Lectures related to Gradient and Hessian of Pullback

Functions Extension and Taylor Expansion

Covers functions extension and Taylor expansion, exploring mathematical concepts in depth.

Explores Riemannian gradient descent, covering Taylor expansions, optimality conditions, algorithm templates, line search, and critical points.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Application of Taylor's approximation formula

Covers the application of Taylor's formula, including composition of functions and detecting local extrema.

Functions: Differentials, Taylor Expansions, Integrals

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Written Correction: Equilibrium and Taylor Expansion

Covers equilibrium in physics and Taylor expansion with exercises.

Limit Calculations Applications

Demonstrates efficient limit calculations using Taylor expansions and basic algebraic operations.

Composition of Taylor Expansions

Covers the computation of Taylor expansions composition up to order 4.

Differentiating vector fields: Why do it?

Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.

Taylor Development: Convexity

Covers the Taylor development theorem, convexity, and computation rules with Taylor.

Laplace's Method: Exercises

Covers exercises related to Laplace's method and complex analysis.

Power series and Taylor series

Covers power series, Taylor series, and their applications in functions like logarithmic functions.

Covariant derivatives along curves

Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.

Developing Cosine Composition

Explores the composition of Taylor expansions through an example, simplifying complex compositions to identify essential terms.

Taylor Expansions: First Order

Explores Taylor expansions of first order in optimization on manifolds.

Taylor Expansion: Derivation and Application

Covers the derivation of a function near a critical point.

Constrained optimization: the basics

Covers the basics of constrained optimization, including tangent directions, trust-region subproblems, and necessary optimality conditions.

Developing Limited Functions

Covers the concept of developing limited functions and includes physical examples.

Power Series and Taylor Series

Explores power series, Taylor series, convergence criteria, and applications in mathematics.

Nonlinear Equations: Fixed-Point Methods, High-Order

Covers fixed-point methods and high-order techniques for solving nonlinear equations.