Lectures related to Series 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.

Functions: Differentials, Taylor Expansions, Integrals

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

Application of Taylor's approximation formula

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

Analysis and Synthesis of Deterministic Signals

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

Analytical Real Functions

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

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.

Solving the Quintic: Dominant Balance

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

Taylor Development: Convexity

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

Taylor Expansions: First Order

Explores Taylor expansions of first order in optimization on manifolds.

Laplace's Method: Exercises

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

Developing Cosine Composition

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

Gradient and Hessian of Pullback

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

Introduction to Definite Integrals

Introduces definite integrals, Taylor expansions, partitions, and area calculations under curves.

Developing Limited Functions

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

Nonlinear Equations: Fixed-Point Methods, High-Order

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

Energy Efficiency in Buildings

Explores optimizing energy use in buildings through solar panels and solving nonlinear equations efficiently.

Linear Recurrence Relations

Explores linear recurrence relations, including examples like the Fibonacci numbers and the proof of related theorems.