Lectures related to Laplace's Method: Exercises

Holomorphic Functions: Taylor Series Expansion

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

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

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.

Uniform Convergence: Series of Functions

Explores uniform convergence of series of functions and its significance in complex analysis.

Laurent Series: Analysis and Applications

Explores Laurent series, regularity, singularities, and residues in complex analysis.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series, residue theorem, and their applications in complex analysis.

Complex Analysis: Laurent Series and Residue Theorem

Discusses Laurent series and the residue theorem in complex analysis, focusing on singularities and their applications in evaluating complex integrals.

Complex Analysis: Simply Connected Domains

Explores simply connected domains in complex analysis, including holomorphic functions, Cauchy's integral formula, and Taylor series.

Complex Analysis: Holomorphic Functions

Explores holomorphic functions, Cauchy-Riemann conditions, and principal argument values in complex analysis.

Functions Extension and Taylor Expansion

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

Complex Exponential: De Moivre's Formula

Covers De Moivre's formula for finding roots of complex numbers and the concept of complex exponential.

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

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.

Complex Analysis: Taylor Series

Explores Taylor series in complex analysis, emphasizing the behavior around singular points.

Complex Analysis: Laurent Series

Explores Laurent series in complex analysis, emphasizing singularities, residues, and the Cauchy theorem.

Holomorphic Functions: Cauchy-Riemann Equations and Applications

Discusses holomorphic functions, focusing on the Cauchy-Riemann equations and their applications in complex analysis.

Complex Integration: Fourier Transform Techniques

Discusses complex integration techniques for calculating Fourier transforms and introduces the Laplace transform's applications.

Power Series Computations

Covers power series, generating functions, and operations like addition, multiplication, differentiation, and integration, with examples and the generalized binomial theorem.

Taylor Polynomials: Calculating Limits and Derivatives

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.