Multivariable CalculusLaajuus (3 ECTS)

Objective

The student is capable to use functions of several variables and multi-variable differential and integral calculus in different applications.

Content

Functions of several variables and multi-variable differential and integral calculus with applications.

Assessment criteria, satisfactory (1)

The student understands the concept of function of several variables, knows how to visualize two-variable functions, knows the meaning of partial derivative and gradient, is able to apply simple rules of differentiation and understands the relationship between partial derivatives and maxima and minima of a function. The student is able to calculate simple double integrals and understand the geometric meaning of the double integral.

Assessment criteria, good (3)

In addition to the requirements above, the student is able to calculate numeric approximations for partial derivatives, has a good command of rules of differentiation, knows the concept of directional derivative and is able to use total differential for error estimation.

Assessment criteria, excellent (5)

In addition to the requirements above, the student is able to use partial derivatives to find maxima and minima of two-variable functions, has a deep understanding about the topics covered in the course and is able to apply them creatively and sensibly in different applications.