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Engineering mathematics 4Laajuus (4 cr)

Code: 8X00CD15

Objective

After completing the course students are able to examine and visualize the behaviour of functions of two-variables with their graphs and contour-lines, calculate limits for functions of several variables, their partial derivates, gradient and directional derivative, find local and global extreme values and use Lagrange's method. Student is able to calculate the derivative matrix of a vector-valued function and use the chain rule. Student is able to calculate plane and space integrals in simple sets and use polar, cylinder and spherical coordinates.

Content

Graph and contour-lines of functions of two variables. Functions of several variables: limits and partial derivatives, directional derivatives, gradient. Jacobian matrix and chain rule. Local and global extremum values, constrained extrema and Lagrange's method.
Plane and space integrals, calculation using polar, cylindrical and spherical coordinates.

Assessment criteria, satisfactory (1)

Grading done by TUT

Assessment criteria, good (3)

Grading done by TUT

Assessment criteria, excellent (5)

Grading done by TUT