Blog Entries

Why do we have blog entries here when the blog itself is searchable.  It is because, they are arranged by numerical methods topics.

With more than 100,000 annual visitors, the blog at http://autarkaw.org answers day-to-day questions asked by students in the classroom, on discussion boards of an LMS, during office hours, on the YouTube channel, and by instructors.  A few blogs are based on disseminating content as well.

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
A Wolfram demo on converting a decimal number to floating point binary representation
Taylor Series in Layman’s terms
Accuracy of Taylor series
Taylor series example
Taylor series revisited
Taylor Series Exercise – Method 1
Taylor Series Exercise – Method 2
Taylor Series Exercise – Method 3
Largest integer that can be represented in a n-bit integer word

Differentiation

Data for aluminum cylinder in iced water experiment
How do I differentiate in MATLAB?
How do I differentiate a discrete function given at equidistant points
A Wolfram demo for numerical differentiation
Order of accuracy of central divided difference scheme for first derivative of a function of one variable

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?
Does the solve command in MATLAB not give you an answer-1?
Does the solve command in MATLAB not give you an answer-2?
A Wolfram demo on how much of a floating ball is under water
Finding the inverse error function
Inverse error function using interpolation
Using int and solve to find inverse error function 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?
Computational Time to Find Determinant Using Cofactor Method
Computational Time to Find Determinant Using Gaussian Elimination
Computational Time for Forward Substitution
Computational Time for Back Substitution

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?
Solving a first order ODE by Laplace transforms: Example
Classical Solution Technique to Solve a First Order ODE
Example: Solving First Order Linear ODE by Integrating Factor

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
Printer cuts off MATLAB code and text
Does the solve command in MATLAB not give you an answer-1?
Does the solve command in MATLAB not give you an answer-2?
A MATLAB program to find quadrature points and weights for Gauss-Legendre quadrature rule

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 text file in MATLAB?
How do I check if a number is n0n-negative or not in MATLAB?
How do I read an excel file in MATLAB?
How do I find inverse error function using interpolation in MATLAB?
How do I find inverse error function using int and solve command in MATLAB?

Informational Blogs

Saylor Foundation Harnesses Numerical Methods Resources
codecademy.com looks promising
Audiovisual Lectures for Novice Programmers
Livescribe
YouTube Videos on Numerical Methods Cross 1-Million Views Mark