Implicit Functions: Tangent Plan Equation

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Implicit Functions Theorem

Discusses finding min and max of functions on compact sets and the theorem of implicit functions.

Implicit Functions Theorem

Explores the implicit functions theorem and the equation of the tangent plane in a graph.

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.

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Tangent Planes and Implicit Functions

Explores tangent planes, implicit functions, and directional derivatives in relation to graphs of functions.

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.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Advanced Analysis II: Demonstration of Functions and Tangent Planes

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

Envelope of Curves

Explores the concept of envelope of curves within families of lines, including implicit equations, super-ellipses, and curvature.