Lectures related to Continuous Functions: Theory and Applications

Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Explains the definition and uniqueness of developments limites for continuous functions on open intervals.

Explores continuous functions and integrability through practical examples.

Covers the concept of limit at a point and function composition in the context of continuous functions.

Discusses the Cauchy problem for ODEs with initial conditions and the importance of homeomorphism and Lipschitz continuity.

Covers the theorem of intermediate values and finding maximum and minimum values of functions on closed intervals.

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.