Lecture

Implicit Functions: Theory and Examples

Related lectures (27)

Optimal Transport: Theory and Applications

Explores the theory of optimal transport, focusing on Lipschitz functions and uniqueness of solutions.

Implicit Functions: Theory and Applications

Explores implicit functions theory, derivatives, solutions existence, and applications.

Natural Transformations: Functors and Categories

Explores functors, natural transformations, and the theory of groups, emphasizing the importance of comparisons and structure preservation.

Differentiable Functions: Definitions and Interpretation

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Implicit Functions: Tangent Line

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

Active Learning Session: Group Theory

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Differentiability and Matrices

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

Implicit functions theorem

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

Differentiable Functions: Definitions and Properties

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.

Tangent to Graph of a Function

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

Introduction to Convexity

Introduces the key concepts of convexity and its applications in different fields.

Hartree-Fock Equations for N Fermions

Discusses the minimization of the Hartree-Fock functional for N fermions and the variational principle in quantum physics.

Active Learning: Group Theory

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Osculating Planes and Parameterized Curves

Covers the concept of osculating planes and parameterized curves, discussing the speed of points and linear independence.

Equivalences of Categories

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Homotopical Algebra

Covers the theory of groups and homotopical algebra, emphasizing natural transformations, identities, and isomorphism of categories.

Vector spaces and norms

Covers vector spaces, differentiable functions, scalar product, and norms in depth.

The Role of Symmetries

Delves into symmetries in physics, covering group theory, perturbation, and quantification.

Differentiability and Tangent Planes in Multivariable Functions

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

Implicit Functions: Lagrange Multipliers

Explores implicit functions and Lagrange multipliers, demonstrating their properties and applications.