Implicit Differentiation: Solving Equations Locally

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Implicit Differentiation

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

Implicit Functions Theorem

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

Local Invertibility: Vector Fields

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

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Local Invertibility: Vector Fields

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

Diffeomorphism and implicit functions

Explores diffeomorphisms, implicit functions, and coordinate transformations in advanced analysis.

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.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Derivable Functions: Partial Derivatives and Jacobian Matrix

Covers derivable functions, partial derivatives, Jacobian matrix, and rule of composition.

Extremum of a Function: Constraints

Explores extremum of a function under constraints and finding candidate points in practice.