Module 2: Properties of z-Transforms and Inverse z-Transforms

Lectures and Content

Folder description

Please click the folder link above to access the Module 2 instructional content. Module 2 contains four video lectures that present the following topics:

Application of z-Transform Theorems (2A)
Computing Inverse z-Transforms (2B)
Solving Discrete-Time Difference Equations Using z-Transforms (2C)
Mathematical Models of Discrete-Time Control Elements (2D)

Technical

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Module at a Glance ObjectivesHow to Complete This Module:

Cell description

Objectives

By the end of this module, you will be able to:

Apply common theorems of the z-Transform to easily solve z-Transforms of interest
Understand and apply three methods for computing the inverse z-Transform.
Develop and understand the mathematical representations/operations of sampling and data-hold functions ( zero-order hold, first-order hold).

How to Complete This Module:

View “Application of z-Transform Theorems” (video 2A)
Read Chapter 2.5 from Ogata 2nd Edition
View “Computing Inverse z-Transforms” (video 2B)
Read Chapter 2.6 from Ogata 2nd Edition
View “Solving Discrete-Time Difference Equations Using z-Transforms” (video 2C)
Read Chapters 3.1 – 3.2 from Ogata 2nd Edition
View “Mathematical Models of Discrete-Time Control Elements” (video 2D)

Technical

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Readings

Cell description

This weeks readings include the following:

Ogata,K. (1995). Discrete-Time Control Systems (2nd Edition). Upper Saddle River, New Jersey. Prentice Hall.

Chapter 2.5 - 2.6
Chapter 3.1 – 3.2

Urbant, T. (2016) Digital Control and System Applications

Module 2A – Handouts
Module 2B – Handouts
Module 2C – Handouts
Module 2D – Handouts

Technical

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Prentice Hall.</p> \n <table summary=\"Discrete-Time Control Text graphic\" border=\"0\"> \n  <tbody> \n   <tr> \n    <td class=\"nowrapCell\"><span class=\"axScoreIndicator axVtbeEmbedded image\"><span data-ally-scoreindicator=\"_103909318_2\"></span></span>\n<img src=\"https://blackboard.jhu.edu/bbcswebdav/pid-9946150-dt-content-rid-103909318_2/xid-103909318_2\" alt=\"Discrete-Time Control Systems Textbook\" title=\"Discrete-Time Control Systems Textbook\" width=\"92\" height=\"119\"> \n<span class=\"contextMenuContainer image\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.535.645.81.SU21/Screen%20Shot%202016-09-29%20at%208.36.15%20AM.png?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00bw&amp;course_id=_233190_1&amp;ctxMenuXythosId=103909318_2&amp;course_id=_233190_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_a026c3ada8af438da7b2487302813f20,open_with_browser_a026c3ada8af438da7b2487302813f20,open_with_bbdrive_a026c3ada8af438da7b2487302813f20,openWebId_a026c3ada8af438da7b2487302813f20,view360Id_a026c3ada8af438da7b2487302813f20,*separator*,*separator*,ax-ally-placeholder_a026c3ada8af438da7b2487302813f20,ax-ally-markForAxAnalysis_a026c3ada8af438da7b2487302813f20,*separator*,*separator*,content_settings_a026c3ada8af438da7b2487302813f20,content_editSettings_a026c3ada8af438da7b2487302813f20,content_edit_a026c3ada8af438da7b2487302813f20,properties_folder_a026c3ada8af438da7b2487302813f20,itemcarot_managerecord_a026c3ada8af438da7b2487302813f20,comments_tool_a026c3ada8af438da7b2487302813f20,subscriptions_list_a026c3ada8af438da7b2487302813f20,content_readfile_a026c3ada8af438da7b2487302813f20,content_overwrite_a026c3ada8af438da7b2487302813f20,passes_tool_a026c3ada8af438da7b2487302813f20,permissions_tool_a026c3ada8af438da7b2487302813f20,content_add_alignment_a026c3ada8af438da7b2487302813f20,content_tracking_a026c3ada8af438da7b2487302813f20,content_versions_a026c3ada8af438da7b2487302813f20,*separator*,*separator*,bookmarkId_a026c3ada8af438da7b2487302813f20,itemsId_a026c3ada8af438da7b2487302813f20,packagesId_a026c3ada8af438da7b2487302813f20,emailId_a026c3ada8af438da7b2487302813f20,removeContentFolderId_a026c3ada8af438da7b2487302813f20,*separator*,copyContentId_a026c3ada8af438da7b2487302813f20,moveContentId_a026c3ada8af438da7b2487302813f20,*separator*,removeContentId_a026c3ada8af438da7b2487302813f20,*separator*,Metadata_General_a026c3ada8af438da7b2487302813f20,Metadata_Dublin_Core_a026c3ada8af438da7b2487302813f20,Metadata_IMS_a026c3ada8af438da7b2487302813f20,Metadata_Full_IMS_a026c3ada8af438da7b2487302813f20,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_a026c3ada8af438da7b2487302813f20\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_a026c3ada8af438da7b2487302813f20',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_a026c3ada8af438da7b2487302813f20',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_a026c3ada8af438da7b2487302813f20',true);\"></a> \n  </span> \n<input type=\"hidden\" name=\"103909318_2_fileReadWritePermAvl\" id=\"103909318_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('a026c3ada8af438da7b2487302813f20');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script></td> \n    <td> \n     <ul> \n      <li>Chapter 2.5 - 2.6</li> \n      <li>Chapter 3.1 – 3.2</li> \n     </ul> </td> \n   </tr> \n  </tbody> \n </table> \n <br> \n <p>&nbsp; Urbant, T. (2016) Digital Control and System Applications</p> \n <ul> \n  <li>Module 2A – Handouts</li> \n  <li>Module 2B – Handouts</li> \n  <li>Module 2C – Handouts</li> \n  <li>Module 2D – Handouts</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_9946150_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Prentice Hall.</p> \n <table summary=\"Discrete-Time Control Text graphic\" border=\"0\"> \n  <tbody> \n   <tr> \n    <td class=\"nowrapCell\"><span class=\"axScoreIndicator axVtbeEmbedded image\"><span data-ally-scoreindicator=\"_103909318_2\"></span></span>\n<img src=\"https://blackboard.jhu.edu/bbcswebdav/pid-9946150-dt-content-rid-103909318_2/xid-103909318_2\" alt=\"Discrete-Time Control Systems Textbook\" title=\"Discrete-Time Control Systems Textbook\" width=\"92\" height=\"119\"> \n<span class=\"contextMenuContainer image\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.535.645.81.SU21/Screen%20Shot%202016-09-29%20at%208.36.15%20AM.png?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00bw&amp;course_id=_233190_1&amp;ctxMenuXythosId=103909318_2&amp;course_id=_233190_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_a026c3ada8af438da7b2487302813f20,open_with_browser_a026c3ada8af438da7b2487302813f20,open_with_bbdrive_a026c3ada8af438da7b2487302813f20,openWebId_a026c3ada8af438da7b2487302813f20,view360Id_a026c3ada8af438da7b2487302813f20,*separator*,*separator*,ax-ally-placeholder_a026c3ada8af438da7b2487302813f20,ax-ally-markForAxAnalysis_a026c3ada8af438da7b2487302813f20,*separator*,*separator*,content_settings_a026c3ada8af438da7b2487302813f20,content_editSettings_a026c3ada8af438da7b2487302813f20,content_edit_a026c3ada8af438da7b2487302813f20,properties_folder_a026c3ada8af438da7b2487302813f20,itemcarot_managerecord_a026c3ada8af438da7b2487302813f20,comments_tool_a026c3ada8af438da7b2487302813f20,subscriptions_list_a026c3ada8af438da7b2487302813f20,content_readfile_a026c3ada8af438da7b2487302813f20,content_overwrite_a026c3ada8af438da7b2487302813f20,passes_tool_a026c3ada8af438da7b2487302813f20,permissions_tool_a026c3ada8af438da7b2487302813f20,content_add_alignment_a026c3ada8af438da7b2487302813f20,content_tracking_a026c3ada8af438da7b2487302813f20,content_versions_a026c3ada8af438da7b2487302813f20,*separator*,*separator*,bookmarkId_a026c3ada8af438da7b2487302813f20,itemsId_a026c3ada8af438da7b2487302813f20,packagesId_a026c3ada8af438da7b2487302813f20,emailId_a026c3ada8af438da7b2487302813f20,removeContentFolderId_a026c3ada8af438da7b2487302813f20,*separator*,copyContentId_a026c3ada8af438da7b2487302813f20,moveContentId_a026c3ada8af438da7b2487302813f20,*separator*,removeContentId_a026c3ada8af438da7b2487302813f20,*separator*,Metadata_General_a026c3ada8af438da7b2487302813f20,Metadata_Dublin_Core_a026c3ada8af438da7b2487302813f20,Metadata_IMS_a026c3ada8af438da7b2487302813f20,Metadata_Full_IMS_a026c3ada8af438da7b2487302813f20,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_a026c3ada8af438da7b2487302813f20\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_a026c3ada8af438da7b2487302813f20',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_a026c3ada8af438da7b2487302813f20',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_a026c3ada8af438da7b2487302813f20',true);\"></a> \n  </span> \n<input type=\"hidden\" name=\"103909318_2_fileReadWritePermAvl\" id=\"103909318_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('a026c3ada8af438da7b2487302813f20');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script></td> \n    <td> \n     <ul> \n      <li>Chapter 2.5 - 2.6</li> \n      <li>Chapter 3.1 – 3.2</li> \n     </ul> </td> \n   </tr> \n  </tbody> \n </table> \n <br> \n <p>&nbsp; Urbant, T. (2016) Digital Control and System Applications</p> \n <ul> \n  <li>Module 2A – Handouts</li> \n  <li>Module 2B – Handouts</li> \n  <li>Module 2C – Handouts</li> \n  <li>Module 2D – Handouts</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_9946150_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Module 2 Discussion Question 1 - MATLAB Isim

Cell description

Share with the class why you think the MATHWORKS MATLAB implemented their linear-time-invariant differential equation solver “lsim” using a z-Transform?

You will be graded on your participation in this activity, not on the accuracy of your answer. Please share your response by Day 3 of Module 2, then provide your feedback to your classmates by Day 5 of Module 2.

Technical

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Module 2 Discussion Question 2 - Practice Assignment

Cell description

For this activity, you will work with a partner to practice solving problems.

Partner’s will be paired up based on the order of initial posts. 1st & 2nd responders will pair up, 3rd & 4th will pair up, etc.
Download the following Practice Assignment and complete the problems. Practice Assignment
After you have completed the problem, scan your work or take a very clear picture with your phone or camera.
Respond to this discussion forum and attach the file with your completed work.
Find your assigned partner’s attached files and download their work.
Review their solution to the problem and provide any corrections or comments on their work. You may want to do this on paper and then scan or take a picture of your corrections.
Reply to their post by attaching a new file with your corrections and comments. You may also choose to respond using the discussion textbox, whatever best allows you to exchange ideas with your partner.

You will be graded on your participation in this activity, not on the accuracy of solving the problem. Please upload your first attempt at solving this problem by Day 4 of Module 2, then provide your feedback by Day 6 of Module 2. Please note that this is a chance to practice solving similar to the Module 2 Assignment where you will be graded on your accuracy, so take full advantage of this exercise.

Technical

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You may want to do this on paper and then scan or take a picture of your corrections.</li> \n  <li><span>Reply to their post by attaching a new file with your corrections and comments. You may also choose to respond using the discussion <span>textbox</span>, whatever best allows you to exchange ideas with your partner.</span></li> \n </ol> \n <p>You will be graded on your participation in this activity, not on the accuracy of solving the problem. <span style=\"text-decoration: underline;\">Please upload your first attempt at solving this problem by Day 4 of Module 2, then provide your feedback by Day 6 of Module 2.</span> Please note that&nbsp;this is a chance to practice solving similar to the Module 2 Assignment where you will be graded on your accuracy, so take full advantage of this exercise.</p> \n</div>\n  </div>\n\n <div id=\"_9826856_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "title": "Module 2 Discussion Question 2 - Practice Assignment"
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2<span>nd</span> responders will pair up, 3rd &amp; 4th will pair up, etc.</span></li> \n  <li>Download the following Practice Assignment and complete the problems.<br><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_103909346_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-9826856-dt-content-rid-103909346_2/xid-103909346_2\" target=\"_blank\">Practice Assignment</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.535.645.81.SU21/Module%2002/Module%202%20Practice%20Assignment.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00by&amp;course_id=_233190_1&amp;ctxMenuXythosId=103909346_2&amp;course_id=_233190_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_4bc981dffbe4430784a473c5c395de80,open_with_browser_4bc981dffbe4430784a473c5c395de80,open_with_bbdrive_4bc981dffbe4430784a473c5c395de80,openWebId_4bc981dffbe4430784a473c5c395de80,view360Id_4bc981dffbe4430784a473c5c395de80,*separator*,*separator*,ax-ally-placeholder_4bc981dffbe4430784a473c5c395de80,ax-ally-markForAxAnalysis_4bc981dffbe4430784a473c5c395de80,*separator*,*separator*,content_settings_4bc981dffbe4430784a473c5c395de80,content_editSettings_4bc981dffbe4430784a473c5c395de80,content_edit_4bc981dffbe4430784a473c5c395de80,properties_folder_4bc981dffbe4430784a473c5c395de80,itemcarot_managerecord_4bc981dffbe4430784a473c5c395de80,comments_tool_4bc981dffbe4430784a473c5c395de80,subscriptions_list_4bc981dffbe4430784a473c5c395de80,content_readfile_4bc981dffbe4430784a473c5c395de80,content_overwrite_4bc981dffbe4430784a473c5c395de80,passes_tool_4bc981dffbe4430784a473c5c395de80,permissions_tool_4bc981dffbe4430784a473c5c395de80,content_add_alignment_4bc981dffbe4430784a473c5c395de80,content_tracking_4bc981dffbe4430784a473c5c395de80,content_versions_4bc981dffbe4430784a473c5c395de80,*separator*,*separator*,bookmarkId_4bc981dffbe4430784a473c5c395de80,itemsId_4bc981dffbe4430784a473c5c395de80,packagesId_4bc981dffbe4430784a473c5c395de80,emailId_4bc981dffbe4430784a473c5c395de80,removeContentFolderId_4bc981dffbe4430784a473c5c395de80,*separator*,copyContentId_4bc981dffbe4430784a473c5c395de80,moveContentId_4bc981dffbe4430784a473c5c395de80,*separator*,removeContentId_4bc981dffbe4430784a473c5c395de80,*separator*,Metadata_General_4bc981dffbe4430784a473c5c395de80,Metadata_Dublin_Core_4bc981dffbe4430784a473c5c395de80,Metadata_IMS_4bc981dffbe4430784a473c5c395de80,Metadata_Full_IMS_4bc981dffbe4430784a473c5c395de80,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_4bc981dffbe4430784a473c5c395de80\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_4bc981dffbe4430784a473c5c395de80',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_4bc981dffbe4430784a473c5c395de80',true);\" class=\"cmimg editmode jsInit   cmimg-hide\" href=\"#contextMenu\" title=\"Click for more options\"> <img src=\"/images/ci/icons/cmlink_generic.gif\" alt=\"Click for more options\" onload=\"page.ContextMenu.LI(event, 'cmdiv_4bc981dffbe4430784a473c5c395de80',true);\"></a> \n  </span> \n<input type=\"hidden\" name=\"103909346_2_fileReadWritePermAvl\" id=\"103909346_2_fileReadWritePermAvl\" value=\"false\"> \n<script type=\"text/javascript\" src=\"/javascript/cdn.js\"></script> \n<script type=\"text/javascript\" src=\"/groupjs/FF147D720E72E17F96127A7085584389.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/dirlistrightframe/dirlist.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\" src=\"/webapps/cmsmain/static/bbDriveUtil.js?v=3800.0.9-rel.16+8f8c3e7\"></script> \n<script type=\"text/javascript\">\n    (function(){\n     var f = function(){\n           if ( window.DWREngine )\n      {\n       if( DWREngine._batch )\n       {\n      \t try {DWREngine.endBatch();} catch(ignore) {}\n       }\n       try {DWREngine.beginBatch();} catch(ignore) {}\n      } \n             page.ContextMenu.hideMenuDiv('4bc981dffbe4430784a473c5c395de80');\n            if ( window.DWREngine )\n      {\n        try {DWREngine.endBatch();} catch(ignore) {}\n      }\n               };\n     var f2 = function()\n     {\n       if ( page.isLoaded )\n       {\n         f();\n       }\n       else\n       {\n         setTimeout( f2, 500 );\n       }\n     }\n     f2();\n    })();\n   </script></li> \n  <li>After you have completed the problem, scan your work or take a very clear picture with your phone or camera.</li> \n  <li>Respond to this discussion forum and attach the file with your completed work.</li> \n  <li>Find your assigned partner’s attached files and download their work.</li> \n  <li>Review their solution to the problem and provide any corrections or comments on their work. You may want to do this on paper and then scan or take a picture of your corrections.</li> \n  <li><span>Reply to their post by attaching a new file with your corrections and comments. You may also choose to respond using the discussion <span>textbox</span>, whatever best allows you to exchange ideas with your partner.</span></li> \n </ol> \n <p>You will be graded on your participation in this activity, not on the accuracy of solving the problem. <span style=\"text-decoration: underline;\">Please upload your first attempt at solving this problem by Day 4 of Module 2, then provide your feedback by Day 6 of Module 2.</span> Please note that&nbsp;this is a chance to practice solving similar to the Module 2 Assignment where you will be graded on your accuracy, so take full advantage of this exercise.</p> \n</div>\n  </div>\n\n <div id=\"_9826856_1previewModule\" class=\"moduleSample\">\n </div>\n",
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file_1.pdf
./attachments/cell_19/file_1.pdf

Module 2 Assignment

Cell description

Please open the attachments above and complete the Problem Set:

Module 2 Assignment

As you complete this Problem Set please show all your work. When you are finished, scan the document containing your final work or take a clear and readable picture with a camera or phone. Submit your response by day 7 of Module 2

Technical

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When you are finished, scan the document containing your final work or take a clear and readable picture with a camera or phone. <span style=\"text-decoration: underline;\">Submit your response by day 7 of Module 2</span></p> \n</div>\n  </div>\n\n <div id=\"_9826857_1previewModule\" class=\"moduleSample\">\n </div>\n",
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</li></ul></div></div>\n\n    <div class=\"vtbegenerated\"> \n <p>Please open the attachments above and complete the Problem Set:</p> \n <ul> \n  <li>Module 2 Assignment</li> \n </ul> \n <p>As you complete this Problem Set please show all your work. 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file_1.pdf
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Module 2 Assignment Solutions

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Technical

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