Lectures related to Implicit Functions: Theory and Applications

Differentiability and Matrices

Explores differentiability, matrices, Jacobian matrix, and derivatives calculation.

Implicit Functions: Tangent Line

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

Implicit Functions Theorem

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

Derivable Functions: Partial Derivatives and Jacobian Matrix

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

Implicit Functions Theorem

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

Implicit Differentiation: Basics

Covers the basics of implicit differentiation, focusing on techniques and applications.

Implicit Functions Theorem: n=2 and n=3

Explains the Implicit Functions Theorem for n=2 and n=3 cases.

Implicit Functions and Taylor Polynomials

Covers implicit functions, Taylor polynomials, and tangent equations.

Advanced Analysis II: Derivatives and Notations

Covers derivatives, notations, composition of functions, and multiple derivatives in advanced analysis.

Differential Equations: Implicit Solutions

Explores implicit solutions for differential equations and their applications in different scenarios.

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.