CONTENTS

1. Differential calculus in R
Completion of the study in real-valued functions of one real variable
Direct and inverse trigonometric functions
Derivation: composition of function and inverse function
Differential of a function

2. Indefinite Integral
Definition, interpretation and geometric properties
Integrals: quasi-immediate, algebraic decomposition of rational functions, by substitution
and by parts

3. Definite Integral
Definition, geometrical interpretation, properties
The Riemann sum. Barrow rule
Application to the calculation of flat areas
Improper Integrals

4. Numerical Series
Definition. A necessary condition for convergence
Series of nonnegative terms. Convergence criteria: DAlembert and Comparison
Alternating series. Absolute convergence vs simple. Leibniz criterion

5. Functional Series
Definition. Analysis and calculation of the interval of convergence
Representation of a function by a series: Taylor and Maclaurin series