Differential Calculus

1. Real variable functions
1.1 The real line: sets of numbers, properties, absolute values
1.2 Elementary functions and curves
1.3 Polar coordinates

2. Limits and continuity
2.1 Limits of functions. Properties and fundamental theorems
2.2 Continuity of functions. Fundamental theorems
2.3 Uniform continuity

3. Derivatives and their applications
3.1 Definition, properties, derivatives of elementary functions
3.2 Meaning of the derivative. Extrema

4 Local study of a function
4.1 Graphic representation
4.2 Taylor's polynomial and its applications

5. Sequences and series of real numbers
5.1 Sequences of numbers.
5.2 Series of positive numbers
5.3 Absolute and conditional convergence

6. Sequences and series of functions
6.1 Sequences of functions. Punctual and uniform convergence
6.2 Series of functions. Punctual and uniform convergence
6.3 Taylor series