Lectures related to Implicit Differentiation: Solving Equations Locally

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.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Untitled

Differential Equations: Implicit Function Theorem Applications

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

Implicit Functions Theorem

Covers the Implicit Functions Theorem and its applications in defining functions implicitly.

Optimization: Lagrange Multipliers

Covers the method of Lagrange multipliers to find extrema subject to constraints.

Inverse Function Theorem

Discusses inverse functions and local invertibility based on the determinant of the Jacobian matrix.

Implicit Functions

Covers directional derivatives, implicit functions, and the concept of the maximum.

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Differentiability and Tangent Planes in Multivariable Functions

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

Advanced Analysis II: Differential Equations and Timers

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.