Lectures related to Stirling's approximation

Stirling's Formula and Functional Equation for Zeta

Covers the proof of Stirling's asymptotic formula for the Gamma function and the functional equation of the Zeta function.

Taylor Series: Expansion and Properties

Explores Taylor series expansion, derivatives, uniqueness, and applications in function approximation.

Taylor's approximation: Analysis & Applications

Covers Taylor's approximation theorem, differentiability, error control, and function expansions.

Binomial Coefficients: Estimation and Stirling's Formula

Explores binomial coefficient estimation, Stirling's formula, and properties of the bell curve.

Taylor Approximation: Understanding the Basics

Explores Taylor approximation for function approximation and error control.

Taylor Polynomials: Examples and Convergence

Covers examples of Taylor polynomials and discusses their convergence when approximating functions.

Taylor Approximation: Matrix and Polynomials

Explores Taylor approximation of functions using polynomials and matrices for quadratic approximation.

Developing Limited Functions

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

Taylor Polynomials Exercise

Covers the calculation of Taylor polynomials and error bounds for function approximation.

Taylor Series: Finding Remainders

Covers Taylor series, remainder order, limits, and convergence criteria in approximating functions.

Taylor Polynomials: Correction Term

Explores the correction term in Taylor polynomials, showcasing its role in refining function approximations.

Stirling's formula: Euler's integral and Gaussian integral

Explores Stirling's formula, Euler's integral, and the Gaussian integral for estimating n factorial.

Gamma Function and Stirling's Approximation: Mathematical Methods

Discusses the gamma function, its properties, and Stirling's approximation for large factorials, emphasizing their significance in mathematical methods for physics.

Taylor Approximation: Extrema in Multivariable Functions

Covers Taylor approximation and extrema in multivariable functions with examples.

Taylor's approximation: Mean Value Theorem, l'Hopital rule, Examples

Covers the Mean Value Theorem, l'Hopital rule, Taylor's approximation, and more.

Taylor Series: Derivatives and Integrals

Explores Taylor series expansions for derivatives and integrals, with a focus on multiple derivatives and error terms.

Taylor Series: Approximating Functions with Polynomials

Explores approximating functions with polynomials using Taylor series and discusses the convergence of series representations.

Approximating Functions with Taylor Series

Explores approximating functions with Taylor series, showcasing step-by-step calculations and practical applications.

Advanced Analysis I - Taylor's Formula Corollary

Explores the corollary of Taylor's formula for function approximation around a point.

Developing Limit Concepts

Explores developing limits using Taylor series for function approximations and understanding functions with derivatives approaching zero.