Douglas Lewit: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=9345
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 19 Oct 2021 15:51:01 GMTTue, 19 Oct 2021 15:51:01 GMTNew applications published by Douglas Lewithttps://www.maplesoft.com/images/Application_center_hp.jpgDouglas Lewit: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=9345
Application of the Modified Gram-Schmidt Algorithm
https://www.maplesoft.com/applications/view.aspx?SID=152382&ref=Feed
<p>Maple's QRDecomposition command basically utilizes one of two routines for generating the Q and R matrices. If the matrix contains only integers and/or symbolic expressions, then Maple performs a QR decomposition using the Classical Gram-Schmidt algorithm. If however, the matrix contains a mixture of integers and floating point decimals or only floating point decimals, then Maple carries out the QR decomposition of the matrix using Householder transformations. My approach below uses a third alternative, the Modified Gram-Schmidt algorithm, which I read about in Chapter 8 of the textbook, NUMERICAL LINEAR ALGEBRA, by Lloyd N. Trefethen and David Bau III.</p><img src="https://www.maplesoft.com/view.aspx?si=152382/05160ad08a75a6b7948e889b5999f0ea.gif" alt="Application of the Modified Gram-Schmidt Algorithm" style="max-width: 25%;" align="left"/><p>Maple's QRDecomposition command basically utilizes one of two routines for generating the Q and R matrices. If the matrix contains only integers and/or symbolic expressions, then Maple performs a QR decomposition using the Classical Gram-Schmidt algorithm. If however, the matrix contains a mixture of integers and floating point decimals or only floating point decimals, then Maple carries out the QR decomposition of the matrix using Householder transformations. My approach below uses a third alternative, the Modified Gram-Schmidt algorithm, which I read about in Chapter 8 of the textbook, NUMERICAL LINEAR ALGEBRA, by Lloyd N. Trefethen and David Bau III.</p>https://www.maplesoft.com/applications/view.aspx?SID=152382&ref=FeedTue, 01 Oct 2013 04:00:00 ZDouglas LewitDouglas LewitDynamics of the Battlefield: The Lanchester Model
https://www.maplesoft.com/applications/view.aspx?SID=146801&ref=Feed
<p>Around the time of World War I, July 28, 1914 to November 11, 1918, many mathematicians and engineers, including Frederick W. Lanchester, became fascinated by the dynamics of the battlefield. Various mathematical models were proposed in an effort to explain--and to predict--how military forces interacted on the battlefield. During World War I these mathematical investigations were mainly academic, although during World War II the United States government actually applied these models to make important decisions about the Battle of Iwo Jima in which the American forces seized control of the Japanese island of Iwo Jima. Outnumbered and outgunned by the Americans, the Japanese were defeated even before the battle began although the American forces suffered many casualties and injuries.</p><img src="https://www.maplesoft.com/view.aspx?si=146801/army2.JPG" alt="Dynamics of the Battlefield: The Lanchester Model" style="max-width: 25%;" align="left"/><p>Around the time of World War I, July 28, 1914 to November 11, 1918, many mathematicians and engineers, including Frederick W. Lanchester, became fascinated by the dynamics of the battlefield. Various mathematical models were proposed in an effort to explain--and to predict--how military forces interacted on the battlefield. During World War I these mathematical investigations were mainly academic, although during World War II the United States government actually applied these models to make important decisions about the Battle of Iwo Jima in which the American forces seized control of the Japanese island of Iwo Jima. Outnumbered and outgunned by the Americans, the Japanese were defeated even before the battle began although the American forces suffered many casualties and injuries.</p>https://www.maplesoft.com/applications/view.aspx?SID=146801&ref=FeedMon, 06 May 2013 04:00:00 ZDouglas LewitDouglas LewitSimulating the Spread of an Infection
https://www.maplesoft.com/applications/view.aspx?SID=144175&ref=Feed
<p>In the problem below I take advantage of Maple's Graph Theory package to simulate how an infection might spread throughout a small community of 15 individuals.</p>
<p>This is a computer simulation project rather than a biology project! For example, the infection may not be a biological infection at all. The 15 vertices could represent 15 different computers, and the "infection" that spreads could be interpreted as a computer virus rather than a biological virus.</p><img src="https://www.maplesoft.com/view.aspx?si=144175/siminfection_thumb.png" alt="Simulating the Spread of an Infection" style="max-width: 25%;" align="left"/><p>In the problem below I take advantage of Maple's Graph Theory package to simulate how an infection might spread throughout a small community of 15 individuals.</p>
<p>This is a computer simulation project rather than a biology project! For example, the infection may not be a biological infection at all. The 15 vertices could represent 15 different computers, and the "infection" that spreads could be interpreted as a computer virus rather than a biological virus.</p>https://www.maplesoft.com/applications/view.aspx?SID=144175&ref=FeedMon, 04 Mar 2013 05:00:00 ZDouglas LewitDouglas LewitUnderstanding the Slope and Y-Intercept of a Line
https://www.maplesoft.com/applications/view.aspx?SID=143408&ref=Feed
<p>This is a Maple application designed to help students understand the slope and y-intercept of a line.</p>
<p>The fun and educational app includes a dynamic plot with two sliders for changing the slope and y-intercept over a range of values from -30 to 30. Enjoy!</p><img src="https://www.maplesoft.com/view.aspx?si=143408/d1e71619e166d2f4ff49688b73f28690.gif" alt="Understanding the Slope and Y-Intercept of a Line" style="max-width: 25%;" align="left"/><p>This is a Maple application designed to help students understand the slope and y-intercept of a line.</p>
<p>The fun and educational app includes a dynamic plot with two sliders for changing the slope and y-intercept over a range of values from -30 to 30. Enjoy!</p>https://www.maplesoft.com/applications/view.aspx?SID=143408&ref=FeedTue, 12 Feb 2013 05:00:00 ZDouglas LewitDouglas LewitCalculation of the Average Duration of an Illness and Computation of the Reproduction Number in the SIR Model
https://www.maplesoft.com/applications/view.aspx?SID=142794&ref=Feed
<p>I prepared this Maple worksheet as part of a presentation to Professor Mubayi's lab group at Northeastern Illinois University. Every member of the research group explores a different aspect of how mathematics is used to study public health. During this presentation, I explore two different SIR models.</p><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Calculation of the Average Duration of an Illness and Computation of the Reproduction Number in the SIR Model" style="max-width: 25%;" align="left"/><p>I prepared this Maple worksheet as part of a presentation to Professor Mubayi's lab group at Northeastern Illinois University. Every member of the research group explores a different aspect of how mathematics is used to study public health. During this presentation, I explore two different SIR models.</p>https://www.maplesoft.com/applications/view.aspx?SID=142794&ref=FeedTue, 29 Jan 2013 05:00:00 ZDouglas LewitDouglas LewitMortgages
https://www.maplesoft.com/applications/view.aspx?SID=142213&ref=Feed
<p>Consider the problem of borrowing $250,000 to buy a house. You borrow the money at a fixed interest rate of 4.8% compounded monthly. The term of the mortgage is for 20 years. However, you decide against making minimum payments. Instead you decide to pay an additional $200 every month. How long will it take you to pay off the loan and how much have you saved on interest by paying off the loan early?</p><img src="https://www.maplesoft.com/view.aspx?si=142213/b8fc2d4d03908eeda63c803f8bbd81c1.gif" alt="Mortgages" style="max-width: 25%;" align="left"/><p>Consider the problem of borrowing $250,000 to buy a house. You borrow the money at a fixed interest rate of 4.8% compounded monthly. The term of the mortgage is for 20 years. However, you decide against making minimum payments. Instead you decide to pay an additional $200 every month. How long will it take you to pay off the loan and how much have you saved on interest by paying off the loan early?</p>https://www.maplesoft.com/applications/view.aspx?SID=142213&ref=FeedFri, 11 Jan 2013 05:00:00 ZDouglas LewitDouglas Lewit