Implicit Functions Theorem

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Related lectures (30)

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Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Taylor Approximation: Extrema in Multivariable Functions

Covers Taylor approximation and extrema in multivariable functions with examples.

Directional Derivatives

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

Extrema and Implicit Functions

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

Implicit Function Theorem

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

Extrema of Functions

Covers the discussion of local extrema, concavity, convexity, and inflection points in functions.

Envelope of Curves

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

Stationary Points and Saddle Points

Explores stationary points, saddle points, symmetric matrices, and orthogonal properties in optimization.

Mathematical Methods for Materials Science: Integrals, Exact Differentials

Explores limits, derivation rules, integrals, and exact differentials for practical applications.

Implicit Curves: Analysis & Regular Points

Covers implicit curves, regular and critical points, convexity, concavity, and inflection points.