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BLOG ENTRIES

With more than 10,000 monthly visitors, the blog at http://autarkaw.wordpress.com answers day-to-day questions asked by students in the classroom, on a piazza discussion board, and on YouTube channel or by instructors.  Below are the blog entries arranged by numerical method topics.

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

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

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

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

AUDIENCE |  AWARDS  |  PEOPLE  |  TRACKS  |  DISSEMINATION  |  PUBLICATIONS

Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

  

ANALYTICS