Taylor Approximation: Understanding the Basics

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Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Explores polynomial operations, properties, and subspaces in vector spaces.

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Delves into Taylor polynomials, showcasing how higher orders improve function approximations and how they can be used to calculate limits.

Covers the topic of approximating functions using polynomials through interpolation, emphasizing the importance of optimal point selection.

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

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

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Covers the theory of polynomials, including definitions, properties, and applications.