The course "Mathematical Analysis"
Description
The Mathematical Analysis course is designed to familiarise students with numerical methods of solving basic problems of mathematical analysis: calculating limits, derivatives, integrals, solving ordinary differential equations and their systems.
Each section of the course contains brief theoretical information, practical examples and tasks for independent fulfilment.
Knowledge Requirements: Completion of the course Welcome to Engee course.
Total course time: ~2 hours.
Course Programme
Calculation of limits.
The concepts of the limit of a function, infinitesimal value, basic types of uncertainties, numerical finding of limits by means of a sequence of function values and calculation of limits with the help of symbolic mathematics Engee are studied.
Numerical differentiation.
The concept of derivative, numerical differentiation methods, direct implementation of numerical differentiation methods and the use of numerical and symbolic differentiation functions in Engee are studied.
Numerical Integration.
The concepts of indefinite and definite integral, methods of numerical integration, direct implementation of numerical integration methods and use of numerical integration functions in Engee are studied.
Numerical solution of ordinary differential equations.
The concepts of first-order ordinary differential equation (ODE), general and partial solution, example of first-order ODE, numerical methods of solving first-order ODE, direct implementation of methods of numerical solution of ODE and numerical solution of first-order ODE using built-in functions Engee are studied.
Numerical solution of systems of ordinary differential equations.
The concept of first-order ODE systems, numerical methods for solving first-order ODE systems, direct implementation of methods for numerical solution of ODE systems and numerical solution of ODE systems using built-in Engee functions are studied.
Numerical solution of ordinary differential equations of higher orders.
The concept of higher-order ODEs, numerical methods for solving higher-order ODEs, direct implementation of methods for numerical solution of higher-order ODEs and numerical solution of higher-order ODEs using built-in Engee functions are studied.