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 5101 APPLIED MATHEMATICS ELECTIVE 3 0 0 9

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR BAŞAK KARPUZ

Offered to

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

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, Othonormal set of functions
6 Second order ordinary differential equations, Homogeneous linear differential equations, Solution by variation of parameters
7 Initial and boundary value problems
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 * 0.40 + FIN * 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

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)

basak.karpuz@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 7 98
Preparation for final exam 1 37 37
Preparation for midterm exam 1 31 31
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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