Análise Matemática III B

Acquire knowledge and skills that enable to:

-Understand the concept of an infinite sum and the definition of convergence.

-Determine when a series is convergent by applying convergence criteria.

-Understand the concept of sequences and series of functions.

-Grasp the difference between pointwise and uniform convergence.

-Determine intervals of convergence and understand their implications for the convergence of the power series and the possibility of differentiating and integrating term by term.

-Understand and be proficient in the algebra of complex numbers, particularly their polar form.

-Understand the concept of a complex function of a complex variable, especially understanding elementary functions as generalizations of the real case.

-Understand the concept of continuity and differentiability for functions of a complex variable and their relationship with the Cauchy-Riemann equations.

-Grasp the concept of the integral of a complex function of a complex variable along a path and its properties.

-Understand Cauchy's integral formula and be able to apply it in practical cases.

-Understand the concept of Taylor and Laurent series.

-Understand the concept of residue, in its various forms, and apply it to the calculation of integrals.