Taylor's Formula: Developments and Applications

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Page 3 of 4

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Application of Taylor's approximation formula

Covers the application of Taylor's formula, including composition of functions and detecting local extrema.

Taylor's Formula in Two Variables

Explores Taylor's formula in two variables, emphasizing its application and importance for functions of a single variable.

Partial Derivatives: Taylor Formula

Explores partial derivatives, Taylor formula, examples, and extrema of functions.

Taylor Polynomials: Approximating Functions

Introduces Taylor polynomials for approximating functions around a point, showcasing their importance in accurately representing functions.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Developing Cosine Composition

Explores the composition of Taylor expansions through an example, simplifying complex compositions to identify essential terms.

Functions and Derivatives

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Nature of Extremum Points

Explores the nature of extremum points in functions of class e² around the point (0,0), emphasizing the importance of understanding their behavior in the vicinity.

Algebraic Identities and Trigonometry

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