Numerical Analysis

Overview

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Explore a series of screencasts covering essential topics in numerical analysis, including differential equations, numerical integration, root finding methods, and bracketing. Learn to use POLYMATH, MATLAB, and Excel software for performing calculations. Dive into various numerical methods such as Runge-Kutta, Euler, Simpson's Rule, and Bisection. Discover how to solve linear ODEs analytically and numerically using different software tools. Practice optimization techniques and explore open root finding methods. Gain hands-on experience in solving ODEs with Mathematica through step-by-step demonstrations.

Syllabus

Runge-Kutta Method Introduction.
4th-Order Runge Kutta Method for ODEs.
Euler Method for ODEs.
Euler Method/Excel and MATLAB.
Numerical ODE Methods Accurate to 1st and 2nd Order.
POLYMATH Excel Add-in to Solve ODEs.
Simpson's Rule/Excel.
Solving Linear ODEs Analytically.
Solving ODEs/POLYMATH.
Bisection Introduction/Excel.
Bisection for Finding Roots.
Bisection Example/Excel.
Bisection Live Method/Excel.
Bracketing a Maximum in Optimization.
False Position Method.
Open Root Finding Methods.
Numerically Solve ODEs with Mathematica 1.
Numerically Solve ODEs with Mathematica 2.