Taylor Polynomials: Approximating Functions with Taylor Polynomials

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Taylor Polynomials: Calculating Limits and Derivatives

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Taylor Polynomial in Two Variables

Covers the Taylor polynomial in two variables and the concept of extrema in functions of several variables.

Lagrange Interpolation

Introduces Lagrange interpolation for approximating data points with polynomials, discussing challenges and techniques for accurate interpolation.

Linear Approximations: Development Order 2

Covers linear approximations up to order 2 and the Hessian matrix.

Derivation and Integration Rules in Analyse 2

Explores derivation and integration rules for Taylor polynomials, showcasing iterative methods to calculate functions like ln(x) and arctan(x).

Complex Numbers: Representations

Explores different ways to represent complex numbers, including geometric and trigonometric representations, simplifying calculations and enhancing intuition.

Taylor Polynomials and Remainders

Explores Taylor polynomials, remainders, and various function expansions around a point.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Functions and Derivatives

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