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With 5,000-9,000 monthly visitors, the blog at http://autarkaw.wordpress.com answers day-to-day questions asked by students in class or on the youtube channel or by an instructor teaching the course at another institution, or just a curious question that pops into the author's head. Below are the entries in the blog by the numerical method topic.
INTRODUCTION Proper modeling needs to precede numerical analysis Round off errors and the Patriot missile Comparing two series to calculate pi Myth: Error caused by chopping a number is called truncation error A better way to exemplify conversion of decimal integer to binary A better way to show conversion of a fractional number to binary Converting large numbers into floating point by hand Accuracy of Taylor series Taylor series example Taylor series revisited
NONLINEAR EQUATIONS How do I solve a nonlinear equation in MATLAB ? How do I solve a nonlinear equation that needs to be setup in MATLAB? Solving a polynomial equation for the longest mast problem A real-life example of having to solve a nonlinear equation numerically?
DIFFERENTIATION Data for aluminum cylinder in iced water experiment How do I differentiate in MATLAB?
SIMULTANEOUS LINEAR EQUATIONS So what does this mean that the computational time is proportional to some power of n in Gaussian Elimination method? Rusty on Matrix Algebra Is a square matrix strictly diagonally dominant? Is a square matrix diagonal? LU Decomposition takes more computational time than Gaussian Elimination! What gives? How do I solve simultaneous linear equations on matrix form in MATLAB ? How do I solve simultaneous linear equations on equation form in MATLAB ?
INTERPOLATION Experiment for spline interpolation and integration Length of a curve experiment Data for length of curve experiment Shortest path for a robot Do quadratic splines really use all the data points? Extrapolation is inexact and may be dangerous Finding the length of curve using MATLAB A simple MATLAB program to show that High order interpolation is a bad idea High order interpolation is a bad idea? If a polynomial of order n or less passes thru (n+1) points, it is unique! How do I do polynomial interpolation in MATLAB? How do I do spline interpolation in MATLAB?
REGRESSION Abuses of regression Finding the optimum polynomial order to use for regression In regression, when is coefficient of determination zero On calculating the height of atmosphere How do I do polynomial regression in MATLAB ? Does it make a difference if we transform data for nonlinear regression models To prove that the regression model corresponds to a minimum of the sum of the square of the residuals
INTEGRATION Is it just a coincidence - true error in multiple segment Trapezoidal rule gets approximately quartered as the number of segments is doubled? Can I use Trapezoidal rule to calculate an improper integral? Experiment for spline interpolation and integration Length of a curve experiment Shortest path for a robot Finding the length of curve using MATLAB Can I use numerical solution of ODE techniques to do numerical integration Example to show how numerical ODE solutions can be used to find integrals Automatic integrator using the trapezoidal rule Another improper integral solved using trapezoidal rule How do I integrate a continuous function in MATLAB ? How do I integrate a discrete function in MATLAB ?
ORDINARY DIFFERENTIAL EQUATIONS Data for aluminum cylinder in iced water experiment Comparing Runge-Kutta 2nd order methods Time of death - a classic ODE problem Runge-Kutta 2nd order method equations derived A MATLAB program for comparing Runge-Kutta 2nd order methods Example to show how numerical ODE solutions can be used to find integrals How do I solve an initial value ordinary differential equation in MATLAB? How do I solve a boundary value ordinary differential equation in MATLAB? How do I numerically solve an ODE in MATLAB?
PROGRAMMING WITH MATLAB Skipping numbers in a lotto program Picking lotto numbers The BMI Index Program ] The Continue Statement in MATLAB The Break Statement in MATLAB Bubble Sorting MATLAB code for bubble sort HOW DO I DO THAT IN MATLAB SERIES? How do I display the data of an array in MATLAB ? How do I differentiate in MATLAB? How do I integrate a continuous function in MATLAB ? How do I integrate a discrete function in MATLAB ? How do I solve a nonlinear equation in MATLAB ? How do I solve a nonlinear equation that needs to be setup in MATLAB? How do I solve simultaneous linear equations in matrix form in MATLAB ? How do I solve simultaneous linear equations in equation form in MATLAB ? How do I do polynomial interpolation in MATLAB? How do I do spline interpolation in MATLAB? How do I do polynomial regression in MATLAB ? How do I solve an initial value ordinary differential equation in MATLAB? How do I solve a boundary value ordinary differential equation in MATLAB? How do I numerically solve an ODE in MATLAB? How do I read a textfile in MATLAB