Characterizations of the exponential function

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Taylor Polynomials: Examples and Convergence

Covers examples of Taylor polynomials and discusses their convergence when approximating functions.

Complex Numbers: Sequences, Series in C, exp, sin, cos

Covers complex numbers, sequences, series, and exponential, sine, and cosine functions in the complex plane.

Algebraic Operations and Taylor Expansions

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

Approximation: Polynomial

Covers orders of magnitude in physics and polynomial approximation for simplifying complex functions.

Taylor Polynomials: Correction Term

Explores the correction term in Taylor polynomials, showcasing its role in refining function approximations.

Power Series Functions: Logarithm and Exponential

Explores power series functions, particularly the logarithm and exponential functions, discussing convergence, extension, and roots of entire functions.

Divergence Examples

Explores examples of divergence in vector fields and their physical meanings.

Pairs of Functions

Discusses reciprocal functions and their graphs, including x² and √x, e^x and ln(x), and tangent and arc tangent.

Riemann Sums and Definite Integrals

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

Taylor Series: Approximating Functions with Polynomials

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