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
MAT 5001 APPLIED MATHEMATICS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

INSTRUCTOR ALI SEVIMLICAN

Offered to

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

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 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50
4 RST RESIT
5 FCGR FINAL COURSE GRADE MTE * 0.50 + RST * 0.50

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 3 39
Preparation for midterm exam 1 15 15
Preparation for final exam 1 25 25
Preparing assignments 5 10 50
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.1544
LO.2444
LO.3544
LO.4444
LO.5444

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

Copyright 2012 DEÜ. BİD

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