Differential calculusLaajuus (5 cr)

Objective

After completing the course the student:
- operate with mathematical expressions related to technology
- to formulate mathematical model
- understand the concept of a function and recognizes the characteristic properties of different functions
- solve equations involving functions and apply them in practical problems
- use derivatives to analyse graphs
- use differentials to approximate changes and errors
- use matrices and determinants (e.g. for solving linear simultaneous equations),
- use dot and cross products in applications
- give the answer in an expected form

Content

Topics covered in course are (in the order shown):
* functions and graphs
* Pythagoras’ theorem and trigonometric functions
* line and slope
* exponential and logarithmic functions
* function composition
* continuity and limit of a function
* definition of the derivative
* derivatives of basic functions
* derivative rules
* derivative of the composition of functions (chain rule)
* product rule and quotient rule
* tangent and differential
* critical points and extreme values
* finding extreme values by examination of critical points
* functions of several variables
* partial derivatives
* differentials and error estimates
* total differential