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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 505HIGHER DIFFERENTIAL GEOMETRY-I3 + 01st Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective The goal of the course is to express geometrical concepts with the differential.
Course Content Inner Product Spaces, Ortogonal Group, Self-Adjoint Mappings and O(n), Multilinear Algebra, Movements, Parametric Curve Differentiable Mappings, Tangent Vectors and Spaces, Cotangent Spaces, Covector, 1-Form and Duality, Coordinate Mappings on Tm(P), Differential with respect to Direction, Algebra of Multi-Linear Function, Tensor Algebra of Vector Spaces, Symmetric Tensors and Alternating, Exterior Product Spaces, Tensor Product of Linear Mappings and Endomorphisms.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Realizes the inner product space, learns ortogonal group.
2Realizes the O (n) and Self- Adjoint transform, learns multi-linear algebra.
3Knows motions, parametric curve, differantiable transform.
4Knows tangent vector and space, cotangent space, covector, 1-form and duality.
5Realizes coordinate transform in Tm(P),directional derivative, algebra of multi-linear functions,tensor algebra of vector space.
6Knows symmetric tensor and alternating, exterior product space, tensor product of linear transforms and endomorphisms.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0015  4   4
LO 0024  4   5
LO 0035  5   4
LO 0045  4   4
LO 0054  5   5
LO 0064  5   5
Sub Total27  27   27
Contribution50050005

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course






195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2023-2024 Spring1CANSEL AYCAN
Details 2022-2023 Spring1CANSEL AYCAN
Details 2021-2022 Spring1CANSEL AYCAN
Details 2019-2020 Fall1CANSEL AYCAN
Details 2016-2017 Fall1CANSEL AYCAN
Details 2015-2016 Fall1CANSEL AYCAN
Details 2014-2015 Fall1ŞEVKET CİVELEK
Details 2013-2014 Fall1ŞEVKET CİVELEK


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 505 HIGHER DIFFERENTIAL GEOMETRY-I 3 + 0 1 Turkish 2023-2024 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. CANSEL AYCAN c_aycan@pau.edu.tr FEN B0318 %80
Goals The goal of the course is to express geometrical concepts with the differential.
Content Inner Product Spaces, Ortogonal Group, Self-Adjoint Mappings and O(n), Multilinear Algebra, Movements, Parametric Curve Differentiable Mappings, Tangent Vectors and Spaces, Cotangent Spaces, Covector, 1-Form and Duality, Coordinate Mappings on Tm(P), Differential with respect to Direction, Algebra of Multi-Linear Function, Tensor Algebra of Vector Spaces, Symmetric Tensors and Alternating, Exterior Product Spaces, Tensor Product of Linear Mappings and Endomorphisms.
Topics
WeeksTopics
1 Fibred manifolds
2 Jet spaces
3 General connections
4 Lagrangian formalism on fibred manifolds
5 De Donder Hamiltonian formalism
6 Instantaneous Hamiltonian formalism
7 Multisymplectic Legendre bundles
8 Midterm exam
9 Multimomentum Hamiltonian forms
10 Hamilton equations
11 Analytical mechanics
12 Hamiltonian theory of constraint systems
13 Cauchy problem
14 Isomultisymplectic structute
Materials
Materials are not specified.
Resources
ResourcesResources Language
Generalized Hamiltonian Formalism for Field Theory, G. SARDANASHVILY, World Scientific, Singapore, 1995Türkçe
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes