Lectures related to Analyse I: Derivatives and Continuity

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

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

Explores finding the equation of the tangent line to a function's graph at a point.

Covers the generalization of the TAF theorem, lateral derivatives, limits of derivatives, and indeterminacy.

Explores derivability and function composition with examples.

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Explores generalized finite increments, derivatives, reciprocals, and Bernoulli-L'Hospital rule.

Explores differentiability in functions and the role of gradients in directional derivatives.

Explores derivability, continuity, and composite functions with illustrative examples.

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Explores the geometric interpretation of derivatives and properties of derivable functions.

Explains partial and directional derivatives, and functions' derivability.

Covers the demonstration of the chain rule and the theorem of Rolle.

Explores reciprocal functions, strict monotonicity, and continuity in advanced analysis.

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