Implicit Functions Theorem

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Geometry of Surfaces in R²

Explores the geometry of surfaces in R², including implicit descriptions, critical points, and regular surfaces.

Implicit Functions: Tangent Plan Equation

Covers implicit functions of class C and the equation of the tangent plane.

Implicit Function Theorem: Tangent Hyperplane

Explores the implicit function theorem for n=2 and n=3, focusing on tangent hyperplanes.

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Implicit Function Theorem: Tangent Planes and Derivatives

Discusses the Implicit Function Theorem and its application to tangent planes and derivatives.

Implicit Functions: Local Existence Theorem

Discusses implicit functions and the local existence theorem for finding solutions.

Tangent spaces to submanifolds

Introduces tangent spaces to submanifolds and their properties in optimization on manifolds.

Advanced Analysis II: Demonstration of Functions and Tangent Planes

Covers the demonstration of functions and the application of tangent planes.

Implicit Functions Theorem

Explores the Implicit Functions Theorem, demonstrating how to find solutions to equations like x²+y²=1 through implicit differentiation and function properties.

Implicit Functions: Advanced Analysis

Covers the advanced analysis of implicit functions, focusing on the application of the theorem of implicit functions.