Master
2022/2023
Some Topics of Calculus, Differential Equations and Nonlinear Dynamics
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type:
Elective course (Cognitive Sciences and Technologies: From Neuron to Cognition)
Area of studies:
Psychology
Delivered by:
School of Psychology
When:
1 year, 1, 2 module
Mode of studies:
offline
Open to:
students of one campus
Master’s programme:
Cognitive Sciences and Technologies: From Neuron to Cognition
Language:
English
ECTS credits:
6
Contact hours:
40
Course Syllabus
Abstract
This course is a continuation of Calculus MT1 174 which is taught for the second-year students. It lasts for one (spring) semester.
Learning Objectives
- - to enable students to acquire skills in additional topics of calculus and help them to acquire math knowledge sufficient to apply for economic modeling, - to prepare students for further courses in mathematics.
Expected Learning Outcomes
- apply Direct Comparison and Limit Comparison Test enabling to assess the convergence of such integrals
- approximate the value of definite integral by the upper and lower estimates of sums
- Appyly Laplace transform to the solution of differential equations
- change the variables technique along with the change in order of integration in repeated integrals
- check the uniform convergence of the improper integrals with parameter, manipulations include: differentiation and integration with respect to parameter along with the continuity of such integrals
- handle the evaluation of the limits by performing changes of the variables/ employing Taylor; expansion and L’Hopitale rule
Course Contents
- Limits
- Improper integrals
- Laplace transforms
- Manipulation of integrals. An introduction to the Lebesgue integral
- Double integrals
- The Riemann integral
