Module 11: More on Conformal Mappings

Module at a Glance ObjectivesHow to Complete This Module:

Cell description

Objectives

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

  • Apply a wider variety of conformal mappings.
  • Apply properties of conformal mappings to predict the behavior of certain mappings, or to design mappings that achieve a certain purpose (e.g., map a region to another in which it is easier to solve a problem of interest).
  • Apply the angle preserving property, principle of the argument, homotopic curves, and the Riemann mapping theorem to solve complex analysis problems.

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. Review the instructions for Mini-Project 2, 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 11. 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 2.
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Readings

Cell description
  • Module 11 Lecture Notes (PDF) : Read the Lecture Notes at least once through, after viewing the complete set of videos. The subject matter is a bit visual in nature, and a number of examples are illustrated in Figures. Make sure you understand the concept behind each Figure.
  • A portion of the topics in this module are covered 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 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 10.
  • You will find the total length of the videos and notes is a bit shorter than the previous module. This is to give you more time to finish the Mini-Project, and also to reflect on the topics covered, as this module is more advanced with more technical proofs than the previous one.
Technical 
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rel=\"noreferrer noopener\">Module 11 Lecture Notes (PDF)</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.625.703.81.SU20/Module11/Module%2011%20Lecture%20Notes.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00ld&amp;course_id=_207703_1&amp;ctxMenuXythosId=92402712_2&amp;course_id=_207703_1\" bb:navitem=\"\" bb:contextparameters=\"\" 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bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_0eeab874ba7e42e88a858d8c340bb74a\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_0eeab874ba7e42e88a858d8c340bb74a',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_0eeab874ba7e42e88a858d8c340bb74a',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_0eeab874ba7e42e88a858d8c340bb74a',true);\"></a> \n  </span> \n<input type=\"hidden\" name=\"92402712_2_fileReadWritePermAvl\" id=\"92402712_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('0eeab874ba7e42e88a858d8c340bb74a');\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>: Read the Lecture Notes at least once through, after viewing the complete set of videos. 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bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_0eeab874ba7e42e88a858d8c340bb74a\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_0eeab874ba7e42e88a858d8c340bb74a',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_0eeab874ba7e42e88a858d8c340bb74a',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_0eeab874ba7e42e88a858d8c340bb74a',true);\"></a> \n  </span> \n<input type=\"hidden\" name=\"92402712_2_fileReadWritePermAvl\" id=\"92402712_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('0eeab874ba7e42e88a858d8c340bb74a');\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>: Read the Lecture Notes at least once through, after viewing the complete set 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This is to give you more time to finish the Mini-Project, and also to reflect on the topics covered, as this module is more advanced with more technical proofs than the previous one.</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_8392387_1previewModule\" class=\"moduleSample\">\n </div>\n",
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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('3b7d6839153d40b5a0115fd08a204748');\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 id=\"gtx-trans\" style=\"position: absolute; left: -26px; top: 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        "url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_207703_1&content_id=_8392388_1&mode=view",
        "title": "Video Lectures"
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Angle_Preserving_Property.mp4
./attachments/cell_284/Angle_Preserving_Property.mp4
Automorphisms.mp4
./attachments/cell_284/Automorphisms.mp4
Principle_of_the_Argument.mp4
./attachments/cell_284/Principle_of_the_Argument.mp4
Riemann_Mapping_Theorem.mp4
./attachments/cell_284/Riemann_Mapping_Theorem.mp4
Some_Examples.mp4
./attachments/cell_284/Some_Examples.mp4
Winding_Number_and_Maximum_Principle.mp4
./attachments/cell_284/Winding_Number_and_Maximum_Principle.mp4
file_1.pdf
./attachments/cell_284/file_1.pdf
file_2.pdf
./attachments/cell_284/file_2.pdf
file_3.pdf
./attachments/cell_284/file_3.pdf
file_4.pdf
./attachments/cell_284/file_4.pdf
file_5.pdf
./attachments/cell_284/file_5.pdf
file_6.pdf
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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 11

Cell description

Assignment 11

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The assignment is due by the end of Module 11, following the Assignment Guidelines.

To submit the assignment, click the Assignment 11 title above.

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file_1.pdf
./attachments/cell_286/file_1.pdf

Mini-Project 2

Cell description

Finish Mini-Project 2

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

The Mini-Project is due by the end of Module 11, 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 2 title above.

Technical 
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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('eef54d36c0004025b657d5e99928a958');\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>&nbsp;and submit it.&nbsp;<strong>Note:</strong> Remember to submit your 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