Diffrential calculus and matricesLaajuus (3 ECTS)

Objective

The student will be familiar with the concept of derivative, be able to employ the derivative to evaluate the rate of change and to examine the graph of a function. The student will be familiar with the basic concepts related to matrices and the applications of matrices.

Content

The derivative. Formulas and rules of differentiation. Differential, evaluation of the change of a function and error estimation. Extreme values. The maximum and minimum value of a function. Higher derivatives. Newton’s method. Matrices. The matrix product. Matrix inverse. The matrix presentation of a linear system of equations.

Assessment criteria, satisfactory (1)

The student
- is able to determine the derivative of a function and knows the difference between the mean rate of change and the momentary rate of change
- is able to employ simple rules of differentiation
- recognizes the extreme value of a function and knows how it is related to the derivative of a function
- is familiar with the concept of a matrix and is able to perform matrix operations

Assessment criteria, good (3)

In addition to the requirements above, the student
- is able to calculate the approximation of a derivative numerically
- has a good command of the rules of differentiation
- is able to evaluate the change of a function by using differential and is able to employ the derivative in simple applications, such as determining the extreme values of a function and calculating rates of change
- is able to employ matrices in solving a linear group of equations

Assessment criteria, excellent (5)

In addition to the requirements above, the student
- is able to synthesize the knowledge acquired during the course and to apply the derivative diversely to analyse phenomena
- is familiar with the applications of matrices in solving mathematical and physical problems