices Linear systems Gauss-Jordan elimination
2 Vector spaces Inner product and norm Linear transformations
3 Determinants Properties of determinant Cramer's rule Inverse matrix
4 Matrix eigenvalue problem Symmetric, skew-symetric and orthogonal matrices Diagonalization
5 Function spaces Inner product and norm in Function spaces Ortogonal, orthonormal set of functions
6 Second order ordinary differential equations Initial and boundary value problems Homogeneous linear differential equations Solution by variation of parameters
7 Midterm
8 The Sturm-Liouville problems Eigenvalues and eigenfunctions Orthogonal eigenfunction expansion
9 Partial differential equations Initial and boundary conditions Vibratig string, wave equation The method of sepation of variables, use of Fourier series
10 Solution of homogeneous and nonhomogeneous diffusion equation Two-dimensional diffusion equation
11 Laplace equation Steady state two-dimensional heat problems Laplace equation in a bounded domain
12 Wave equation Two-dimensional homogeneous and nonhomogeneus wave equations
13 Fourier integrals Heat equations in the whole and half spaces
14 Wave equation in unbounded domains, use of Fourier integrals

Recomended or Required Reading

Erwing Kreyszig, Advanced Engineering Mathematics, John Wiley&Sons, 9th edition, 2006.
Peter O'Neil, Advanced Engineering Mathematics, Thomson, 2007.

Planned Learning Activities and Teaching Methods

Lecture notes
Presentation
Problem solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.25 +ASG * 0.35 +FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.25 +ASG * 0.35 + RST * 0.40


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

ali.sevimlican@deu.edu.tr
melda.duman@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 6 78
Preparation for final exam 1 28 28
Preparing assignments 5 9 45
Preparation for midterm exam 1 18 18
Final 1 3 3
Midterm 1 2 2
TOTAL WORKLOAD (hours) 213

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.1
LO.2343
LO.34334
LO.4
LO.543

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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