Mathematics II 2600-DSMdz1MATII
Functions of many variables, partial derivatives, gradient, partial derivatives of second order and local extrema of functions of two variables.
Antiderivatives and the definite integral of a function of one variable, the fundamental theorem of Calculus, area between curves, integration by substitution and by parts.
Matrices, elementary operations on matrices, solving systems of linear equasions by the Gauss elimination.
Matrix multiplication, rank of a matrix, invertible matrices and finding the inverse of a matrix.
The determinant of a square matrix, the Cauchy formula, the adjoint of a square matrix, Cramer's rule.
Type of course
Learning outcomes
The student understands the notions of partial derivatives and the gradient and is able to compute them.
The student knows how to determine local extrema of functions of two variables by means of the second order partial derivatives.
The student knows basic methods of finding antiderivatives and their applications in computing definite integrals and areas between curves.
The student can apply the Gauss elimination method to solve systems of linear equations and can interprete the sets of solutions of such systems.
The student knows the operations of addition and multiplication of matrices,
is able to determine the rank of a matrix and can find the inverse of an
invertible matrix.
The student understands the notion of the determinant of a square matrix
and is able to compute the determinant using the elementary operations,
knows how to use the Cauchy formula and can apply Cramer's rule to
solve some systems of linear equations.
Assessment criteria
Grading based on two written exams.
Bibliography
M.Kysiak, R.Pol, Mathematics for the students of the Faculty of Managment (in Polish, accessible online).
J.Chaber, E.Pol, R.Pol, Mathematics for the students of the Faculty of Managment - second part (in Polish, accessible online).