Lectures related to Implicit Functions Theorem

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Explores Peano's existence theorem, compactness properties, uniqueness of solutions, Ascoli-Arzela theorem, and ripeness in differential equations.

Explores the Supremum Theorem, its properties, proofs, and exercises.

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Discusses optimization techniques, focusing on local and global extrema in functions.

Covers Markov chains, coupled chains, and their applications, emphasizing the importance of irreducibility.

Covers the duality principle in linear algebra and its implications in mathematics.