Mathematical Analysis

Enumerability; concept of infimum and supremum; construction of real numbers. Sequences and numerical series: notion of limit, Monotonous Sequence Theorem, Embedded Intervals Theorem, Cauchy sequence, Bolzano-Weierstrass Theorem, convergence criteria. Line topology: open, closed, convex, connected sets. Real functions. Limit. Continuity: Bolzano's Theorem, Intermediate Values Theorem, Weierstrass Theorem, Uniform continuity. Derivation: monotony, Mean-Value Theorem, L'Hôpital Rules, Taylor, optimality criteria. Riemann integral; Fundamental Theorem of Calculus; Mean-Value Theorem for Integrals. Mention to the integral and Lebesgue measure. Sequences and series of functions: punctual, uniform convergence, limit under the integral sign. 

Basic Information

45 hours


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