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Concept

Inverse function theorem

Related lectures (32)

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Implicit Differentiation: Solving Equations Locally

Explores implicit differentiation and the Implicit Function Theorem for finding unique functions locally.

Fixed Point Method: Global Convergence

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Implicit Differentiation

Explores implicit differentiation and the Implicit Function Theorem for finding unique local functions.

Implicit Functions Theorem: n=2 and n=3

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Linear Algebra Basics

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Local Invertibility: Vector Fields

Covers local invertibility of vector fields and the Inverse Function Theorem.

Implicit Function Theorem: Tangent Hyperplane

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

Derivability Conditions

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Implicit Function Theorem: Local Extrema

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Implicit Function Theorem

Explores the Implicit Function Theorem, supporting hyperplanes, local extrema, and higher-order derivatives, concluding with the classification of stationary points.

Implicit Functions: Lagrange Multipliers

Explores implicit functions and Lagrange multipliers, demonstrating their properties and applications.

Implicit Functions Theorem Log in to Mediaspace to watch this video

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Derivable Functions: Partial Derivatives and Jacobian Matrix Log in to Mediaspace to watch this video

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Partial Differential Equations and Hessians Log in to Mediaspace to watch this video

Covers partial differential equations, Hessians, and the Implicit Function Theorem, with a focus on exam question resolution.

Implicit Function Theorem Log in to Mediaspace to watch this video

Covers the Implicit Function Theorem for functions of two variables and explores graphical representations and tangent lines.

Local Inversion Theorem Log in to Mediaspace to watch this video

Explores the Local Inversion Theorem and extremum points in functions.

Local Inversion Theorem Log in to Mediaspace to watch this video

Explores the local inversion theorem, demonstrating uniqueness of solutions and continuity of functions.

Implicit Functions Theorem Log in to Mediaspace to watch this video

Covers the theorem of implicit functions for n>2, with examples demonstrating the application of the theorem.