Analyse II: Theorems on Continuous Functions and Extremums

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Directional Derivatives

Explores directional derivatives in two-variable functions and extremum points.

Optimization: Extrema of Functions

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

Functions: Parametric, Integrals, Multi-variable

Covers parametric functions, integrals, and the origin of plasticity in metals.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Derivatives and Local Extrema

Explores derivatives, local extrema, and function variation in mathematical analysis.

Lagrange Multipliers: Extremum Points

Explains Lagrange multipliers for extremum points and multiple integration methods for volume and area calculations.

Continuous Functions: Theory and Applications

Explores continuous functions, Cauchy criterion, and function extension by continuity.

Cantor-Heine Theorem

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

Derivability and Maximum Values

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

Local Extremum Points Determination

Focuses on determining local extremum points of functions through various examples.