Lectures related to Complex Numbers: Sequences, Series in C, exp, sin, cos

Introduces fundamental concepts of Analysis I, focusing on functions of a variable and numerical sequences.

Explores approximating functions with polynomials using Taylor series and discusses the convergence of series representations.

Explores the representation and rotation of complex numbers in the complex plane.

Provides solutions to an Analysis I exam, covering various topics.

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Covers convergence of power series, complex equations, exponential functions, and function properties.

Explores the limit of the quotient for sequences and the periodicity of functions.

Explores odd and even functions in Fourier series applications, including half-range series and cosine/sine series.

Explores complex numbers, Euler's formula, Moivre's formula, and proof by induction.

Explores algebraic operations on Taylor expansions and the development of various functions.

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Covers the correction of a mock exam for Analysis I, focusing on sequences, series, and limits.

Covers De Moivre's formula for finding roots of complex numbers and the concept of complex exponential.

Covers the demonstration of Euler's formula and its applications.

Explores complex numbers in polar form, powers, and roots, including trigonometric relationships and rotation matrices.

Explores properties and applications of complex numbers, including De Moivre's theorem and finding complex roots.

Delves into complex exponential functions, their properties, and polar representation of complex numbers.

Explores holomorphic functions, Cauchy-Riemann conditions, and principal argument values in complex analysis.

Covers the properties of complex numbers, sequences, and series.