Lectures related to Asymptotic expansion

Functions Extension and Taylor Expansion

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

Solving the Quintic: Dominant Balance Analysis

Explores dominant balance analysis in solving the quintic polynomial, revealing insights into root behavior and the importance of symbolic expressions.

Laplace Method: Asymptotic Analysis

Explores the Laplace method for asymptotic analysis through a mathematical exercise with exponential functions and Taylor expansions.

Von Neumann Extractor: Extensions

Covers the von Neumann Extractor and its extensions, aiming to derive and analyze an optimal extractor.

Holomorphic Functions: Taylor Series Expansion

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

Analysis and Synthesis of Deterministic Signals

Explores the representation of signals as vectors, projection theorem, orthogonal functions, and examples.

Written Correction: Equilibrium and Taylor Expansion

Covers equilibrium in physics and Taylor expansion with exercises.

Analytical Real Functions

Explores analytical real functions, focusing on series expansion and properties of u(x) in different neighborhoods.

Laplace's Method: Exercises

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

Limit Calculations Applications

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

Statistical Theory: Maximum Likelihood Estimation

Explores the consistency and asymptotic properties of the Maximum Likelihood Estimator, including challenges in proving its consistency and constructing MLE-like estimators.

Laurent Series: Definition and Properties

Covers the definition and properties of Laurent series, including convergence and function expansion.

Developing Limited Functions

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

Composition of Taylor Expansions

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

Taylor Development: Convexity

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

Taylor Series: Cosine Function

Explains the Taylor series expansion of order 4 for the cosine function.

Solving the Quintic: Dominant Balance

Explores dominant balance analysis in solving the quintic polynomial, with a focus on non-dimensionalization and series expansions.

Effort Informed Roadmaps: Efficient Multiquery Planning with EIRM*

Introduces EIRM*, a planner that efficiently solves multiple planning problems by reusing information and managing graph size effectively.

Taylor Expansions: First Order

Explores Taylor expansions of first order in optimization on manifolds.

Gradient and Hessian of Pullback

Explores the connection between Riemannian and Euclidean gradients and Hessians at critical points.