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University of Structural Engineering & Architecture
(VSU) "Lyuben Karavelov" - Sofia

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Course Descriptions

Degree program: Civil Egineering, Curriculum 2014

Course: ССС-10 Mathematical Analysis 2

Faculty: Mechanics and Mathematics

Lecturers:
Assoc. Prof. Dr. Veselin Kantchev - vkantchev@yahoo.com

Contact hours: 75h, 30h lectures, 45h seminars

Self-study hours: 0h,

Assessment: written examination

Year, semester, weekly workload: Year 1, semester 2, lectures 2.0h, seminars 3.0h

ECTS - 6

Main topics: Functional series and sequences – convergence and uniform convergence. Power series. Abel’s theorem. Expanding a function to a power series. Trigonometric series. Fourier series. Conditions of Dirichlet for the expansion of a function in a Fourier series. Functions of n variables – limits, continuity, partial derivatives and differentials. Direction derivative. Gradient. Taylor’s formula. Extremums and conditional extremums. Implicit functions. Vector function of a scalar argument. Curves in the plane and in the space. Curvature and torsion. Vector function of two scalar arguments. Surfaces. Double and 3-fold integrals – definition, properties, calculation, change of variables, geometrical and mechanical applications. Contour line integrals of first and second kind – formula of Green-Gauss, conditions for independence from the integration path, applications. Surface integrals of first and second kind – formulas of Stokes and Gauss-Ostrogradski. Elements of the field theory.

 

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