Module Code Number
Number of ECTS Credits
Hours / Week
Module Lecturer
Year / Term
Type of Course
(Compulsory / Elective)
Pre requisites / Recommended
DİFFERENTİAL GEOMETRY-I
MAT-305
5
4 hours/week
Dr. Mahmut ERGÜT
3/ 1
Compulsory
Linear Algebra, Analytical Geometry
Differential Topology, Tangent Vectors and Tangent Spaces, Tensors and
Tensor Spaces, Curvature Theory, Parameter Changes, Special Curves.
Aims and Objectives of the The aim of this module is to provide an introduction to the basic concepts and
module
techniques used in described in the module contents.
Method of assessment
One written midterm exam (40%) and one written final exam (60%)
Teaching Language
Turkish
Textbook /
Differential Geometry, University of Inönü.
recommended readings
Module Contents
Module Code Number
Number of Credits
Hours / Week
Module Lecturer
Year / Term
Type of Course
(Compulsory / Elective)
Pre requisites / Recommended
Module Contents
PARTIAL DIFFERENTIAL EQUATIONS -I
MAT-313
5
4 hours/week
Prof.Dr.Necdet ÇATALBAŞ
1st / Fall
Compulsory
Mathematical Analysis, Ordinary Differential Equations
Introduction to partial differential equations, first order equations,
notation, formation of equations, geometric examples, linear first order
equations, Method of Lagrange , characteristic curves, Method of Charpit,
compatible systems, Lagrange-Charpit method, Cauchy problem for general
first order equations, Method of Characteristics.
Aims and Objectives of the The aim of this lecture is to provide an introduction to the basic concepts and
module
general solution techniques of the first - order partial differential equations .
Method of assessment
Teaching Language
Textbook /
recommended readings
One written midterm exam(40% ) and one written final exam (60%)
Turkish
Introduction to partial differential equations and boundary
problems,R.Dennemeyer,McGraw- Hill Book Company.
value
Module Code Number
Number of Credits
Hours / Week
Module Lecturer
Year / Term
Type of Course
(Compulsory / Elective)
Pre requisites / Recommended
Module Contents
PARTIAL DIFFERENTIAL EQUATIONS -II
MAT-316
5
4 hours/week
Prof.Dr.Necdet ÇATALBAŞ
2 st / Spring
Compulsory
Mathematical Analysis, Ordinary Differential Equations
Introduction, linear second-order equations in two independent variables,
linear second-order equations in n independent variables, normal forms,
hyperbolic parabolic and elliptic equations, classification of almost-linear
equations in n independent variables, Cauchy problem, Cauchy-Kowalewski
theorem, Cauchy problem for linear second -order equations in n
independent variables, adjoint operator.
Aims and Objectives of the The aim of this lecture is to provide an introduction to the basic concepts and
module
general solution techniques of the second - order partial differential
equations .
Method of assessment
One written midterm exam(40% ) and one written final exam (60%)
Teaching Language
Turkish
Textbook /
Introduction to partial differential equations and boundary value
recommended readings
problems,R.Dennemeyer,McGraw- Hill Book Company.
Module Code Number
Number of ECTS Credits
Hours / Week
Module Lecturer
Year / Term
Type of Course
(Compulsory / Elective)
Pre requisites / Recommended
Module Contents
NUMERICAL ANALYSIS
MAT-309
6
3 hours/week
Dr. Doğan KAYA
3rd / Fall
Compulsory
Calculus I-IV/ Integral Computations/ Ordinary Differential Equation.
Basic concepts: Convergence, stability, error analysis and conditioning. Solutions
of nonlinear equations. Biscestion, Newton’s, secant and fixed point iteration
methods. Iterative Methods for the solution of large systems of linear and
nonlinear equations. Polynomial interpolation: Lagrange and Newton
interpolation formulas, Hermite interpolation, piecewise polynomial interpolation.
Numerical ordinary and partial derivative. Numerical integration: Gaussian
quadrature adaptive quadrature, extrapolation methods. Numerical methods for
Ordinary Differential Equations. General Literature on Numerical Methods.
Aims and Objectives of the The aim of this module is to provide an introduction to the basic concepts and
module
techniques used on Numerical Methods.
Method of assessment
One written midterm exam (40%) and one written final exam (60%)
Teaching Language
Turkish
Textbook /
W. Cheney, D. Kincaid, Numerical Mathematics and Computing, Brooks/Cole
recommended readings
Publishing, QA297, C426, 1999
Module Code Number
Number of ECTS Credits
Hours / Week
Module Lecturer
Year / Term
Type of Course
(Compulsory / Elective)
Pre requisites / Recommended
Module Contents
REAL ANALYSIS
MAT 314
6
4 hours/week
Yrd.Doç.Dr. A.GÖKHAN
3rd / Fall
Compulsory
None / Circuit theory, Electrotechnics, Advanced Mathematics I and II.
Measure Theory, Measurable Functions, Lebesque Integrals
Aims and Objectives of the
module
Method of assessment
Teaching Language
Textbook /
recommended readings
The aim of this module is to provide an introduction to the basic concepts
and techniques used in measure and Integral theory.
One written midterm exam (40%) and one written final exam (60%)
Turkish
Reel Analiz ‘Prof. Dr. Mustafa Balcı, A.Ü.’ , Real Analysis ‘Schaum’s Outline
Series ,
Measure, Lebesque Integral and Hilbert Spaces ‘A.N.Kolmogorov- S.V.
Fomin’
ABSTRACT ALGEBRA AND NUMBERS THEORY-I
Module Code Number
MAT-303
Number of ECTS Credits
5
Hours / Week
4 hours/week
Module Lecturer
Yrd.Doç.Dr.Essin TURHAN
Year / Term
3/1
Module Contents
Algebraic structures of one operation (semi-group, group, commutative
group),algebraic structures of two operation(ring, field, commutative field),
homomorphism and isomorphism in the algebraic structures , substructures
algebraic substructures .
Group theory, subgroups, commutative group, remain classes,
homomorphism and isomorphism in groups, in the variant subgroups with
Period groups.
Teaching Language
Turkish
ABSTRACT ALGEBRA AND NUMBERS THEORY II
Module Code Number
MAT-304
Number of ECTS Credits
5
Hours / Week
4 hours/week
Module Lecturer
Yrd.Doç.Dr.Essin TURHAN
Year / Term
3/1
Module Contents
Rings, ring and field properties, subring, homomorphism and isomorphism
in the ring integral domain, characteristic of integral domain, field of
fraction, ideal, polinom, polinoms ring, become division in the integral
domain, Euclidean rings, characteristic of a field.
Teaching Language
Turkish
VECTOR ANALYSIS-I
MAT-317
4
2 hours/week
Dr.Abdullah ÖZEL
3/ 1
Module Code Number
Number of ECTS Credits
Hours / Week
Module Lecturer
Year / Term
Type of Course
(Compulsory / Elective)
Elective
Pre requisites / Recommended
Analytical Geometry, Calculus, Linear Algebra
Module Contents
Addition an Subtraction on vectors, Multiplying, with a scalar, linear functions,
scalar product of two vectors , vector product, rotation around a constant axis,
functions with one scalar variable, linear differential equations with vector, position
functions, continuity, Gradient of a scalar function,  operator, derivation formulas,
functional relations, Diverges a rotational of a vector.
Aims and Objectives
module
Method of assessment
Teaching Language
Textbook /
recommended readings
of
the The aim of this module is to provide
basic calculation on vectors and
techniques used in the module contents.
One written midterm exam (40%) and one written final exam (60%)
Turkish
Vector Analysis, H. B. Philips, Ankara University
TRANSFORMATIONS GEOMETRY -I
Module Code Number
MAT-319
Number of ECTS Credits
4
Hours / Week
2 hours/week
Module Lecturer
Yrd.Doç.Dr.Essin TURHAN
Year / Term
3ttr /Fall
Module Contents
Introduction to transformations, a short history, definition of geometry
transformation, transformation groups, geometry invariant, transformations
of linear equation, motions of Euclide plane, general properties of motions ,
motions and kongurans , translasyon, rotasyon, refleksion, transfleksion ,
similary transformations, general properties of similary transformations ,
equations of similarity groups,metric geometry.
Teaching Language
Turkish
Module Code Number
Number of ECTS Credits
Hours / Week
Module Lecturer
Year / Term
Type of Course
(Compulsory / Elective)
Pre requisites / Recommended
Module Contents
Aims and Objectives
module
Method of assessment
Teaching Language
Textbook /
recommended readings
of
VECTOR ANALYSIS -II
MAT-320
4
2 hours/week
Dr. Abdullah ÖZEL
3/ 2
Elective
Analytical Geometry, Calculus, Linear Algebra
Integration, space curve, line integral, work and potential, circulation, integration in
a plane, surface integral, curvilinear coordinates, spherical coordinates, volume
integrals coordinates on a surface.
theThe aim of this module is to provide basic concepts of integration on a surface
which is described in the module contents.
One written midterm exam (40%) and one written final exam (60%)
Turkish
Vector Analysis, H. B. Philips, Ankara University