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

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

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.10
LO.115
LO.24
LO.334
LO.43
LO.5

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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