Content (Syllabus outline)
Introduction. Mathematics and biology, motivating examples.
Numbers and sets.
Combinatorics. Basic combinatorial counting.
Sequences. Convergence of sequences, calculating limits.
Number series. Convergence, properties, applications.
Functions. Basic properties. Functions of real variables. Elementary functions, limits and continuity.
Derivative. Definitions, rules, use of derivatives, local extrema, global extrema.
Integral. Indefinite integral, definite integral, generalized integral, applications.
Series of functions. Power series. Taylor series. Applications.
Differential equations. Separable equations, ordinary first-order equations, linear equations with constant coefficients, systems of differential equations, applications.
Linear algebra, geometry in space. Matrices, determinants, systems of linear equations, eigenvalues and eigenvectors of matrices, applications.
Functions of several real variables. Partial derivatives and total differentials, local extrema, extrema with constraints, least squares method.
Fundamentals of probability. Conditional probability, distribution function, applications.
Prerequisites
Prerequisites for inclusion in the work:
· enrolment in the appropriate academic year
Prerequisites for performing study obligations:
Practical examination (colloquium):
· presence at practicals
· solving homeworks
Exam:
practical examination (colloquium)