Calculus
Description
The Calculus course is designed to familiarize students with numerical methods for solving basic problems of calculus: 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 self-study tasks.
Knowledge requirements: completion of the course Welcome to Engee.
Total course time: ~2 hours.
Course program
Calculating limits
The concepts of the limit of a function, an infinitesimal quantity, the main types of indeterminate forms, numerical finding of limits using a sequence of function values and calculation of limits using the means of Engee symbolic mathematics 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 Engee functions 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 Engee functions are studied.