Functions of a single real variable ? bounded, monotone, one-to-one functions. Composite functions, inverse functions. Overview of elementary functions. Sequences of real numbers ? bounded, monotone sequences. Limit of a sequence, convergent and divergent sequences; limes superior, limes inferior . Limit of a function ? definition, geometrical interpretation, computing rules. One-sided limits, infinite limits and limits at infinity. Continuity of functions ? in a point, on an interval; points of discontinuity. Continuity of composite and inverse functions. Differentiation ? definition, geometrical meaning, computing rules. Differentiation of composite and inverse functions. Differentiation of elementary functions. Differential of a function, basic theorems of differential calculus. Graph sketching ? extreme values, convex and concave functions, asymptotes. Primitive function, table of basic primitive functions. Computing rules ? per partes, substitutions, integration of rational functions. Riemann integral ? definition, the fundamental theorem of integral calculus. Integration by parts, substitution methods for computing definite integral. Geometrical applications of the definite integral ? computing areas, length of curves, volumes of bodies.
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