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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-14 Differential Equations and Mathematical Statistics

Faculty: Mechanics and Mathematics

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

Contact hours: 60h, 30h lectures, 30h seminars

Self-study hours: 0h,

Assessment: written examination

Year, semester, weekly workload: Year 2, semester 3, lectures 2.0h, seminars 2.0h

ECTS - 5

Main topics: Ordinary differential equations (ODE) of I order – differential equations (DE) with separable variables, homogeneous, linear and reduced to them ones, exact DE. Decreasing the order of ODE. Linear ODE from the n-th order with variable and constant coefficients. Linear homogeneous and inhomogeneous ODE with constant coefficients. Linear ODE with constant coefficients and special right part. Method of Lagrange. Euler ODE. Systems of ODE – basic concepts, normal form. Solving linear systems with constant coefficients. Systems of non-linear ODE in symmetric form. First integral. General solution. Runge-Kutta method. Network methods. Euler method.

  • Partial differential equations (PDE) – basic concepts; functional dependence and independence of functions. Relation between an ODE system and linear I order PDE. Linear homogeneous and inhomogeneous I order PDE, Cauchy problem. II order PDE – classification and canonization, general solution. Hyperbolic PDE. Fourier method. DAlembert’s method.
  • Theory of probabilities (TP) and Mathematical statistics (MS) – stochastic events; statistical, classical, geometric and conditional probability; formula for the total probability and formula of Bayes. Random quantities, numerical characteristics and basic distributions. Basic concepts in mathematical statistics, limit theorems, point assessments. Covariation. Correlation and regression analysis. Checking statistical hypotheses. 

 

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