Master
2022/2023
Some Topics of Calculus, Differential Equations and Nonlinear Dynamics
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
