Lectures related to Analysis I: Indeterminate Forms and Gendarmes' Role

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Covers the Implicit Functions Theorem and its applications in finding extremums under constraints.

Explores elastic and inelastic collisions, kinetic energy conservation, and work principles with practical examples.

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

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

Explores the properties of exponential and logarithmic functions, emphasizing limits and continuity.

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