COURSE UNIT TITLE

: APPLIED MATHEMATICS

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

ASSOCIATE PROFESSOR BAŞAK KARPUZ

Offered to

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


*** 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 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) 213

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6
LO.1
LO.233
LO.3
LO.434
LO.53