Implicit Functions: Theory and Applications

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Related lectures (27)

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Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Advanced Analysis II: Sequences and Integrals

Explores sequences, integrals, symmetrical functions, differential equations, and the Cauchy problem in advanced analysis.

Differentiability and Derivatives

Covers differentiability, derivatives, continuity, and matrices in functions from R^n to R^m.

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Derivatives of Functions: Differentiability and Matrices

Explores differentiability, matrices, and composite functions through examples and mathematical notations.

Derivatives and Continuity in Multivariable Functions

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

Introduction to Derivatives

Introduces derivatives, forward contracts, options, and their financial uses.

Differentiation and Coordinate Changes in Multivariable Functions

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

Implicit Function Theorem: Tangent Hyperplane

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

Implicit functions theorem

Explores the implicit functions theorem, showcasing examples of implicit differentiation and function definition.