Advanced Analysis I: Taylor with Integral Remainder

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Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Explains the Euclidean division of polynomials and demonstrates its application through examples and root-based divisibility.

Explores the process of division euclidienne in polynomials, emphasizing the importance of polynomial degrees during operations.

Covers polynomials, their operations, division theorem, and provides illustrative examples.

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

Introduces calculus concepts, focusing on Taylor series and integrals, including their applications and significance in mathematical analysis.

Explores Taylor's formula, uniqueness of Taylor series, Mean Value Theorem, inflection points, and convexity.

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

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

Explores Taylor approximation for function approximation and error control.