Module 12: Harmonic Functions

Final Exam

Folder description

The Final Exam will be available starting at 9pm EST on 8/15 and will be due by 11:59pm EST on 8/17.

Click the folder name to access the exam file and submission link after the start time.

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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 concepts of complex analysis to certain types of boundary value problems through the notion of harmonic functions.
  • Obtain representations and properties of harmonic and holomorphic functions, using relations such as the Poisson integral formula and Hilbert transform.

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.
  3. Read the Lecture Notes that accompany the module.
  4. Submit Assignment 12. 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.
  5. Submit the Final Exam.
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Readings

Cell description
  • Module 12 Lecture Notes (PDF) : Read the Lecture Notes at least once through, after viewing the complete set of videos.
  • A portion of the topics in this module are covered in briefly in the Stein book, with the specific references given in the Assignment pages. However, 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 problem.
  • The content of this module (videos, lectures notes and length of the assignment) is less compared to other modules, so you have time to review for the Final Exam. You should spend time reviewing prior material, including graded assignments, and participate in discussions with other students and the instructor.
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Video Lectures

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bb:menuorder=\"openId_5ca3dd576c2b4f0d9ed512633efbffb5,open_with_browser_5ca3dd576c2b4f0d9ed512633efbffb5,open_with_bbdrive_5ca3dd576c2b4f0d9ed512633efbffb5,openWebId_5ca3dd576c2b4f0d9ed512633efbffb5,view360Id_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,*separator*,ax-ally-placeholder_5ca3dd576c2b4f0d9ed512633efbffb5,ax-ally-markForAxAnalysis_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,*separator*,content_settings_5ca3dd576c2b4f0d9ed512633efbffb5,content_editSettings_5ca3dd576c2b4f0d9ed512633efbffb5,content_edit_5ca3dd576c2b4f0d9ed512633efbffb5,properties_folder_5ca3dd576c2b4f0d9ed512633efbffb5,itemcarot_managerecord_5ca3dd576c2b4f0d9ed512633efbffb5,comments_tool_5ca3dd576c2b4f0d9ed512633efbffb5,subscriptions_list_5ca3dd576c2b4f0d9ed512633efbffb5,content_readfile_5ca3dd576c2b4f0d9ed512633efbffb5,content_overwrite_5ca3dd576c2b4f0d9ed512633efbffb5,passes_tool_5ca3dd576c2b4f0d9ed512633efbffb5,permissions_tool_5ca3dd576c2b4f0d9ed512633efbffb5,content_add_alignment_5ca3dd576c2b4f0d9ed512633efbffb5,content_tracking_5ca3dd576c2b4f0d9ed512633efbffb5,content_versions_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,*separator*,bookmarkId_5ca3dd576c2b4f0d9ed512633efbffb5,itemsId_5ca3dd576c2b4f0d9ed512633efbffb5,packagesId_5ca3dd576c2b4f0d9ed512633efbffb5,emailId_5ca3dd576c2b4f0d9ed512633efbffb5,removeContentFolderId_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,copyContentId_5ca3dd576c2b4f0d9ed512633efbffb5,moveContentId_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,removeContentId_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,Metadata_General_5ca3dd576c2b4f0d9ed512633efbffb5,Metadata_Dublin_Core_5ca3dd576c2b4f0d9ed512633efbffb5,Metadata_IMS_5ca3dd576c2b4f0d9ed512633efbffb5,Metadata_Full_IMS_5ca3dd576c2b4f0d9ed512633efbffb5,\" 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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('5ca3dd576c2b4f0d9ed512633efbffb5');\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=\"_92875138_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875138_2/xid-92875138_2\" target=\"_blank\" rel=\"noreferrer noopener\">12E_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12E_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m5&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875138_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_ff92cf1da9164061a4d16b784f58ae2d,open_with_browser_ff92cf1da9164061a4d16b784f58ae2d,open_with_bbdrive_ff92cf1da9164061a4d16b784f58ae2d,openWebId_ff92cf1da9164061a4d16b784f58ae2d,view360Id_ff92cf1da9164061a4d16b784f58ae2d,*separator*,*separator*,ax-ally-placeholder_ff92cf1da9164061a4d16b784f58ae2d,ax-ally-markForAxAnalysis_ff92cf1da9164061a4d16b784f58ae2d,*separator*,*separator*,content_settings_ff92cf1da9164061a4d16b784f58ae2d,content_editSettings_ff92cf1da9164061a4d16b784f58ae2d,content_edit_ff92cf1da9164061a4d16b784f58ae2d,properties_folder_ff92cf1da9164061a4d16b784f58ae2d,itemcarot_managerecord_ff92cf1da9164061a4d16b784f58ae2d,comments_tool_ff92cf1da9164061a4d16b784f58ae2d,subscriptions_list_ff92cf1da9164061a4d16b784f58ae2d,content_readfile_ff92cf1da9164061a4d16b784f58ae2d,content_overwrite_ff92cf1da9164061a4d16b784f58ae2d,passes_tool_ff92cf1da9164061a4d16b784f58ae2d,permissions_tool_ff92cf1da9164061a4d16b784f58ae2d,content_add_alignment_ff92cf1da9164061a4d16b784f58ae2d,content_tracking_ff92cf1da9164061a4d16b784f58ae2d,content_versions_ff92cf1da9164061a4d16b784f58ae2d,*separator*,*separator*,bookmarkId_ff92cf1da9164061a4d16b784f58ae2d,itemsId_ff92cf1da9164061a4d16b784f58ae2d,packagesId_ff92cf1da9164061a4d16b784f58ae2d,emailId_ff92cf1da9164061a4d16b784f58ae2d,removeContentFolderId_ff92cf1da9164061a4d16b784f58ae2d,*separator*,copyContentId_ff92cf1da9164061a4d16b784f58ae2d,moveContentId_ff92cf1da9164061a4d16b784f58ae2d,*separator*,removeContentId_ff92cf1da9164061a4d16b784f58ae2d,*separator*,Metadata_General_ff92cf1da9164061a4d16b784f58ae2d,Metadata_Dublin_Core_ff92cf1da9164061a4d16b784f58ae2d,Metadata_IMS_ff92cf1da9164061a4d16b784f58ae2d,Metadata_Full_IMS_ff92cf1da9164061a4d16b784f58ae2d,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_ff92cf1da9164061a4d16b784f58ae2d\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_ff92cf1da9164061a4d16b784f58ae2d',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_ff92cf1da9164061a4d16b784f58ae2d',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_ff92cf1da9164061a4d16b784f58ae2d',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"92875138_2_fileReadWritePermAvl\" id=\"92875138_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('ff92cf1da9164061a4d16b784f58ae2d');\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=\"_92875139_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875139_2/xid-92875139_2\" target=\"_blank\" rel=\"noreferrer noopener\">12F_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12F_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m7&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875139_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_b449f737a39f4573aa6960e36e7c0518,open_with_browser_b449f737a39f4573aa6960e36e7c0518,open_with_bbdrive_b449f737a39f4573aa6960e36e7c0518,openWebId_b449f737a39f4573aa6960e36e7c0518,view360Id_b449f737a39f4573aa6960e36e7c0518,*separator*,*separator*,ax-ally-placeholder_b449f737a39f4573aa6960e36e7c0518,ax-ally-markForAxAnalysis_b449f737a39f4573aa6960e36e7c0518,*separator*,*separator*,content_settings_b449f737a39f4573aa6960e36e7c0518,content_editSettings_b449f737a39f4573aa6960e36e7c0518,content_edit_b449f737a39f4573aa6960e36e7c0518,properties_folder_b449f737a39f4573aa6960e36e7c0518,itemcarot_managerecord_b449f737a39f4573aa6960e36e7c0518,comments_tool_b449f737a39f4573aa6960e36e7c0518,subscriptions_list_b449f737a39f4573aa6960e36e7c0518,content_readfile_b449f737a39f4573aa6960e36e7c0518,content_overwrite_b449f737a39f4573aa6960e36e7c0518,passes_tool_b449f737a39f4573aa6960e36e7c0518,permissions_tool_b449f737a39f4573aa6960e36e7c0518,content_add_alignment_b449f737a39f4573aa6960e36e7c0518,content_tracking_b449f737a39f4573aa6960e36e7c0518,content_versions_b449f737a39f4573aa6960e36e7c0518,*separator*,*separator*,bookmarkId_b449f737a39f4573aa6960e36e7c0518,itemsId_b449f737a39f4573aa6960e36e7c0518,packagesId_b449f737a39f4573aa6960e36e7c0518,emailId_b449f737a39f4573aa6960e36e7c0518,removeContentFolderId_b449f737a39f4573aa6960e36e7c0518,*separator*,copyContentId_b449f737a39f4573aa6960e36e7c0518,moveContentId_b449f737a39f4573aa6960e36e7c0518,*separator*,removeContentId_b449f737a39f4573aa6960e36e7c0518,*separator*,Metadata_General_b449f737a39f4573aa6960e36e7c0518,Metadata_Dublin_Core_b449f737a39f4573aa6960e36e7c0518,Metadata_IMS_b449f737a39f4573aa6960e36e7c0518,Metadata_Full_IMS_b449f737a39f4573aa6960e36e7c0518,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_b449f737a39f4573aa6960e36e7c0518\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_b449f737a39f4573aa6960e36e7c0518',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_b449f737a39f4573aa6960e36e7c0518',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_b449f737a39f4573aa6960e36e7c0518',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"92875139_2_fileReadWritePermAvl\" id=\"92875139_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('b449f737a39f4573aa6960e36e7c0518');\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=\"_92875140_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875140_2/xid-92875140_2\" target=\"_blank\" rel=\"noreferrer noopener\">12G_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12G_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m9&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875140_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_d92da0e21231461d8d220e9320c46cda,open_with_browser_d92da0e21231461d8d220e9320c46cda,open_with_bbdrive_d92da0e21231461d8d220e9320c46cda,openWebId_d92da0e21231461d8d220e9320c46cda,view360Id_d92da0e21231461d8d220e9320c46cda,*separator*,*separator*,ax-ally-placeholder_d92da0e21231461d8d220e9320c46cda,ax-ally-markForAxAnalysis_d92da0e21231461d8d220e9320c46cda,*separator*,*separator*,content_settings_d92da0e21231461d8d220e9320c46cda,content_editSettings_d92da0e21231461d8d220e9320c46cda,content_edit_d92da0e21231461d8d220e9320c46cda,properties_folder_d92da0e21231461d8d220e9320c46cda,itemcarot_managerecord_d92da0e21231461d8d220e9320c46cda,comments_tool_d92da0e21231461d8d220e9320c46cda,subscriptions_list_d92da0e21231461d8d220e9320c46cda,content_readfile_d92da0e21231461d8d220e9320c46cda,content_overwrite_d92da0e21231461d8d220e9320c46cda,passes_tool_d92da0e21231461d8d220e9320c46cda,permissions_tool_d92da0e21231461d8d220e9320c46cda,content_add_alignment_d92da0e21231461d8d220e9320c46cda,content_tracking_d92da0e21231461d8d220e9320c46cda,content_versions_d92da0e21231461d8d220e9320c46cda,*separator*,*separator*,bookmarkId_d92da0e21231461d8d220e9320c46cda,itemsId_d92da0e21231461d8d220e9320c46cda,packagesId_d92da0e21231461d8d220e9320c46cda,emailId_d92da0e21231461d8d220e9320c46cda,removeContentFolderId_d92da0e21231461d8d220e9320c46cda,*separator*,copyContentId_d92da0e21231461d8d220e9320c46cda,moveContentId_d92da0e21231461d8d220e9320c46cda,*separator*,removeContentId_d92da0e21231461d8d220e9320c46cda,*separator*,Metadata_General_d92da0e21231461d8d220e9320c46cda,Metadata_Dublin_Core_d92da0e21231461d8d220e9320c46cda,Metadata_IMS_d92da0e21231461d8d220e9320c46cda,Metadata_Full_IMS_d92da0e21231461d8d220e9320c46cda,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_d92da0e21231461d8d220e9320c46cda\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_d92da0e21231461d8d220e9320c46cda',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_d92da0e21231461d8d220e9320c46cda',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_d92da0e21231461d8d220e9320c46cda',true);\"></a> \n </span></p>  \n<input type=\"hidden\" name=\"92875140_2_fileReadWritePermAvl\" id=\"92875140_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('d92da0e21231461d8d220e9320c46cda');\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=\"_8477552_1previewModule\" class=\"moduleSample\">\n </div>\n",
        "url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_207703_1&content_id=_8477552_1&mode=view",
        "title": "Video Lectures"
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data-ally-scoreindicator=\"_92875138_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875138_2/xid-92875138_2\" target=\"_blank\" rel=\"noreferrer noopener\">12E_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12E_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m5&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875138_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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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('ff92cf1da9164061a4d16b784f58ae2d');\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=\"_92875139_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875139_2/xid-92875139_2\" target=\"_blank\" rel=\"noreferrer noopener\">12F_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12F_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m7&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875139_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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data-ally-scoreindicator=\"_92875140_2\"></span></span>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875140_2/xid-92875140_2\" target=\"_blank\" rel=\"noreferrer noopener\">12G_Slides</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12G_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m9&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875140_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_d92da0e21231461d8d220e9320c46cda,open_with_browser_d92da0e21231461d8d220e9320c46cda,open_with_bbdrive_d92da0e21231461d8d220e9320c46cda,openWebId_d92da0e21231461d8d220e9320c46cda,view360Id_d92da0e21231461d8d220e9320c46cda,*separator*,*separator*,ax-ally-placeholder_d92da0e21231461d8d220e9320c46cda,ax-ally-markForAxAnalysis_d92da0e21231461d8d220e9320c46cda,*separator*,*separator*,content_settings_d92da0e21231461d8d220e9320c46cda,content_editSettings_d92da0e21231461d8d220e9320c46cda,content_edit_d92da0e21231461d8d220e9320c46cda,properties_folder_d92da0e21231461d8d220e9320c46cda,itemcarot_managerecord_d92da0e21231461d8d220e9320c46cda,comments_tool_d92da0e21231461d8d220e9320c46cda,subscriptions_list_d92da0e21231461d8d220e9320c46cda,content_readfile_d92da0e21231461d8d220e9320c46cda,content_overwrite_d92da0e21231461d8d220e9320c46cda,passes_tool_d92da0e21231461d8d220e9320c46cda,permissions_tool_d92da0e21231461d8d220e9320c46cda,content_add_alignment_d92da0e21231461d8d220e9320c46cda,content_tracking_d92da0e21231461d8d220e9320c46cda,content_versions_d92da0e21231461d8d220e9320c46cda,*separator*,*separator*,bookmarkId_d92da0e21231461d8d220e9320c46cda,itemsId_d92da0e21231461d8d220e9320c46cda,packagesId_d92da0e21231461d8d220e9320c46cda,emailId_d92da0e21231461d8d220e9320c46cda,removeContentFolderId_d92da0e21231461d8d220e9320c46cda,*separator*,copyContentId_d92da0e21231461d8d220e9320c46cda,moveContentId_d92da0e21231461d8d220e9320c46cda,*separator*,removeContentId_d92da0e21231461d8d220e9320c46cda,*separator*,Metadata_General_d92da0e21231461d8d220e9320c46cda,Metadata_Dublin_Core_d92da0e21231461d8d220e9320c46cda,Metadata_IMS_d92da0e21231461d8d220e9320c46cda,Metadata_Full_IMS_d92da0e21231461d8d220e9320c46cda,\" 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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('d92da0e21231461d8d220e9320c46cda');\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=\"_8477552_1previewModule\" class=\"moduleSample\">\n </div>\n",
    "url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_207703_1&content_id=_8477552_1&mode=view",
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bb:menuorder=\"openId_ef67fc6cbd494098ad1f362074cf5f50,open_with_browser_ef67fc6cbd494098ad1f362074cf5f50,open_with_bbdrive_ef67fc6cbd494098ad1f362074cf5f50,openWebId_ef67fc6cbd494098ad1f362074cf5f50,view360Id_ef67fc6cbd494098ad1f362074cf5f50,*separator*,*separator*,ax-ally-placeholder_ef67fc6cbd494098ad1f362074cf5f50,ax-ally-markForAxAnalysis_ef67fc6cbd494098ad1f362074cf5f50,*separator*,*separator*,content_settings_ef67fc6cbd494098ad1f362074cf5f50,content_editSettings_ef67fc6cbd494098ad1f362074cf5f50,content_edit_ef67fc6cbd494098ad1f362074cf5f50,properties_folder_ef67fc6cbd494098ad1f362074cf5f50,itemcarot_managerecord_ef67fc6cbd494098ad1f362074cf5f50,comments_tool_ef67fc6cbd494098ad1f362074cf5f50,subscriptions_list_ef67fc6cbd494098ad1f362074cf5f50,content_readfile_ef67fc6cbd494098ad1f362074cf5f50,content_overwrite_ef67fc6cbd494098ad1f362074cf5f50,passes_tool_ef67fc6cbd494098ad1f362074cf5f50,permissions_tool_ef67fc6cbd494098ad1f362074cf5f50,content_add_alignment_ef67fc6cbd494098ad1f362074cf5f50,content_tracking_ef67fc6cbd494098ad1f362074cf5f50,content_versions_ef67fc6cbd494098ad1f362074cf5f50,*separator*,*separator*,bookmarkId_ef67fc6cbd494098ad1f362074cf5f50,itemsId_ef67fc6cbd494098ad1f362074cf5f50,packagesId_ef67fc6cbd494098ad1f362074cf5f50,emailId_ef67fc6cbd494098ad1f362074cf5f50,removeContentFolderId_ef67fc6cbd494098ad1f362074cf5f50,*separator*,copyContentId_ef67fc6cbd494098ad1f362074cf5f50,moveContentId_ef67fc6cbd494098ad1f362074cf5f50,*separator*,removeContentId_ef67fc6cbd494098ad1f362074cf5f50,*separator*,Metadata_General_ef67fc6cbd494098ad1f362074cf5f50,Metadata_Dublin_Core_ef67fc6cbd494098ad1f362074cf5f50,Metadata_IMS_ef67fc6cbd494098ad1f362074cf5f50,Metadata_Full_IMS_ef67fc6cbd494098ad1f362074cf5f50,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_ef67fc6cbd494098ad1f362074cf5f50\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_ef67fc6cbd494098ad1f362074cf5f50',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_ef67fc6cbd494098ad1f362074cf5f50',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n </span></p>  \n \n \n \n \n \n \n <p>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875144_2/xid-92875144_2\" target=\"_blank\" rel=\"noreferrer noopener\">12B_Slides</a> \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12B_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00lz&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875144_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_d49b74935d6c4074b300d084a393f43a,open_with_browser_d49b74935d6c4074b300d084a393f43a,open_with_bbdrive_d49b74935d6c4074b300d084a393f43a,openWebId_d49b74935d6c4074b300d084a393f43a,view360Id_d49b74935d6c4074b300d084a393f43a,*separator*,*separator*,ax-ally-placeholder_d49b74935d6c4074b300d084a393f43a,ax-ally-markForAxAnalysis_d49b74935d6c4074b300d084a393f43a,*separator*,*separator*,content_settings_d49b74935d6c4074b300d084a393f43a,content_editSettings_d49b74935d6c4074b300d084a393f43a,content_edit_d49b74935d6c4074b300d084a393f43a,properties_folder_d49b74935d6c4074b300d084a393f43a,itemcarot_managerecord_d49b74935d6c4074b300d084a393f43a,comments_tool_d49b74935d6c4074b300d084a393f43a,subscriptions_list_d49b74935d6c4074b300d084a393f43a,content_readfile_d49b74935d6c4074b300d084a393f43a,content_overwrite_d49b74935d6c4074b300d084a393f43a,passes_tool_d49b74935d6c4074b300d084a393f43a,permissions_tool_d49b74935d6c4074b300d084a393f43a,content_add_alignment_d49b74935d6c4074b300d084a393f43a,content_tracking_d49b74935d6c4074b300d084a393f43a,content_versions_d49b74935d6c4074b300d084a393f43a,*separator*,*separator*,bookmarkId_d49b74935d6c4074b300d084a393f43a,itemsId_d49b74935d6c4074b300d084a393f43a,packagesId_d49b74935d6c4074b300d084a393f43a,emailId_d49b74935d6c4074b300d084a393f43a,removeContentFolderId_d49b74935d6c4074b300d084a393f43a,*separator*,copyContentId_d49b74935d6c4074b300d084a393f43a,moveContentId_d49b74935d6c4074b300d084a393f43a,*separator*,removeContentId_d49b74935d6c4074b300d084a393f43a,*separator*,Metadata_General_d49b74935d6c4074b300d084a393f43a,Metadata_Dublin_Core_d49b74935d6c4074b300d084a393f43a,Metadata_IMS_d49b74935d6c4074b300d084a393f43a,Metadata_Full_IMS_d49b74935d6c4074b300d084a393f43a,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_d49b74935d6c4074b300d084a393f43a\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_d49b74935d6c4074b300d084a393f43a',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_d49b74935d6c4074b300d084a393f43a',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n </span></p>  \n \n \n \n \n \n \n <p>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875145_2/xid-92875145_2\" target=\"_blank\" rel=\"noreferrer noopener\">12C_Slides</a> \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12C_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m1&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875145_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_fc809c74a5e9426db35da323fcaf204b,open_with_browser_fc809c74a5e9426db35da323fcaf204b,open_with_bbdrive_fc809c74a5e9426db35da323fcaf204b,openWebId_fc809c74a5e9426db35da323fcaf204b,view360Id_fc809c74a5e9426db35da323fcaf204b,*separator*,*separator*,ax-ally-placeholder_fc809c74a5e9426db35da323fcaf204b,ax-ally-markForAxAnalysis_fc809c74a5e9426db35da323fcaf204b,*separator*,*separator*,content_settings_fc809c74a5e9426db35da323fcaf204b,content_editSettings_fc809c74a5e9426db35da323fcaf204b,content_edit_fc809c74a5e9426db35da323fcaf204b,properties_folder_fc809c74a5e9426db35da323fcaf204b,itemcarot_managerecord_fc809c74a5e9426db35da323fcaf204b,comments_tool_fc809c74a5e9426db35da323fcaf204b,subscriptions_list_fc809c74a5e9426db35da323fcaf204b,content_readfile_fc809c74a5e9426db35da323fcaf204b,content_overwrite_fc809c74a5e9426db35da323fcaf204b,passes_tool_fc809c74a5e9426db35da323fcaf204b,permissions_tool_fc809c74a5e9426db35da323fcaf204b,content_add_alignment_fc809c74a5e9426db35da323fcaf204b,content_tracking_fc809c74a5e9426db35da323fcaf204b,content_versions_fc809c74a5e9426db35da323fcaf204b,*separator*,*separator*,bookmarkId_fc809c74a5e9426db35da323fcaf204b,itemsId_fc809c74a5e9426db35da323fcaf204b,packagesId_fc809c74a5e9426db35da323fcaf204b,emailId_fc809c74a5e9426db35da323fcaf204b,removeContentFolderId_fc809c74a5e9426db35da323fcaf204b,*separator*,copyContentId_fc809c74a5e9426db35da323fcaf204b,moveContentId_fc809c74a5e9426db35da323fcaf204b,*separator*,removeContentId_fc809c74a5e9426db35da323fcaf204b,*separator*,Metadata_General_fc809c74a5e9426db35da323fcaf204b,Metadata_Dublin_Core_fc809c74a5e9426db35da323fcaf204b,Metadata_IMS_fc809c74a5e9426db35da323fcaf204b,Metadata_Full_IMS_fc809c74a5e9426db35da323fcaf204b,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_fc809c74a5e9426db35da323fcaf204b\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_fc809c74a5e9426db35da323fcaf204b',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_fc809c74a5e9426db35da323fcaf204b',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n </span></p>  \n \n \n \n \n \n \n <p>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875137_2/xid-92875137_2\" target=\"_blank\" rel=\"noreferrer noopener\">12D_Slides</a> \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12D_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m3&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875137_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_5ca3dd576c2b4f0d9ed512633efbffb5,open_with_browser_5ca3dd576c2b4f0d9ed512633efbffb5,open_with_bbdrive_5ca3dd576c2b4f0d9ed512633efbffb5,openWebId_5ca3dd576c2b4f0d9ed512633efbffb5,view360Id_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,*separator*,ax-ally-placeholder_5ca3dd576c2b4f0d9ed512633efbffb5,ax-ally-markForAxAnalysis_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,*separator*,content_settings_5ca3dd576c2b4f0d9ed512633efbffb5,content_editSettings_5ca3dd576c2b4f0d9ed512633efbffb5,content_edit_5ca3dd576c2b4f0d9ed512633efbffb5,properties_folder_5ca3dd576c2b4f0d9ed512633efbffb5,itemcarot_managerecord_5ca3dd576c2b4f0d9ed512633efbffb5,comments_tool_5ca3dd576c2b4f0d9ed512633efbffb5,subscriptions_list_5ca3dd576c2b4f0d9ed512633efbffb5,content_readfile_5ca3dd576c2b4f0d9ed512633efbffb5,content_overwrite_5ca3dd576c2b4f0d9ed512633efbffb5,passes_tool_5ca3dd576c2b4f0d9ed512633efbffb5,permissions_tool_5ca3dd576c2b4f0d9ed512633efbffb5,content_add_alignment_5ca3dd576c2b4f0d9ed512633efbffb5,content_tracking_5ca3dd576c2b4f0d9ed512633efbffb5,content_versions_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,*separator*,bookmarkId_5ca3dd576c2b4f0d9ed512633efbffb5,itemsId_5ca3dd576c2b4f0d9ed512633efbffb5,packagesId_5ca3dd576c2b4f0d9ed512633efbffb5,emailId_5ca3dd576c2b4f0d9ed512633efbffb5,removeContentFolderId_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,copyContentId_5ca3dd576c2b4f0d9ed512633efbffb5,moveContentId_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,removeContentId_5ca3dd576c2b4f0d9ed512633efbffb5,*separator*,Metadata_General_5ca3dd576c2b4f0d9ed512633efbffb5,Metadata_Dublin_Core_5ca3dd576c2b4f0d9ed512633efbffb5,Metadata_IMS_5ca3dd576c2b4f0d9ed512633efbffb5,Metadata_Full_IMS_5ca3dd576c2b4f0d9ed512633efbffb5,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_5ca3dd576c2b4f0d9ed512633efbffb5\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_5ca3dd576c2b4f0d9ed512633efbffb5',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_5ca3dd576c2b4f0d9ed512633efbffb5',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n </span></p>  \n \n \n \n \n \n \n <p>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875138_2/xid-92875138_2\" target=\"_blank\" rel=\"noreferrer noopener\">12E_Slides</a> \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12E_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m5&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875138_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_ff92cf1da9164061a4d16b784f58ae2d,open_with_browser_ff92cf1da9164061a4d16b784f58ae2d,open_with_bbdrive_ff92cf1da9164061a4d16b784f58ae2d,openWebId_ff92cf1da9164061a4d16b784f58ae2d,view360Id_ff92cf1da9164061a4d16b784f58ae2d,*separator*,*separator*,ax-ally-placeholder_ff92cf1da9164061a4d16b784f58ae2d,ax-ally-markForAxAnalysis_ff92cf1da9164061a4d16b784f58ae2d,*separator*,*separator*,content_settings_ff92cf1da9164061a4d16b784f58ae2d,content_editSettings_ff92cf1da9164061a4d16b784f58ae2d,content_edit_ff92cf1da9164061a4d16b784f58ae2d,properties_folder_ff92cf1da9164061a4d16b784f58ae2d,itemcarot_managerecord_ff92cf1da9164061a4d16b784f58ae2d,comments_tool_ff92cf1da9164061a4d16b784f58ae2d,subscriptions_list_ff92cf1da9164061a4d16b784f58ae2d,content_readfile_ff92cf1da9164061a4d16b784f58ae2d,content_overwrite_ff92cf1da9164061a4d16b784f58ae2d,passes_tool_ff92cf1da9164061a4d16b784f58ae2d,permissions_tool_ff92cf1da9164061a4d16b784f58ae2d,content_add_alignment_ff92cf1da9164061a4d16b784f58ae2d,content_tracking_ff92cf1da9164061a4d16b784f58ae2d,content_versions_ff92cf1da9164061a4d16b784f58ae2d,*separator*,*separator*,bookmarkId_ff92cf1da9164061a4d16b784f58ae2d,itemsId_ff92cf1da9164061a4d16b784f58ae2d,packagesId_ff92cf1da9164061a4d16b784f58ae2d,emailId_ff92cf1da9164061a4d16b784f58ae2d,removeContentFolderId_ff92cf1da9164061a4d16b784f58ae2d,*separator*,copyContentId_ff92cf1da9164061a4d16b784f58ae2d,moveContentId_ff92cf1da9164061a4d16b784f58ae2d,*separator*,removeContentId_ff92cf1da9164061a4d16b784f58ae2d,*separator*,Metadata_General_ff92cf1da9164061a4d16b784f58ae2d,Metadata_Dublin_Core_ff92cf1da9164061a4d16b784f58ae2d,Metadata_IMS_ff92cf1da9164061a4d16b784f58ae2d,Metadata_Full_IMS_ff92cf1da9164061a4d16b784f58ae2d,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_ff92cf1da9164061a4d16b784f58ae2d\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_ff92cf1da9164061a4d16b784f58ae2d',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_ff92cf1da9164061a4d16b784f58ae2d',true);\" href=\"#contextMenu\" title=\"Click for more options\"> </a> \n </span></p>  \n \n \n \n \n \n \n <p>\n<a href=\"https://blackboard.jhu.edu/bbcswebdav/pid-8477552-dt-content-rid-92875139_2/xid-92875139_2\" target=\"_blank\" rel=\"noreferrer noopener\">12F_Slides</a> \n<span bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module12/12F_Slides.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00m7&amp;course_id=_207703_1&amp;ctxMenuXythosId=92875139_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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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.

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Assignment 12

Cell description

Assignment 12

 has three problems, with the first one being somewhat longer and more involved than the other two.

The assignment is due by the end of Module 12, following the Assignment Guidelines.

To submit the assignment, click the Assignment 12 title above.

Note: This Assignment is due on Day 6 of the module, NOT Day 7!

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