Mathematical analysis
Description
The course Mathematical Analysis is designed to familiarize students with numerical methods for solving basic problems of mathematical analysis: calculation of limits, derivatives, integrals, solution of ordinary differential equations and their systems.
Each section of the course contains brief theoretical information, practical examples and tasks for self-completion.
Knowledge requirements: course completion Welcome to Engee.
Total course time: ~2 hours.
Course program
Calculation of limits.
The concepts of the limit of a function, an infinitesimal quantity, the main types of uncertainties, numerical finding of limits using a sequence of function values and calculation of limits using the means of symbolic mathematics Engee are studied.
Numerical differentiation.
The concept of derivative, numerical differentiation methods, direct implementation of numerical differentiation methods and the usage of numerical and symbolic differentiation functions in Engee are studied.
Numerical integration.
The concepts of indefinite and definite integral, numerical integration methods, direct implementation of numerical integration methods and the usage of numerical integration functions in Engee are studied.
Numerical solution of ordinary differential equations.
The concepts of a first-order ordinary differential equation (ODE), general and particular solutions, an example of a first-order ODE, numerical methods for solving first-order ODES, direct implementation of methods for numerical solution of ODES and numerical solution of first-order ODES using built-in functions Engee are studied.
Numerical solution of systems of ordinary differential equations.
The concept of a first-order ODE system, 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 higher-order ordinary differential equations.
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 functions Engee are studied.