Calculus I

Real numbers, functions, their inverses and graphs. Transcendental functions: trigonometric and inverse trigonometric, logarithm and exponential, hyperbolic. Limits of functions, continuity at a point, continuity on an interval. Differentiability, derivatives of functions, chain rule, implicit differentiation, derivatives of higher order. Local maxima and local minima, Rolle's Theorem and Mean Value Theorem, points of inflection, first-derivative and second-derivative tests, L'Hospital's Rule. Antidifferentiation. Indefinite integrals, substitution rule, integration by parts.