Implicit Functions: Theory and Examples

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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.