Module 9: Inverse Transforms and Functions of Matrices

Module at a Glance ObjectivesHow to Complete This Module:

Cell description

Objectives

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

  • Compute inverse Laplace and z-transforms via residue integration.
  • Apply Laplace and z-transforms to study discrete-time and continuous-time signal processing, and dynamical systems.
  • Determine the properties of a holomorphic function of a matrix.
  • Apply matrix functions to the study of dynamical systems.

How to Complete This Module:

  1. View the video lectures in sequence. As you go through the videos, participate in the class discussion group.
  2. Read the assigned problems. Note that the problem labelled in boldface (on Bromwich contour for a branch cut) extends some of the concepts discussed in the lectures.
  3. Review the instructions for Mini-Project 1, identifying in particular those tasks that will require application of the new material presented in this module.
  4. Read the Lecture Notes that accompany the module.
  5. Submit Assignment 9. As you work on the problems:
    • Participate in the class discussions.
    • Refer to the notes or review certain videos as necessary.
    • You may find that you need to review some topics covered in prior modules. It is important to pose questions to the instructor who can guide you through a review process if it is necessary.
  6. Submit Mini-Project 1.
Technical
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        "body": "\n    <div> \n <h3><span>Objectives</span></h3> \n <p>By the end of this module, you will be able to:</p> \n <ul> \n  <li>Compute inverse Laplace and z-transforms via residue integration.</li> \n  <li>Apply Laplace and z-transforms to study discrete-time and continuous-time signal processing, and dynamical systems.</li> \n  <li>Determine the properties of a holomorphic function of a matrix.</li> \n  <li>Apply matrix functions to the study of dynamical systems.</li> \n </ul> \n <h3><span>How to Complete This Module:</span></h3> \n <ol> \n  <li>View the video lectures in sequence. As you go through the videos, participate in the class discussion group.</li> \n  <li>Read the assigned problems. Note that the problem labelled in boldface (on Bromwich contour for a branch cut) extends some of the concepts discussed in the lectures.</li> \n  <li>Review the instructions for Mini-Project 1, identifying in particular those tasks that will require application of the new material presented in this module.</li> \n  <li>Read the Lecture Notes that accompany the module.</li> \n  <li>Submit Assignment 9. As you work on the problems:</li> \n  <ul> \n   <li>Participate in the class discussions.</li> \n   <li>Refer to the notes or review certain videos as necessary.</li> \n   <li>You may find that you need to review some topics covered in prior modules. It is important to pose questions to the instructor who can guide you through a review process if it is necessary.</li> \n  </ul> \n  <li>Submit Mini-Project 1.</li> \n </ol> \n</div>\n  "
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Readings

Cell description
  • Module 9 Lecture Notes (PDF) : Read the Lecture Notes at least once through. Some of the more technical points regarding proofs may be a bit challenging, but the experience gained in reading through those sections at least once is worthwhile.
  • There is no single external source to supplement the notes. You should contact the instructor if there is a particular topic you would like to see in another source, whether for now or after the course ends. In any case, your time is most productively spent on going through the given notes and videos, working on the problems and Mini-Project, and discussing the material with other students and the instructor.
  • Since this module is a direct continuation of the previous one, you may find you need to review certain topics from Module 8.
Technical
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Some of the more technical points regarding proofs may be a bit challenging, but the experience gained in reading through those sections at least once is worthwhile.<br><br></li> \n  <li>There is no single external source to supplement the notes. You should contact the instructor if there is a particular topic you would like to see in another source, whether for now or after the course ends. In any case, your time is most productively spent on going through the given notes and videos, working on the problems and Mini-Project, and discussing the material with other students and the instructor.<br><br></li> \n  <li>Since this module is a direct continuation of the previous one, you may find you need to review certain topics from Module 8.</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_8341844_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Some of the more technical points regarding proofs may be a bit challenging, but the experience gained in reading through those sections at least once is worthwhile.<br><br></li> \n  <li>There is no single external source to supplement the notes. You should contact the instructor if there is a particular topic you would like to see in another source, whether for now or after the course ends. In any case, your time is most productively spent on going through the given notes and videos, working on the problems and Mini-Project, and discussing the material with other students and the instructor.<br><br></li> \n  <li>Since this module is a direct continuation of the previous one, you may find you need to review certain topics from Module 8.</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_8341844_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Video Lectures

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bb:menuorder=\"openId_64d70cc9ebe146c09715ed28d0552885,open_with_browser_64d70cc9ebe146c09715ed28d0552885,open_with_bbdrive_64d70cc9ebe146c09715ed28d0552885,openWebId_64d70cc9ebe146c09715ed28d0552885,view360Id_64d70cc9ebe146c09715ed28d0552885,*separator*,*separator*,ax-ally-placeholder_64d70cc9ebe146c09715ed28d0552885,ax-ally-markForAxAnalysis_64d70cc9ebe146c09715ed28d0552885,*separator*,*separator*,content_settings_64d70cc9ebe146c09715ed28d0552885,content_editSettings_64d70cc9ebe146c09715ed28d0552885,content_edit_64d70cc9ebe146c09715ed28d0552885,properties_folder_64d70cc9ebe146c09715ed28d0552885,itemcarot_managerecord_64d70cc9ebe146c09715ed28d0552885,comments_tool_64d70cc9ebe146c09715ed28d0552885,subscriptions_list_64d70cc9ebe146c09715ed28d0552885,content_readfile_64d70cc9ebe146c09715ed28d0552885,content_overwrite_64d70cc9ebe146c09715ed28d0552885,passes_tool_64d70cc9ebe146c09715ed28d0552885,permissions_tool_64d70cc9ebe146c09715ed28d0552885,content_add_alignment_64d70cc9ebe146c09715ed28d0552885,content_tracking_64d70cc9ebe146c09715ed28d0552885,content_versions_64d70cc9ebe146c09715ed28d0552885,*separator*,*separator*,bookmarkId_64d70cc9ebe146c09715ed28d0552885,itemsId_64d70cc9ebe146c09715ed28d0552885,packagesId_64d70cc9ebe146c09715ed28d0552885,emailId_64d70cc9ebe146c09715ed28d0552885,removeContentFolderId_64d70cc9ebe146c09715ed28d0552885,*separator*,copyContentId_64d70cc9ebe146c09715ed28d0552885,moveContentId_64d70cc9ebe146c09715ed28d0552885,*separator*,removeContentId_64d70cc9ebe146c09715ed28d0552885,*separator*,Metadata_General_64d70cc9ebe146c09715ed28d0552885,Metadata_Dublin_Core_64d70cc9ebe146c09715ed28d0552885,Metadata_IMS_64d70cc9ebe146c09715ed28d0552885,Metadata_Full_IMS_64d70cc9ebe146c09715ed28d0552885,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_64d70cc9ebe146c09715ed28d0552885\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_64d70cc9ebe146c09715ed28d0552885',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_64d70cc9ebe146c09715ed28d0552885',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_64d70cc9ebe146c09715ed28d0552885',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"91999377_2_fileReadWritePermAvl\" id=\"91999377_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('64d70cc9ebe146c09715ed28d0552885');\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><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_91999378_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8341845-dt-content-rid-91999378_2/xid-91999378_2\" target=\"_blank\" rel=\"noreferrer noopener\">09E_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module09/09E_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00kf&amp;course_id=_207703_1&amp;ctxMenuXythosId=91999378_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_975bd45e9b7345d19b9466b02942243b,open_with_browser_975bd45e9b7345d19b9466b02942243b,open_with_bbdrive_975bd45e9b7345d19b9466b02942243b,openWebId_975bd45e9b7345d19b9466b02942243b,view360Id_975bd45e9b7345d19b9466b02942243b,*separator*,*separator*,ax-ally-placeholder_975bd45e9b7345d19b9466b02942243b,ax-ally-markForAxAnalysis_975bd45e9b7345d19b9466b02942243b,*separator*,*separator*,content_settings_975bd45e9b7345d19b9466b02942243b,content_editSettings_975bd45e9b7345d19b9466b02942243b,content_edit_975bd45e9b7345d19b9466b02942243b,properties_folder_975bd45e9b7345d19b9466b02942243b,itemcarot_managerecord_975bd45e9b7345d19b9466b02942243b,comments_tool_975bd45e9b7345d19b9466b02942243b,subscriptions_list_975bd45e9b7345d19b9466b02942243b,content_readfile_975bd45e9b7345d19b9466b02942243b,content_overwrite_975bd45e9b7345d19b9466b02942243b,passes_tool_975bd45e9b7345d19b9466b02942243b,permissions_tool_975bd45e9b7345d19b9466b02942243b,content_add_alignment_975bd45e9b7345d19b9466b02942243b,content_tracking_975bd45e9b7345d19b9466b02942243b,content_versions_975bd45e9b7345d19b9466b02942243b,*separator*,*separator*,bookmarkId_975bd45e9b7345d19b9466b02942243b,itemsId_975bd45e9b7345d19b9466b02942243b,packagesId_975bd45e9b7345d19b9466b02942243b,emailId_975bd45e9b7345d19b9466b02942243b,removeContentFolderId_975bd45e9b7345d19b9466b02942243b,*separator*,copyContentId_975bd45e9b7345d19b9466b02942243b,moveContentId_975bd45e9b7345d19b9466b02942243b,*separator*,removeContentId_975bd45e9b7345d19b9466b02942243b,*separator*,Metadata_General_975bd45e9b7345d19b9466b02942243b,Metadata_Dublin_Core_975bd45e9b7345d19b9466b02942243b,Metadata_IMS_975bd45e9b7345d19b9466b02942243b,Metadata_Full_IMS_975bd45e9b7345d19b9466b02942243b,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_975bd45e9b7345d19b9466b02942243b\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_975bd45e9b7345d19b9466b02942243b',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_975bd45e9b7345d19b9466b02942243b',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_975bd45e9b7345d19b9466b02942243b',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"91999378_2_fileReadWritePermAvl\" id=\"91999378_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('975bd45e9b7345d19b9466b02942243b');\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><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_91999379_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8341845-dt-content-rid-91999379_2/xid-91999379_2\" target=\"_blank\" rel=\"noreferrer noopener\">09F_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module09/09F_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00kh&amp;course_id=_207703_1&amp;ctxMenuXythosId=91999379_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_def207ebd308477480e6a6e23bf89d41,open_with_browser_def207ebd308477480e6a6e23bf89d41,open_with_bbdrive_def207ebd308477480e6a6e23bf89d41,openWebId_def207ebd308477480e6a6e23bf89d41,view360Id_def207ebd308477480e6a6e23bf89d41,*separator*,*separator*,ax-ally-placeholder_def207ebd308477480e6a6e23bf89d41,ax-ally-markForAxAnalysis_def207ebd308477480e6a6e23bf89d41,*separator*,*separator*,content_settings_def207ebd308477480e6a6e23bf89d41,content_editSettings_def207ebd308477480e6a6e23bf89d41,content_edit_def207ebd308477480e6a6e23bf89d41,properties_folder_def207ebd308477480e6a6e23bf89d41,itemcarot_managerecord_def207ebd308477480e6a6e23bf89d41,comments_tool_def207ebd308477480e6a6e23bf89d41,subscriptions_list_def207ebd308477480e6a6e23bf89d41,content_readfile_def207ebd308477480e6a6e23bf89d41,content_overwrite_def207ebd308477480e6a6e23bf89d41,passes_tool_def207ebd308477480e6a6e23bf89d41,permissions_tool_def207ebd308477480e6a6e23bf89d41,content_add_alignment_def207ebd308477480e6a6e23bf89d41,content_tracking_def207ebd308477480e6a6e23bf89d41,content_versions_def207ebd308477480e6a6e23bf89d41,*separator*,*separator*,bookmarkId_def207ebd308477480e6a6e23bf89d41,itemsId_def207ebd308477480e6a6e23bf89d41,packagesId_def207ebd308477480e6a6e23bf89d41,emailId_def207ebd308477480e6a6e23bf89d41,removeContentFolderId_def207ebd308477480e6a6e23bf89d41,*separator*,copyContentId_def207ebd308477480e6a6e23bf89d41,moveContentId_def207ebd308477480e6a6e23bf89d41,*separator*,removeContentId_def207ebd308477480e6a6e23bf89d41,*separator*,Metadata_General_def207ebd308477480e6a6e23bf89d41,Metadata_Dublin_Core_def207ebd308477480e6a6e23bf89d41,Metadata_IMS_def207ebd308477480e6a6e23bf89d41,Metadata_Full_IMS_def207ebd308477480e6a6e23bf89d41,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_def207ebd308477480e6a6e23bf89d41\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_def207ebd308477480e6a6e23bf89d41',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_def207ebd308477480e6a6e23bf89d41',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_def207ebd308477480e6a6e23bf89d41',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"91999379_2_fileReadWritePermAvl\" id=\"91999379_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('def207ebd308477480e6a6e23bf89d41');\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><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_91999380_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8341845-dt-content-rid-91999380_2/xid-91999380_2\" target=\"_blank\" rel=\"noreferrer noopener\">09G_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module09/09G_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00kj&amp;course_id=_207703_1&amp;ctxMenuXythosId=91999380_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_9031056f7f954e30af4acb39d6a8fb52,open_with_browser_9031056f7f954e30af4acb39d6a8fb52,open_with_bbdrive_9031056f7f954e30af4acb39d6a8fb52,openWebId_9031056f7f954e30af4acb39d6a8fb52,view360Id_9031056f7f954e30af4acb39d6a8fb52,*separator*,*separator*,ax-ally-placeholder_9031056f7f954e30af4acb39d6a8fb52,ax-ally-markForAxAnalysis_9031056f7f954e30af4acb39d6a8fb52,*separator*,*separator*,content_settings_9031056f7f954e30af4acb39d6a8fb52,content_editSettings_9031056f7f954e30af4acb39d6a8fb52,content_edit_9031056f7f954e30af4acb39d6a8fb52,properties_folder_9031056f7f954e30af4acb39d6a8fb52,itemcarot_managerecord_9031056f7f954e30af4acb39d6a8fb52,comments_tool_9031056f7f954e30af4acb39d6a8fb52,subscriptions_list_9031056f7f954e30af4acb39d6a8fb52,content_readfile_9031056f7f954e30af4acb39d6a8fb52,content_overwrite_9031056f7f954e30af4acb39d6a8fb52,passes_tool_9031056f7f954e30af4acb39d6a8fb52,permissions_tool_9031056f7f954e30af4acb39d6a8fb52,content_add_alignment_9031056f7f954e30af4acb39d6a8fb52,content_tracking_9031056f7f954e30af4acb39d6a8fb52,content_versions_9031056f7f954e30af4acb39d6a8fb52,*separator*,*separator*,bookmarkId_9031056f7f954e30af4acb39d6a8fb52,itemsId_9031056f7f954e30af4acb39d6a8fb52,packagesId_9031056f7f954e30af4acb39d6a8fb52,emailId_9031056f7f954e30af4acb39d6a8fb52,removeContentFolderId_9031056f7f954e30af4acb39d6a8fb52,*separator*,copyContentId_9031056f7f954e30af4acb39d6a8fb52,moveContentId_9031056f7f954e30af4acb39d6a8fb52,*separator*,removeContentId_9031056f7f954e30af4acb39d6a8fb52,*separator*,Metadata_General_9031056f7f954e30af4acb39d6a8fb52,Metadata_Dublin_Core_9031056f7f954e30af4acb39d6a8fb52,Metadata_IMS_9031056f7f954e30af4acb39d6a8fb52,Metadata_Full_IMS_9031056f7f954e30af4acb39d6a8fb52,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_9031056f7f954e30af4acb39d6a8fb52\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_9031056f7f954e30af4acb39d6a8fb52',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_9031056f7f954e30af4acb39d6a8fb52',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_9031056f7f954e30af4acb39d6a8fb52',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"91999380_2_fileReadWritePermAvl\" id=\"91999380_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('9031056f7f954e30af4acb39d6a8fb52');\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><p></p> \n</div>\n  </div>\n\n <div id=\"_8341845_1previewModule\" class=\"moduleSample\">\n </div>\n",
        "url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_207703_1&content_id=_8341845_1&mode=view",
        "title": "Video Lectures"
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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('64d70cc9ebe146c09715ed28d0552885');\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><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_91999378_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8341845-dt-content-rid-91999378_2/xid-91999378_2\" target=\"_blank\" rel=\"noreferrer noopener\">09E_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module09/09E_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00kf&amp;course_id=_207703_1&amp;ctxMenuXythosId=91999378_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_975bd45e9b7345d19b9466b02942243b\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_975bd45e9b7345d19b9466b02942243b',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_975bd45e9b7345d19b9466b02942243b',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_975bd45e9b7345d19b9466b02942243b',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"91999378_2_fileReadWritePermAvl\" id=\"91999378_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('975bd45e9b7345d19b9466b02942243b');\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><p></p> \n <p><span class=\"axScoreIndicator axVtbeEmbedded application\"><span data-ally-scoreindicator=\"_91999379_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8341845-dt-content-rid-91999379_2/xid-91999379_2\" target=\"_blank\" rel=\"noreferrer noopener\">09F_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module09/09F_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00kh&amp;course_id=_207703_1&amp;ctxMenuXythosId=91999379_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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data-ally-scoreindicator=\"_91999380_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8341845-dt-content-rid-91999380_2/xid-91999380_2\" target=\"_blank\" rel=\"noreferrer noopener\">09G_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module09/09G_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00kj&amp;course_id=_207703_1&amp;ctxMenuXythosId=91999380_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_9031056f7f954e30af4acb39d6a8fb52,open_with_browser_9031056f7f954e30af4acb39d6a8fb52,open_with_bbdrive_9031056f7f954e30af4acb39d6a8fb52,openWebId_9031056f7f954e30af4acb39d6a8fb52,view360Id_9031056f7f954e30af4acb39d6a8fb52,*separator*,*separator*,ax-ally-placeholder_9031056f7f954e30af4acb39d6a8fb52,ax-ally-markForAxAnalysis_9031056f7f954e30af4acb39d6a8fb52,*separator*,*separator*,content_settings_9031056f7f954e30af4acb39d6a8fb52,content_editSettings_9031056f7f954e30af4acb39d6a8fb52,content_edit_9031056f7f954e30af4acb39d6a8fb52,properties_folder_9031056f7f954e30af4acb39d6a8fb52,itemcarot_managerecord_9031056f7f954e30af4acb39d6a8fb52,comments_tool_9031056f7f954e30af4acb39d6a8fb52,subscriptions_list_9031056f7f954e30af4acb39d6a8fb52,content_readfile_9031056f7f954e30af4acb39d6a8fb52,content_overwrite_9031056f7f954e30af4acb39d6a8fb52,passes_tool_9031056f7f954e30af4acb39d6a8fb52,permissions_tool_9031056f7f954e30af4acb39d6a8fb52,content_add_alignment_9031056f7f954e30af4acb39d6a8fb52,content_tracking_9031056f7f954e30af4acb39d6a8fb52,content_versions_9031056f7f954e30af4acb39d6a8fb52,*separator*,*separator*,bookmarkId_9031056f7f954e30af4acb39d6a8fb52,itemsId_9031056f7f954e30af4acb39d6a8fb52,packagesId_9031056f7f954e30af4acb39d6a8fb52,emailId_9031056f7f954e30af4acb39d6a8fb52,removeContentFolderId_9031056f7f954e30af4acb39d6a8fb52,*separator*,copyContentId_9031056f7f954e30af4acb39d6a8fb52,moveContentId_9031056f7f954e30af4acb39d6a8fb52,*separator*,removeContentId_9031056f7f954e30af4acb39d6a8fb52,*separator*,Metadata_General_9031056f7f954e30af4acb39d6a8fb52,Metadata_Dublin_Core_9031056f7f954e30af4acb39d6a8fb52,Metadata_IMS_9031056f7f954e30af4acb39d6a8fb52,Metadata_Full_IMS_9031056f7f954e30af4acb39d6a8fb52,\" 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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('9031056f7f954e30af4acb39d6a8fb52');\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><p></p> \n</div>\n  </div>\n\n <div id=\"_8341845_1previewModule\" class=\"moduleSample\">\n </div>\n",
    "url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_207703_1&content_id=_8341845_1&mode=view",
    "parent": 61,
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        "title": "Video Lectures",
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bb:menuorder=\"openId_12f2b7ddd36341169deb2037fb9a62dc,open_with_browser_12f2b7ddd36341169deb2037fb9a62dc,open_with_bbdrive_12f2b7ddd36341169deb2037fb9a62dc,openWebId_12f2b7ddd36341169deb2037fb9a62dc,view360Id_12f2b7ddd36341169deb2037fb9a62dc,*separator*,*separator*,ax-ally-placeholder_12f2b7ddd36341169deb2037fb9a62dc,ax-ally-markForAxAnalysis_12f2b7ddd36341169deb2037fb9a62dc,*separator*,*separator*,content_settings_12f2b7ddd36341169deb2037fb9a62dc,content_editSettings_12f2b7ddd36341169deb2037fb9a62dc,content_edit_12f2b7ddd36341169deb2037fb9a62dc,properties_folder_12f2b7ddd36341169deb2037fb9a62dc,itemcarot_managerecord_12f2b7ddd36341169deb2037fb9a62dc,comments_tool_12f2b7ddd36341169deb2037fb9a62dc,subscriptions_list_12f2b7ddd36341169deb2037fb9a62dc,content_readfile_12f2b7ddd36341169deb2037fb9a62dc,content_overwrite_12f2b7ddd36341169deb2037fb9a62dc,passes_tool_12f2b7ddd36341169deb2037fb9a62dc,permissions_tool_12f2b7ddd36341169deb2037fb9a62dc,content_add_alignment_12f2b7ddd36341169deb2037fb9a62dc,content_tracking_12f2b7ddd36341169deb2037fb9a62dc,content_versions_12f2b7ddd36341169deb2037fb9a62dc,*separator*,*separator*,bookmarkId_12f2b7ddd36341169deb2037fb9a62dc,itemsId_12f2b7ddd36341169deb2037fb9a62dc,packagesId_12f2b7ddd36341169deb2037fb9a62dc,emailId_12f2b7ddd36341169deb2037fb9a62dc,removeContentFolderId_12f2b7ddd36341169deb2037fb9a62dc,*separator*,copyContentId_12f2b7ddd36341169deb2037fb9a62dc,moveContentId_12f2b7ddd36341169deb2037fb9a62dc,*separator*,removeContentId_12f2b7ddd36341169deb2037fb9a62dc,*separator*,Metadata_General_12f2b7ddd36341169deb2037fb9a62dc,Metadata_Dublin_Core_12f2b7ddd36341169deb2037fb9a62dc,Metadata_IMS_12f2b7ddd36341169deb2037fb9a62dc,Metadata_Full_IMS_12f2b7ddd36341169deb2037fb9a62dc,\" 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Q&A

Cell description

Continue to ask questions and answer your classmates' questions in Piazza.

Participation in the class discussion is expected. It is unlikely you will go through the material without any questions. Please be sure to make at least one technically relevant posting, whether a question or comment.

To access Piazza, click Piazza Discussions on the course menu.

Technical
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Assignment 9

Cell description

Assignment 9

has three problems. The first two are fairly straightforward specific examples of topics covered in the module. The third problem involves extending topics covered in this module to a new context. Specifically, whereas the module notes focused on methods for computing the inverse Laplace transform integral for rational functions, in this problem the function of interest has a fractional exponent.

The assignment is due by the end of Module 9, following the Assignment Guidelines.

To submit the assignment, click the Assignment 9 title above.

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Mini-Project 1

Cell description

Finish Mini-Project 1

 and submit it. Note: Remember to submit your computer code, not just results!

The Mini-Project is due by the end of Module 9, following the Mini-Project Guidelines. Your grade for the project will be based on your final submission only, so do not be concerned if you already submitted preliminary work was incomplete or has errors.

To submit the mini-project, click the Mini-Project 1 title above.

Technical
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