1.    Real Variable Functions

1.1.     The real line: Different kinds of numbers. Inequalities, absolute value and subsets. Elementary curves.

2.2.     Elementary functions: First definitions. Properties. Trigonometric functions. Logarithm and exponential. Operations with functions. Inverse functions. Polar coordinates.

2.    Limits and Continuity

2.1.     Limits: Definitions and basic properties. Calculus of limits.

2.2.    Continuity: Continuity at a point. Fundamental theorems. Uniform continuity.

3.    Derivatives and their Applications

3.1.     Differentiability: Definition and basic derivatives. Basic properties.

3.2.     Meaning of the derivative: First and second derivatives. Strong theorems. Extrema.

4.    Local study of a function

4.1.     Graphic representation: Convexity. Asymptotes.

4.2.     Other applications of the derivative: Implicit derivative. Logarithmic derivative.

4.3.     Taylor polynomial: Construction. Properties. Applications.

5.    Sequences and Series of Real Numbers

5.1.     Sequences of numbers: Definitions and properties. Limits. Recurring sequences.

5.2.     Series of numbers: Preliminaries. Series of non-negative terms. Absolute convergence of series.

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: Convergence set. Properties.


Last modified: Thursday, 6 July 2023, 11:07 AM