1. Functions o real variable
1.1 Sets of numbers. Real line, Mathemathical induction. Inequalities and absolute value.
1.2 Elementary functions, elementary trnasformations. Composition of functions, inverse function. Polar coordinates.
1.3 Limits of functions, definition, main theorems.
1.4 Continuous functions, properties and main theorems.
2. Differential Calculus
2.1 Diffentiation of functions, definitions, differentiation rules, differentiation of elementary functions.
2.2 Main theorems of differentiation, L'Hopital rule. Extrema of functions.
2.3 Local study of functions: Convexity and asymptotes. Graph of functions.
2.4 Taylor polinomial, definition, main theorems and known taylor expansions. Evaluations of limits with taylor polynomial.
3. Sequences and series.
3.1 Sequence of numbers, main notions, limits of sequences, recurrent sequences.
3.2 Series of numbers, main notions. Tests for convergence for series of positive numbers, absolute and conditional convergence. Leibniz's test. Sum of some series.
3.3 Taylor series, definitions, properties, convergence interval. Main examples.
4. Integration in one variable.
4.1 Integration, antiderivatives, integration by parts, substitution.
4.2 Definite integral. Fundamental theorem of Calculus and applications.
4.3 Application of integration: Areas, volumes and lengths.