Lectures related to Implicit Function Theorem: Tangent Hyperplane

Curves in Space: Parametric Equations and Surfaces

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Parametric Curves: Envelope and Caustics

Explores parametric curves, focusing on finding envelopes and caustics.

Tangent Plane to Implicit Function

Explores the tangent plane to implicit functions, emphasizing equations and graphical representations.

Implicit Function Theorem: Tangent Planes and Derivatives

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

Tangent to Graph of a Function

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

Implicit Functions Theorem

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

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Differentiability and Tangent Planes in Multivariable Functions

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

Derivatives and Tangent Lines: Understanding Functions and Limits

Explores derivatives, functions, limits, and tangent lines in calculus.

Implicit Functions Theorem: n=2 and n=3

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

Analysis Reminder: Open Sets and Denseness

Reviews open sets, denseness, real numbers, convergence, curves, continuity, and derivatives in analysis.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Surface Integrals: Implicit Surfaces

Covers implicit surfaces, parametric descriptions, regular parametrization, normal vectors, and orientable surfaces.

Curves and Surfaces

Covers the representation of plane curves and the nature of obtained curves.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Derivatives and Functions: Definitions and Interpretations

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Derivable Functions: Partial Derivatives and Jacobian Matrix

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

Implicit Function Theorem

Covers the Implicit Function Theorem for functions of two variables and explores graphical representations and tangent lines.