Jim Herod: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=36
en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 31 May 2016 05:59:11 GMTTue, 31 May 2016 05:59:11 GMTNew applications published by Jim Herodhttp://www.mapleprimes.com/images/mapleapps.gifJim Herod: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=36
Partial Differential Equations: Complete Set of Lessons
http://www.maplesoft.com/applications/view.aspx?SID=4730&ref=Feed
This is a complete set of 40 Maple lessons for an undergraduate course in Partial Differential Equations. The course covers linear spaces; Fourier series; symbolic solutions to the heat, wave and Laplace equations with various boundary conditions; numerical methods; and general theory of first-order PDE's.
Prof. Jim Herod, Ret., formerly of Georgia Tech, developed the lessons. Dr. Herod has used and polished them through dozens of iterations of his course.<img src="/view.aspx?si=4730/thumb.jpg" alt="Partial Differential Equations: Complete Set of Lessons" align="left"/>This is a complete set of 40 Maple lessons for an undergraduate course in Partial Differential Equations. The course covers linear spaces; Fourier series; symbolic solutions to the heat, wave and Laplace equations with various boundary conditions; numerical methods; and general theory of first-order PDE's.
Prof. Jim Herod, Ret., formerly of Georgia Tech, developed the lessons. Dr. Herod has used and polished them through dozens of iterations of his course.4730Wed, 01 Oct 2003 00:00:00 ZJim HerodJim HerodProperty Surveying
http://www.maplesoft.com/applications/view.aspx?SID=4361&ref=Feed
This Maple application computes the perimeter of a tract of land based on the latitude and longitude measurements marking its corners. The distance formula used comes from http://jan.ucc.nau.edu/~cvm/latlongdist.html This formula is not a Great Circle Distance Formula. However, the Great Circle Distance for points as close together as those in a tract of farm land will not differ appreciably from the straight line formula. There is probably more error due to the topography of the terrain.<img src="/view.aspx?si=4361//applications/images/app_image_blank_lg.jpg" alt="Property Surveying" align="left"/>This Maple application computes the perimeter of a tract of land based on the latitude and longitude measurements marking its corners. The distance formula used comes from http://jan.ucc.nau.edu/~cvm/latlongdist.html This formula is not a Great Circle Distance Formula. However, the Great Circle Distance for points as close together as those in a tract of farm land will not differ appreciably from the straight line formula. There is probably more error due to the topography of the terrain.4361Mon, 10 Feb 2003 11:44:10 ZJim HerodJim HerodPeriodic solutions for a first order PDE with periodic forcing function
http://www.maplesoft.com/applications/view.aspx?SID=4158&ref=Feed
This Maple worksheet provides a method for finding solutions for non-homogeneous partial differential equation of the form
<br><img src="http://www.mapleapps.com/categories/mathematics/pdes/html/images/PeriodSum/PeriodSum1.gif" width=41 height=58 alt="diff(u,t)" align=middle>
<font color=#000000> = </font>
<img src="http://www.mapleapps.com/categories/mathematics/pdes/html/images/PeriodSum/PeriodSum2.gif" width=53 height=76 alt="diff(u,`$`(x,2))" align=middle>
<font color=#000000> + </font>
<img src="http://www.mapleapps.com/categories/mathematics/pdes/html/images/PeriodSum/PeriodSum3.gif" width=60 height=32 alt="F(t,x)" align=middle>
<font color=#000000>, u(t, 0) = 0 = u(t, 1).</font>
<br>More important, if the function F(t,x) is periodic as a function of t, it provides a method for finding a periodic solution for the partial differential equation. Even more. Techniques are used to emphasize a general structure suitable for finding a periodic solution for ordinary differential equations having the same general form of Y' = AY + F
where F is periodic.
<img src="/view.aspx?si=4158//applications/images/app_image_blank_lg.jpg" alt="Periodic solutions for a first order PDE with periodic forcing function" align="left"/>This Maple worksheet provides a method for finding solutions for non-homogeneous partial differential equation of the form
<br><img src="http://www.mapleapps.com/categories/mathematics/pdes/html/images/PeriodSum/PeriodSum1.gif" width=41 height=58 alt="diff(u,t)" align=middle>
<font color=#000000> = </font>
<img src="http://www.mapleapps.com/categories/mathematics/pdes/html/images/PeriodSum/PeriodSum2.gif" width=53 height=76 alt="diff(u,`$`(x,2))" align=middle>
<font color=#000000> + </font>
<img src="http://www.mapleapps.com/categories/mathematics/pdes/html/images/PeriodSum/PeriodSum3.gif" width=60 height=32 alt="F(t,x)" align=middle>
<font color=#000000>, u(t, 0) = 0 = u(t, 1).</font>
<br>More important, if the function F(t,x) is periodic as a function of t, it provides a method for finding a periodic solution for the partial differential equation. Even more. Techniques are used to emphasize a general structure suitable for finding a periodic solution for ordinary differential equations having the same general form of Y' = AY + F
where F is periodic.
4158Tue, 30 Oct 2001 10:39:16 ZJim HerodJim HerodFiltering and signal processing examples
http://www.maplesoft.com/applications/view.aspx?SID=3805&ref=Feed
This application uses Maple to clearly communicate filtering and signal processing concepts to students in an educational setting. An intuitive way to understand the projections of functions is to consider the application in signal processing for filtering. The word filtering refers to an attempt to extract the important part of some data, while eliminating random contributions referred to as noise, or to remove other unwanted features which obscure the signal. To illustrate the procedure, we choose a simple selection of features that are regarded as good and bad , to create low-pass and high-pass filters. Suppose that we have a signal f(t) which contains some pure frequencies in which we are interested. That is, we suppose the signal consists of some interesting part corresponding to pure vibratory functions represented as multiples and sums of
<img src="/view.aspx?si=3805//applications/images/app_image_blank_lg.jpg" alt="Filtering and signal processing examples" align="left"/>This application uses Maple to clearly communicate filtering and signal processing concepts to students in an educational setting. An intuitive way to understand the projections of functions is to consider the application in signal processing for filtering. The word filtering refers to an attempt to extract the important part of some data, while eliminating random contributions referred to as noise, or to remove other unwanted features which obscure the signal. To illustrate the procedure, we choose a simple selection of features that are regarded as good and bad , to create low-pass and high-pass filters. Suppose that we have a signal f(t) which contains some pure frequencies in which we are interested. That is, we suppose the signal consists of some interesting part corresponding to pure vibratory functions represented as multiples and sums of
3805Tue, 19 Jun 2001 00:00:00 ZJim HerodJim HerodTaylor, Legendre, and Bernstein polynomials
http://www.maplesoft.com/applications/view.aspx?SID=3486&ref=Feed
This worksheet illustrates the convergence of the Taylor (power) series for a function bounded and defined on (-1,1). You can modify the number of terms that will be used, and then view the animation as the terms are gradually added from lowest to highest power. To get started, just press enter after all of the statements. Then try your own f(x) and play with N.
<img src="/view.aspx?si=3486//applications/images/app_image_blank_lg.jpg" alt="Taylor, Legendre, and Bernstein polynomials" align="left"/>This worksheet illustrates the convergence of the Taylor (power) series for a function bounded and defined on (-1,1). You can modify the number of terms that will be used, and then view the animation as the terms are gradually added from lowest to highest power. To get started, just press enter after all of the statements. Then try your own f(x) and play with N.
3486Mon, 18 Jun 2001 00:00:00 ZJim HerodJim Herod