Implicit Functions Theorem: n=2 and n=3

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Differential Equations: Implicit Function Theorem Applications

Discusses the reduction of higher-order differential equations to first-order systems using the implicit function theorem.

Implicit Function Theorem: Tangent Planes and Derivatives

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

Implicit Functions: Tangent Line

Explores implicit functions and tangent lines to find local minimum points.

Differentiability and Tangent Planes in Multivariable Functions

Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Implicit Functions and Taylor Polynomials

Covers implicit functions, Taylor polynomials, and tangent equations.

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Geometric Interpretation of Derivatives

Explores the geometric interpretation of derivatives and properties of derivable functions.

Derivatives and Tangent Planes

Covers derivatives, differentiability, and tangent planes for functions of one and two variables.