Extrema: Local and Global

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Rolle's Theorem: Applications and Examples

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

Mean Value Theorem (Mittelwertsatz)

Covers the Mean Value Theorem in differential calculus, focusing on critical points and global extrema within intervals.

Extreme Values of Continuous Functions

Covers extreme values of continuous functions on compact sets and differentiability.

Derivability and Maximum Values

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

Properties of Continuous Functions: Maximum and Minimum

Explores the properties of continuous functions, including maximum and minimum values and intermediate values.

Continuous Functions: Derivability and Global Properties

Covers continuous functions, derivability, and global properties in differential calculus.

Fubini's Theorem: Multiple Integrals

Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

Analyse II: Theorems on Continuous Functions and Extremums

Covers the theorems on continuous functions and extremums in compact sets.

Continuous Functions and Derivatives

Covers the definitions of continuous functions and derivatives, emphasizing the concept of functions being continuous at a point and the notion of derivatives.

Extrema and Implicit Functions

Explores conditions for local extrema in two and three variables, along with implicit functions and finding absolute minima and maxima.