- • Gain understanding of the concept of functions, continuous functions and different kind of discontinuous functions
- • Gain skills in evaluating derivatives and integrals.
- • Gain skills in expansion of a function into a Taylor series and finding its convergence interval.
- • Gain skills in solving of homogeneous and nonhomogeneous linear differential equations.
- • Gain understanding of Fourier series, Fourier transforms and their applications.
- • Gain understanding of a Laplace transform and its applications for solving of differential equations
- • Gain understanding of dynamical systems analysis.
- • Know main operations, rules and properties of sets, real numbers, functions, continued functionsю
- Know man rules and properties of derivatives and integrals
- Know main operations, rules and properties of infinite series, functional series as well as Taylor series
- Know basic facts about Fourier series, Fourier transforms and their applications
- Know basic methods for solving of linear differential equations
- Know basic facts about Laplace transforms and their applications in solving of ordinary differential equations
- Be able to analyze one dimensional and two dimensional flows
- Special elementary functions. Limit function of one variable. Continuous and discontinuous functions.
- Infinite series. Functional series. Taylor Series. Interval of convergence.
- Derivatives and antiderivatives. Definite and improper integrals.
- Fourier Analysis.
- Linear homogenous and non-homogeneous differential equations. Rules of solving.
- Laplace transform. Solving of ordinary differential equations using a Laplace transform.
- Dynamical systems. One dimensional flows: steady states, stability and bifurcations. Two dimensional flows: steady states, limit cycles, stability, bifurcations, phase portraits. Dynamical chaos.
- testsThe tests, which are given at the end of each topics, consists of 5-6 typical tasks which have been considered during the seminars. Test duration is 45 minutes.
- Final examThe final exam is written and consists of 2 theoretical questions and 2 tasks for solving. Grading formula for the first and the second re-takings is exactly the same as the grading formula of the basic exam.
- Anton, H., Bivens, I. C., & Davis, S. (2016). Calculus (Vol. 11th ed). New York: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1639210
- Gorain, G. C. (2014). Introductory Course on Differential Equations. New Delhi: Alpha Science Internation Limited. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1878058
- Strogatz, S. H. (2000). Nonlinear Dynamics and Chaos : With Applications to Physics, Biology, Chemistry, and Engineering (Vol. 1st pbk. print). Cambridge, MA: Westview Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=421098
- Nekorkin, V. I. (2015). Introduction to Nonlinear Oscillations. Weinheim: Wiley-VCH. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1099772