Lectures related to Analysis I: Limits and Continuity

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Explains how to find local extrema of functions using derivatives and critical points.

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Explores functions of class C^p, emphasizing continuity and differentiability properties.

Covers the concept of partial derivatives and their applications in mathematical analysis.

Explores partial derivatives, Taylor formula, examples, and extrema of functions.

Covers the concepts of optimization, focusing on finding maximum and minimum values.

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Explores derivatives, reciprocal functions, and continuity of functions with examples and formulas.

Explores derivatives, functions, limits, and tangent lines in calculus.

Covers the concept of functional derivatives and their calculation process with examples.

Explores the conditions for continuity and differentiability of functions on a closed interval.

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Explores derivability and continuity of functions, showcasing examples of functions with differentiability properties.

Covers differentiability, derivatives, continuity, and matrices in functions from R^n to R^m.

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Covers differentiability of functions in two variables and the conditions for a function to be differentiable.

Introduces mathematical notations and functions essential for general physics.

Explores functions, derivatives, classes in neighborhoods, and compound functions.