COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 505HIGHER DIFFERENTIAL GEOMETRY-I3 + 02nd Semester6

COURSE DESCRIPTION
Course Level Doctorate 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
Data not found.

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration14342
Hours for off-the-classroom study (Pre-study, practice)14570
Assignments144
Mid-terms11313
Final examination12727
Total Work Load

ECTS Credit of the Course






156

6

COURSE DETAILS
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L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes
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