Lectures related to Solving the Quintic: Dominant Balance

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.

Attack on RSA using LLL

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

Numerical Differentiation: Part 1

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Numerical Differentiation and Integration

Covers numerical differentiation, integration, finite differences, Taylor expansions, and interpolation polynomials.

Linear Recurrence Relations

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

Root Finding Methods: Bisection and Secant Techniques

Covers root-finding methods, focusing on the bisection and secant techniques, their implementations, and comparisons of their convergence rates.

Numerical Methods: Iterative Techniques

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Nonlinear Equations: Bisection Method

Introduces root finding using the bisection method for nonlinear equations, illustrated with a three-tanks system example.

Numerical Methods: Stopping Criteria, SciPy, and Matplotlib

Discusses numerical methods, focusing on stopping criteria, SciPy for optimization, and data visualization with Matplotlib.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Root Finding Methods: Secant, Newton, and Fixed Point Iteration

Covers numerical methods for finding roots, including secant, Newton, and fixed point iteration techniques.

Numerical Differentiation and Integration

Explores numerical differentiation and integration methods, emphasizing the accuracy of finite differences in computing derivatives and integrals.

Polynomial Division: Terms and Factors

Covers polynomial division, terms, factors, and integration methods.

Square Roots with Newton's Methods

Explores the computation of square roots using Newton's method and addresses precision challenges in the process.

Simpson's Rule

Covers Simpson's rule for numerical integration and its accuracy for polynomial functions.

Numerical Methods in Chemistry

Covers the implementation of numerical methods in MATLAB for solving chemical problems.

Numerical Methods: Bisection and Multidimensional Arrays

Discusses the bisection method for solving nonlinear equations and its implementation using Python with NumPy and Matplotlib.

Nonlinear Equation Resolution: Introduction to Bisection Method

Introduces the bisection method for resolving nonlinear equations using numerical techniques and Python programming.

Interpolatory Quadrature Formulas

Covers interpolatory quadrature formulas for approximating definite integrals using polynomials and discusses the uniqueness of solutions and practical applications in numerical integration.

Energy Efficiency in Buildings

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