An analysis-algebra problem that studies the stability conditions of the following differential equation \[ \left\{ \begin{array}{ll} y'=\varphi(y)& \\ y(0)=x_0& \end{array} \right. \] where \(\varphi\) is a \(C^1\) map from \(\mathbb{R}^n\) to \(…

A rather interesting analysis problem that studies the Wallis function: \[ \begin{alignat*}{1} f:]-1,+\infty[&\to\mathbb{R}^{+*}\\ x&\mapsto \int_0^{\frac{\pi}{2}}(\sin t)^x \mathrm{d} t \end{alignat*} \] which is a generalization of the well-known integ…

A very long algebra problem set on polynomials and umbral calculus. At the heart of this formalism is the Pincherle derivation. We introduce the operator \(\mathbf{x}\) which is an endomorphism of polynomials: \[ \begin{alignat*}{1} \mathbf{x}:\math…

Quite an interesting, coherent problem, combining analysis and probability. There were some pretty tricky sections: Questions 22 to 25, which demonstrated the uniform convergence of a sequence of functions to the density of the normal distribution \(\…

The first part of the solutions for Maths 2 MP. Answers to the Maths 2 test on May 12 in the MP Centrale Supelec 2023 exam: Problem set: …