Laurie Lacey: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=208
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 26 Feb 2021 08:05:51 GMTFri, 26 Feb 2021 08:05:51 GMTNew applications published by Laurie Laceyhttps://www.maplesoft.com/images/Application_center_hp.jpgLaurie Lacey: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=208
Directed vs Undirected RootedTrees
https://www.maplesoft.com/applications/view.aspx?SID=4589&ref=Feed
When this maplet is run, it allows the student to examine various aspects of rooted trees. The results from Dijkstra's algorithm for shortest path spanning tree, Floyd's allpairs shortest path algorithm, and Prim's Algorithm may be examined. The maplet opens with a window asking the student to input either a directed or undirected graph. A different Maplet appears depending on the student's response. The maplet was constructed using Maple 9.5<img src="https://www.maplesoft.com/view.aspx?si=4589/thumb.gif" alt="Directed vs Undirected RootedTrees" style="max-width: 25%;" align="left"/>When this maplet is run, it allows the student to examine various aspects of rooted trees. The results from Dijkstra's algorithm for shortest path spanning tree, Floyd's allpairs shortest path algorithm, and Prim's Algorithm may be examined. The maplet opens with a window asking the student to input either a directed or undirected graph. A different Maplet appears depending on the student's response. The maplet was constructed using Maple 9.5https://www.maplesoft.com/applications/view.aspx?SID=4589&ref=FeedMon, 01 Nov 2004 00:00:00 ZLaurie LaceyLaurie LaceyMax Flow - Min Cut
https://www.maplesoft.com/applications/view.aspx?SID=4513&ref=Feed
When this maplet is run, it allows the student to examine the Max Flow - Min Cut Theorem. Students can compare the value of the maximum flow to the value of the minimum cut, and determine the edges of the minimum cut as well as the saturated edges. Students can observe the graph with the minimum cut edges removed. The maplet was constructed using Maple 9.5. A sample graph has been loaded into the first textfield so the student can see the syntax.<img src="https://www.maplesoft.com/view.aspx?si=4513//applications/images/app_image_blank_lg.jpg" alt="Max Flow - Min Cut" style="max-width: 25%;" align="left"/>When this maplet is run, it allows the student to examine the Max Flow - Min Cut Theorem. Students can compare the value of the maximum flow to the value of the minimum cut, and determine the edges of the minimum cut as well as the saturated edges. Students can observe the graph with the minimum cut edges removed. The maplet was constructed using Maple 9.5. A sample graph has been loaded into the first textfield so the student can see the syntax.https://www.maplesoft.com/applications/view.aspx?SID=4513&ref=FeedWed, 07 Jul 2004 09:19:33 ZLaurie LaceyLaurie LaceyA Maplet for Graph Drawing
https://www.maplesoft.com/applications/view.aspx?SID=4406&ref=Feed
When this maplet is run, it allows the student to examine a graph and its spanning tree visually. The student may also examine the adjacency matrix, the chromatic polynomial, the degree sequence, and the diameter of the graph. The maplet was built using the Maple 9 Classic worksheet.<img src="https://www.maplesoft.com/view.aspx?si=4406//applications/images/app_image_blank_lg.jpg" alt="A Maplet for Graph Drawing" style="max-width: 25%;" align="left"/>When this maplet is run, it allows the student to examine a graph and its spanning tree visually. The student may also examine the adjacency matrix, the chromatic polynomial, the degree sequence, and the diameter of the graph. The maplet was built using the Maple 9 Classic worksheet.https://www.maplesoft.com/applications/view.aspx?SID=4406&ref=FeedThu, 14 Aug 2003 09:29:49 ZLaurie LaceyLaurie LaceyHypocycloids and Epicycloids Project
https://www.maplesoft.com/applications/view.aspx?SID=4297&ref=Feed
The chapter on parametric equations and plane curves found in the seventh edition of Calculus by Larson, Hostetler, and Edwards [1] contains an interesting section project on hypocycloids and epicycloids. This worksheet explores this project and invites students to experiment with the examples<img src="https://www.maplesoft.com/view.aspx?si=4297//applications/images/app_image_blank_lg.jpg" alt="Hypocycloids and Epicycloids Project" style="max-width: 25%;" align="left"/>The chapter on parametric equations and plane curves found in the seventh edition of Calculus by Larson, Hostetler, and Edwards [1] contains an interesting section project on hypocycloids and epicycloids. This worksheet explores this project and invites students to experiment with the exampleshttps://www.maplesoft.com/applications/view.aspx?SID=4297&ref=FeedWed, 14 Aug 2002 12:21:03 ZLaurie LaceyLaurie LaceyProof of Jacobi's Identity
https://www.maplesoft.com/applications/view.aspx?SID=4296&ref=Feed
Calculus III is one of the first courses where students are introduced to proofs. Often the algebraic proofs concerning vectors can be stressful for the students. Moreover, students tend to substitute numbers in for the vector components and "prove" the theorem by example rather than in generality.
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We use Maple to help us prove Jacobi's Identity:
Jacobi's Identity: Given vectors <b>u </b>, <b>v </b>, and <b>w</b> in R3, <b>u</b> x ( <b>v</b> x <b>w</b> ) + <b>v</b> x ( <b>w</b> x <b>u</b> ) + <b>w</b> x ( <b>u</b> x <b>v</b> ) = 0 .<img src="https://www.maplesoft.com/view.aspx?si=4296//applications/images/app_image_blank_lg.jpg" alt="Proof of Jacobi's Identity" style="max-width: 25%;" align="left"/>Calculus III is one of the first courses where students are introduced to proofs. Often the algebraic proofs concerning vectors can be stressful for the students. Moreover, students tend to substitute numbers in for the vector components and "prove" the theorem by example rather than in generality.
<br><br>
We use Maple to help us prove Jacobi's Identity:
Jacobi's Identity: Given vectors <b>u </b>, <b>v </b>, and <b>w</b> in R3, <b>u</b> x ( <b>v</b> x <b>w</b> ) + <b>v</b> x ( <b>w</b> x <b>u</b> ) + <b>w</b> x ( <b>u</b> x <b>v</b> ) = 0 .https://www.maplesoft.com/applications/view.aspx?SID=4296&ref=FeedWed, 14 Aug 2002 12:14:55 ZLaurie LaceyLaurie LaceyCross-Hatched Cube
https://www.maplesoft.com/applications/view.aspx?SID=1379&ref=Feed
This aesthetically pleasing, albeit sinister creature, showed up while Calculus III applications of Maple were being investigated<img src="https://www.maplesoft.com/view.aspx?si=1379/hatchedcube.gif" alt="Cross-Hatched Cube" style="max-width: 25%;" align="left"/>This aesthetically pleasing, albeit sinister creature, showed up while Calculus III applications of Maple were being investigatedhttps://www.maplesoft.com/applications/view.aspx?SID=1379&ref=FeedTue, 21 Aug 2001 14:45:51 ZLaurie LaceyLaurie Lacey