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