Mathematics: Mathematics for Scientists 1

<p>The course is an elective course in the first cycle for a degree of Bachelor's of Science in chemistry, chemistry / molecular biology or biology. The course provides basic mathematical knowledge for further studies in science, mainly in the subject areas of biology and chemistry, as well as economics.</p><p>The course treats:<br /> • logic and set theory; the number system; equalities and inequalities; absolute value; powers and logarithms; second degree curves and equations, polynomials; complex numbers; trigonometry;<br /> • number sequences; arithmetic and geometric sums; mathematical induction; the binomial theorem;<br /> • functions, monotone functions, inverse functions; the properties of the elementary functions: graphs, formulas;<br /> • limits, continuous functions, asymptotes;<br /> • derivatives: definition and properties, applications; derivatives of elementary functions; properties of differentiable functions; local extremas, optimization, curve schetching; basic mathematical models;<br /> • primitive functions; basic integration methods: partial integration and substitution of variables; partial fraction decomposition;<br /> • definition of the Riemann integral; Riemann sums; applications; generalized integrals;<br /> • Taylor and Maclaurin expansions: expansions of elementary functions, applications;<br /> • first-order differential equations: linear, separable; second order linear differential equations with constant coefficients, solving homogeneous equations and certain inhomogeneous equations; applications;<br /> • introduction to functions of several variables, partial derivatives;<br /> • linear systems of equations, matrices and determinants;<br /> • vectors and scalar product in three-dimensional space.</p>