Introduction to Mathematics II 3501-KOG-WM2
I. Basics of differential calculus: sequences (e.g. squeeze theorem, theorem of Bolzano-Weierstrass, the number e), convergence of number series (criteria of d'Alembert, Cauchy and Leibniz, two comparison criteria), limits of functions and continuity (e.g. Darboux property, asymptotes), derivative, its properties and applications (tangent line, linear approximation, theorems of Fermat, Rolle, Lagrange and Cauchy, largest value on a closed segment, intervals of monotonicity, convexity, necessary condition and two sufficient conditions of local extrema, de l'Hospital rule, graph sketching), indefinite and definite integrals (integration by guessing, by substitution and by parts, applications in calculation of area and length). II Basics of linear algebra: operations on matrices with real entries (including rank and inverting), determinants, applications to linear systems. If time permits: eigenvectors and eigenvalues of matrices.
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