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Introduction Epilogue: What Were the Top Ten Algorithms from the 20th Century? Dongarra and Sullivan, Computing in Science and Engineering, Vol 2 (1), 2000. Top in Chronological Order - Cipra Cornell course The Top 10 Algorithms in Applied Mathematics - Higham History of Numerical Analysis Who invented the great numerical algorithms? - Trefethen Another History of Numerical Algorithms The History of Numerical Analysis and Scientific Computing Key Moments - slides Some Remarks On The History Of Numerical Analysis Especially in Prague A Chronology of Interpolation Computer Algebra Systems History of CA Systems - Brian Evans CAS Systems - Wikipedia Interview with Moler Essay on Numerical Analysis - Trefethen Challenges of Numerical Algorithms Computational Mathematics Review I Computational Mathematics Review II Computation Mathematics Final Review - New FNC Julia Demo Notebooks - at FNC site Notebooks - Python, Julia, MATLAB, Octave MATLAB Files - See list of examples by chapter and class examples such as Euler's Method - Euler.mlx Euler for systems - Euler_2D.mlx Modified Euler and RK Methods - ModifiedEuler.mlx RK4 for Systems - RK4systems.mlx, RK4systems.pdf, RK4systems.html Singular Values - SingularValues.mlx, See also SVD Links Random Numbers - RandomNumbers.mlx, See also Random Number Section Monte Carlo Method Perfect Shuffle - PerfectShuffle.mlx Fourier Transforms - FFTsignal.mlx, NorthernCardinal.mp3, MockingBird.mp3, LVBsymph5.mp3 Floating Point Numbers from Cleve's Corner - and his 1996 paper IEEE Standard 754 Floating Point Numbers IEEE-754 Floating Point Converter Loss of Significance Condition and Stability Finding Roots Bisection Method Class Example in Matlab: bisect.m, func.m Fixed Point Iteration Fixed Point Applet Matlab: fixedpt.m, func2.m Newton's Method Matlab: newton.m, func.m, dfunc.m MathCAD: newton.mcd Secant Method Matlab: secant.m Several Methods in Maple: roots.mws Interpolation Data Sets Lagrange Interpolation - Math World Fornberg Algorihhm Original 1988 paper See also Bengt Fornberg (2011) Finite difference method. Scholarpedia, 6(10):9685. Numerical tests comment Applet with draggable points Using Maple for Lagrange Interpolation Maple 8 File Pade Approximations Matlab Files For Interpolation and Associated Plotting Routines Lagrange Interpolation interpL.m , plotinterpL.m Lagrange Interpolation done piecewise interpL2.m, plotinterpL2.m, points.m Neville's Method nevilleQ.m, plotneville.m Divided Differences divdiff.m, ddfun, plotdivdiff.m Hermite Interpolation hermite.m, hermfun.m, plothermite.m Matlab Help Interpolation (1d) Cubic Spline Example Numerical Differentiation Maple Implementation Matlab Implementations Richardson's Extrapolation Numerical Integration Matlab Files for Numerical Integration - use functions intf.m and intf2.m Composite Trapezoidal trapezoid.m Composite Simpson's simpson.m Composite Midpoint midpoint.m Romberg Integration romberg.m Maple Implementation NumInt.mws Monte Carlo Technique monte.m Gauss-Legendre Quadrature gauss.m, quadfun.m, vander2.m, LegendrePoly.m Survey of Extrapolation ... paper at JSTOR Euler-Maclaurin Summation Formula Richardson Extrapolation Shanks Transformation, Simplified Explanation Initial Value Problems for ODEs Runge-Kutta and Butcher Tableau Algorithm Misnaming A History - Butcher Recent blog Mathematica Tutorial Slides, #2 List of Methods Graphical Representation. Video - Improved Euler Math Source Lib Error Bounds - Ralston Numerical solution of Differential Equations in Julia ODE course material, including using Maple, links to applets, etc Chapter on Numerical Solutions of ODEs - R. Herman Solving Differential Equations Using Simulink - R. Herman Matlab Files - using defunc.m Euler's Method euler.m Modified Euler modeuler.m Huen's Method huen.m Runge-Kutta Order Four rk4.m Adams-Bashforth Order Four AdamsBash4.m Adams-Bashforth-Moulton Predictor-Corrector ABM.m Maple File - NumODE.mws Other Code - Systems discussion included Stability.mws Solving Linear Systems LU Decomposition in Maple Matlab Routines Example Usage MatEx.m Forward Substitution LF.m Backward Substitution UB.m LU Factorization lufac.m LTriSol.m LU Factorization Examples Matrix Methods Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods Iterative Methods for Sparse Systems Matlab Example of Matrix Iterations MaxIter.m Matrix Iteration and BVP ODEIt.m Approximation Theory Linear Least Squares - Math World Least Squares Polynomial Fit by clicking Least Squares Fitting of Data from the Physical Sciences & Engineering Singular Value Decomposition Driscoll and Braun Chapter 7 - Matrix Analysis Video Lectures, Notes SVD Elucidated, SVD for Data Science SVD Quantifies Increasing Partisanship in the U. S. Senate - by Moler Partisan Politics and the SVD - More explanation. The Extraordinary SVD - MAA Monthly Random Numbers Random Numbers Chapter in Numerical Recipes Moler's Chapter A brief history Brief Look at History of Probability and Statistics - JSTOR P l'Ecuyer - A more extensive history, his slides The Middle Square Method Wikipedia The Middle Square Method Cyclies, Rosettacode Pseudorandom number generator Linear Congruential Generator Wikipedia Rosettacode Blum Blum Shub Wikipedia MATLAB code Mersenne Twister Mersenne Twister Home Page Wikipedia Mersenne primes GIMPS Distributions Box-Muller Algorithm Box-Muller Derivation and FORTRAN MATLAB code Perfect Shuffle - Rosettacode Cleve's Corner The Mathematics of Perfect Shuffles Card Shuffling as a Dynamical System - Russ Herman or, at SlideToDoc Monte Carlo Method The Beginning of ... Estimating pi predict money to budget for sales commissions Random Numbers on Planes Random Numbers Fall Mainly in the Planes, 1968 Again, random numbers fall mainly in the planes, 2019 FFT Touch-Tone Telephone Dialing Problems The Rattleback - and here Napkin Ring Problem Bailey�Borwein�Plouffe formula High-Precision Arithmetic in Mathematical Physics - paper World on a String Some Disasters Numerical analysis projects - time-reversed van der Pol oscillator, Final Projects, Other Links Matlab Central Olver's Matlab Routines Tutorials MATLAB Basic MATLAB Brief Introduction Introduction PDF A Jupyter kernel for MATLAB Maple Basic Maple Brief Introduction Introduction PDF Long Introduction to Maple Python Python Programming And Numerical Methods: A Guide For Engineers And Scientists Numerical Programming with Python SciPy Tutorial (2021): For Physicists, Engineers, and Mathematicians (1:33:28) Introduction to Sympy and the Jupyter Notebook for engineering calculations Simulink Differential Equations SageMath A Jupyter Notebook from a SageMath tutorial Julia Numerical Analysis Class How to Add Julia kernel to Jupyter Hands on Julia R R Tutorial An Introduction to R Hidden Gems from here MATLAB�Python�Julia cheatsheet Scientific Python Cheatsheet Top

E-Mail: Dr. Russell Herman		Last Updated: May 02, 2022

Materials