# COURSE UNIT TITLE

: MATHEMATICAL METHODS

#### Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5141 MATHEMATICAL METHODS 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

ASSISTANT PROFESSOR ASLI GÜÇLÜKAN ILHAN

#### Offered to

MARINE CHEMISTRY
MARINE GEOLOGY AND GEOPHYSICS
GEOGRAPHICAL INFORMATION SYSTEMS - NON THESIS (EVENING PROGRAM)
NATURAL BUILDING STONES AND GEMSTONES
ENVIRONMENTAL EARTH SCIENCES
GEOGRAPHICAL INFORMATION SYSTEMS
Biomedical Tehnologies (English)
Industrial Ph.D. Program In Advanced Biomedical Technologies
MARINE LIVING RESOURCES
MARINE LIVING RESOURCES
MARINE CHEMISTRY
ENVIRONMENTAL EARTH SCIENCES-NON THESIS
Geothermal Energy
M.Sc. Metallurgical and Material Engineering
UNDERWATER ARCHAELOGY
COASTAL ZONE MANAGEMENT
Mathematics
EARTHQUAKE MANAGEMENT - NON THESIS
Mathematics
Geophysical Engineering
Geographical Information Systems (Non-Thesis)
EARTHQUAKE MANAGEMENT
M.Sc. Geothermal Energy (Non-Thesis-Evening)
Metallurgical and Material Engineering
GEOGRAPHIC INFORMATION SYSTEMS
GEOPHYSICAL ENGINEERING
MARINE GEOLOGY AND GEOPHYSICS
Metallurgical and Material Engineering

#### Course Objective

This course aims to remind and teach basic concepts of calculus and linear algebra to the students without strong mathematical background.

#### Learning Outcomes of the Course Unit

 1 Will be able to express the continuity and limit concepts theoretically. 2 Will be able to use calculus in applied problems by interpreting derivatives and integral concept. 3 Will be able to find local or absolute maxima and minima of several variables using multivariable methods such as Second Derivative Test and Lagrange Multipliers. 4 Will be able to evaluate areas, volumes, line integrals and surface integrals. 5 Will be able to analyse linear system of equations. 6 Will be able to operate diagonalization. 7 Will be able to apply inner product operation to Gram-Schmidt s ortogonalization process.

Face -to- Face

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#### Course Contents

 Week Subject Description 1 Limit of a function and limit laws, precise definition of limits, continuity, limits involving infinity, asymptotes. 2 Tangent line, rate of convergence, derivative, linearization and differentials, differentiation rules. 3 Application of derivatives: Extreme values of a function, maximum and minimum problems, optimization and related rate problems. 4 Integration, Application of integration: work, moments and center of mass. 5 Sequences and series, convergence of series: integral test, comparision test, ratio and root test, alternating seires, absolute convergence. 6 Power series, Taylor and Maclaurin series, convergence of Taylor series. 7 Vector functions and their derivatives, integral of vector functions. 8 Midterm 9 Functions of several variables, limit and continuity in higher dimensions, partial derivatives and its applications, Lagrange Multipliers for constrained maxima and minima. 10 Multiple integrals and its applications, area by double integration, volume by tripple integration, double integrals in polar form. 11 System of linear equations, matrix, determinant, rank of a matrix, homogeneous and nonhomogeneous linear systems, Cramer's Rule. 12 Vector spaces, subspaces, bases and dimension, coordinates 13 Eigenvalues and Eigenvectors, Jordan canonical form. 14 Inner product spaces, Orthogonality, Gram-Schmidt s ortogonalization process.

#### Recomended or Required Reading

Stewart, J., Calculus: Concepts and Contexts, 2nd edition, Brooks/Cole.
Leon, S.J., Linear Algebra with Applications, 7th edition, Pearson Prentice Hall.

#### 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 * 0.20 + ASG * 0.40 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.20 + ASG * 0.40 + RST * 0.40

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

None

To be announced.

English

#### Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

To be announced.

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