Module 8: Electric Potential and Gauss' Law for Magnetic Fields

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    "html": "\n\n<img alt=\"Content Folder\" src=\"/images/ci/sets/set01/folder_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_6258518_1\">\n\n <h3 id=\"anonymous_element_13\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/blackboard/content/listContent.jsp?course_id=_177474_1&amp;content_id=_6258518_1\"><span style=\"color:#0067ac;\">Lectures &amp; Videos</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_6258518_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Lectures &amp; Videos\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p>Module 8 contains the following lectures and videos:</p> \n <ol> \n  <li>Electric Potential (8A)</li> \n  <li>Method of Weighted Residuals (8B)</li> \n  <li>Oersted's Experiment (8C)</li> \n  <li>Magentic field lines (8CC)</li> \n  <li>Voltaic Pile (8D)</li> \n  <li>Biot Savart Law (8E)</li> \n  <li>Videos of Examples (8F) \n   <ol> \n    <li>Example 2.1</li> \n    <li>Example 2.2</li> \n    <li>Example 2.3</li> \n    <li>Example 2.4</li> \n   </ol></li> \n </ol> \n <p>Click the Lectures &amp; Videos link above to access the videos.</p> \n</div>\n  </div>\n\n <div id=\"_6258518_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "body": "\n    <div> \n <p>Module 8 contains the following lectures and videos:</p> \n <ol> \n  <li>Electric Potential (8A)</li> \n  <li>Method of Weighted Residuals (8B)</li> \n  <li>Oersted's Experiment (8C)</li> \n  <li>Magentic field lines (8CC)</li> \n  <li>Voltaic Pile (8D)</li> \n  <li>Biot Savart Law (8E)</li> \n  <li>Videos of Examples (8F) \n   <ol> \n    <li>Example 2.1</li> \n    <li>Example 2.2</li> \n    <li>Example 2.3</li> \n    <li>Example 2.4</li> \n   </ol></li> \n </ol> \n <p>Click the Lectures &amp; Videos link above to access the videos.</p> \n</div>\n  "
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        "html": "\n\n<img alt=\"Item\" src=\"/images/ci/sets/set01/document_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_6258515_1\">\n\n <h3 id=\"anonymous_element_8\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n\n     <span style=\"color:#0067ac;\">Overview</span>\n </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_6258515_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n\n     Overview\n </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p>Following the introduction of Gauss’s law for electric fields the first part of this module shows how to define potential and how the electric field can be computed from the electric potential. This allows us to express Coulomb’s law in terms of the electric potential.&nbsp; The next part of the module introduces a numerical method for solving for a charge distribution if the electric potential is known.&nbsp; As an example the case of the charge distribution of a wire with constant electric potential is solved by using numerical method of the method of weighted residuals.</p> \n <p>In the third part of the module, Gauss’s law for constant magnetic fields in both integral and differential or point form is introduced and used to solve magnetostatic problems.</p> \n <h3 id=\"anonymous_element_9\"><span style=\"color: #0067ac;\">Summary</span></h3> \n <p>In this module we examine Electric Potential, the method of weighted residuals and Gauss’ law for magnetic fields.&nbsp; We give some historical context by examining the effects of the invention of the voltaic pile, Oersted’s experiment, and the Biot Savart Law.</p> \n <h3 id=\"anonymous_element_10\"><span style=\"color: #0067ac;\">Objectives</span></h3> \n <p>By the end of this module, you will be able to:</p> \n <ul> \n  <li>Explain the concept of the method of weighted residuals and use the physics of Coulomb’s law to verify that the answers the method produces are reasonable.</li> \n  <li>Use the concept of circulation of the static magnetic field to solve for the magnetic field and flux.</li> \n  <li>Given an electric current and geometry solve for the magnetic field.</li> \n  <li>Solve a surface integral and explain if the results are reasonable given the concept of a surface integral.</li> \n  <li>Explain surface integration in Cartesian, cylindrical and spherical coordinate systems.</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_6258515_1previewModule\" class=\"moduleSample\">\n </div>\n",
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    "html": "\n\n<img alt=\"Item\" src=\"/images/ci/sets/set01/document_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_6258515_1\">\n\n <h3 id=\"anonymous_element_8\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n\n     <span style=\"color:#0067ac;\">Overview</span>\n </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_6258515_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n\n     Overview\n </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p>Following the introduction of Gauss’s law for electric fields the first part of this module shows how to define potential and how the electric field can be computed from the electric potential. This allows us to express Coulomb’s law in terms of the electric potential.&nbsp; The next part of the module introduces a numerical method for solving for a charge distribution if the electric potential is known.&nbsp; As an example the case of the charge distribution of a wire with constant electric potential is solved by using numerical method of the method of weighted residuals.</p> \n <p>In the third part of the module, Gauss’s law for constant magnetic fields in both integral and differential or point form is introduced and used to solve magnetostatic problems.</p> \n <h3 id=\"anonymous_element_9\"><span style=\"color: #0067ac;\">Summary</span></h3> \n <p>In this module we examine Electric Potential, the method of weighted residuals and Gauss’ law for magnetic fields.&nbsp; We give some historical context by examining the effects of the invention of the voltaic pile, Oersted’s experiment, and the Biot Savart Law.</p> \n <h3 id=\"anonymous_element_10\"><span style=\"color: #0067ac;\">Objectives</span></h3> \n <p>By the end of this module, you will be able to:</p> \n <ul> \n  <li>Explain the concept of the method of weighted residuals and use the physics of Coulomb’s law to verify that the answers the method produces are reasonable.</li> \n  <li>Use the concept of circulation of the static magnetic field to solve for the magnetic field and flux.</li> \n  <li>Given an electric current and geometry solve for the magnetic field.</li> \n  <li>Solve a surface integral and explain if the results are reasonable given the concept of a surface integral.</li> \n  <li>Explain surface integration in Cartesian, cylindrical and spherical coordinate systems.</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_6258515_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "title": "Overview\n SummaryObjectives",
        "body": "\n    <div> \n <p>Following the introduction of Gauss’s law for electric fields the first part of this module shows how to define potential and how the electric field can be computed from the electric potential. This allows us to express Coulomb’s law in terms of the electric potential.&nbsp; The next part of the module introduces a numerical method for solving for a charge distribution if the electric potential is known.&nbsp; As an example the case of the charge distribution of a wire with constant electric potential is solved by using numerical method of the method of weighted residuals.</p> \n <p>In the third part of the module, Gauss’s law for constant magnetic fields in both integral and differential or point form is introduced and used to solve magnetostatic problems.</p> \n <h3 id=\"anonymous_element_9\"><span>Summary</span></h3> \n <p>In this module we examine Electric Potential, the method of weighted residuals and Gauss’ law for magnetic fields.&nbsp; We give some historical context by examining the effects of the invention of the voltaic pile, Oersted’s experiment, and the Biot Savart Law.</p> \n <h3 id=\"anonymous_element_10\"><span>Objectives</span></h3> \n <p>By the end of this module, you will be able to:</p> \n <ul> \n  <li>Explain the concept of the method of weighted residuals and use the physics of Coulomb’s law to verify that the answers the method produces are reasonable.</li> \n  <li>Use the concept of circulation of the static magnetic field to solve for the magnetic field and flux.</li> \n  <li>Given an electric current and geometry solve for the magnetic field.</li> \n  <li>Solve a surface integral and explain if the results are reasonable given the concept of a surface integral.</li> \n  <li>Explain surface integration in Cartesian, cylindrical and spherical coordinate systems.</li> \n </ul> \n</div>\n  "
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        "body": "\n    <div> \n <p>First read the theory for a method for solution of charges using Poisson’s equation for electric potential and next start on the method of weighted residuals.&nbsp; Read the reference paper on the Method of Weighted Residuals along with viewing the videos on the method and the numerical solution of a wire with constant electric potential simultaneously. This is a very powerful and general method for solving physical problems with boundary conditions. Then work with a script that solves and plots the charge distribution and explain the results based upon Coulomb and Gauss’s law for electric fields.&nbsp;You will again use the companion web site to the text book to access podcasts covering the chapter 2 concepts.&nbsp; Make sure to make use of the historical presentations that put the invention of the battery or voltaic pile and the discovery of magnetic fields from constant current by Oersted. You will watch video presentations solving example problems in the chapter which emphasize the method of solution rather than the equations.</p> \n</div>\n  "
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Method of Moments.pdf</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.525.201.81.SP19/Mod08/Nagel%20-%20Method%20of%20Moments.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00rm&amp;course_id=_177474_1&amp;ctxMenuXythosId=76869625_2&amp;course_id=_177474_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_6cc445026ea84190a05ae2bead81e013,open_with_browser_6cc445026ea84190a05ae2bead81e013,open_with_bbdrive_6cc445026ea84190a05ae2bead81e013,openWebId_6cc445026ea84190a05ae2bead81e013,view360Id_6cc445026ea84190a05ae2bead81e013,*separator*,*separator*,ax-ally-placeholder_6cc445026ea84190a05ae2bead81e013,ax-ally-markForAxAnalysis_6cc445026ea84190a05ae2bead81e013,*separator*,*separator*,content_settings_6cc445026ea84190a05ae2bead81e013,content_editSettings_6cc445026ea84190a05ae2bead81e013,content_edit_6cc445026ea84190a05ae2bead81e013,properties_folder_6cc445026ea84190a05ae2bead81e013,itemcarot_managerecord_6cc445026ea84190a05ae2bead81e013,comments_tool_6cc445026ea84190a05ae2bead81e013,subscriptions_list_6cc445026ea84190a05ae2bead81e013,content_readfile_6cc445026ea84190a05ae2bead81e013,content_overwrite_6cc445026ea84190a05ae2bead81e013,passes_tool_6cc445026ea84190a05ae2bead81e013,permissions_tool_6cc445026ea84190a05ae2bead81e013,content_add_alignment_6cc445026ea84190a05ae2bead81e013,content_tracking_6cc445026ea84190a05ae2bead81e013,content_versions_6cc445026ea84190a05ae2bead81e013,*separator*,*separator*,bookmarkId_6cc445026ea84190a05ae2bead81e013,itemsId_6cc445026ea84190a05ae2bead81e013,packagesId_6cc445026ea84190a05ae2bead81e013,emailId_6cc445026ea84190a05ae2bead81e013,removeContentFolderId_6cc445026ea84190a05ae2bead81e013,*separator*,copyContentId_6cc445026ea84190a05ae2bead81e013,moveContentId_6cc445026ea84190a05ae2bead81e013,*separator*,removeContentId_6cc445026ea84190a05ae2bead81e013,*separator*,Metadata_General_6cc445026ea84190a05ae2bead81e013,Metadata_Dublin_Core_6cc445026ea84190a05ae2bead81e013,Metadata_IMS_6cc445026ea84190a05ae2bead81e013,Metadata_Full_IMS_6cc445026ea84190a05ae2bead81e013,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_6cc445026ea84190a05ae2bead81e013\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_6cc445026ea84190a05ae2bead81e013',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_6cc445026ea84190a05ae2bead81e013',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_6cc445026ea84190a05ae2bead81e013',true);\"></a> \n  </span> \n<input type=\"hidden\" name=\"76869625_2_fileReadWritePermAvl\" id=\"76869625_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('6cc445026ea84190a05ae2bead81e013');\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> (<span id=\"/xid-76869625_2_fileSize\">283.456 KB</span>) </li></ul></div></div>\n\n    <div class=\"vtbegenerated\"> \n <p>Fleisch, D. (2008). <em>A student's guide to Maxwell's equations</em>. New York: Cambridge University Press.</p> \n <ul> \n  <li>Chapter 2 - <em>Gauss's Law for Magnetic Fields</em><em></em></li> \n </ul> \n <br> \n <p>Nagel, J.R. (2012). Solution to the static charge distribution on a thin wire using the method of moments. Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, UT. </p> \n <ul> \n  <li>Attached as PDF above. <em></em></li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_6258517_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Method of Moments.pdf</a> \n<span class=\"contextMenuContainer application\" style=\" display: inline;\" bb:menugeneratorurl=\"/webapps/cmsmain/webui/courses/EN.525.201.81.SP19/Mod08/Nagel%20-%20Method%20of%20Moments.pdf?action=details&amp;subaction=generateFileMenuItem&amp;uniq=vd00rm&amp;course_id=_177474_1&amp;ctxMenuXythosId=76869625_2&amp;course_id=_177474_1\" bb:navitem=\"\" bb:contextparameters=\"\" bb:menuorder=\"openId_6cc445026ea84190a05ae2bead81e013,open_with_browser_6cc445026ea84190a05ae2bead81e013,open_with_bbdrive_6cc445026ea84190a05ae2bead81e013,openWebId_6cc445026ea84190a05ae2bead81e013,view360Id_6cc445026ea84190a05ae2bead81e013,*separator*,*separator*,ax-ally-placeholder_6cc445026ea84190a05ae2bead81e013,ax-ally-markForAxAnalysis_6cc445026ea84190a05ae2bead81e013,*separator*,*separator*,content_settings_6cc445026ea84190a05ae2bead81e013,content_editSettings_6cc445026ea84190a05ae2bead81e013,content_edit_6cc445026ea84190a05ae2bead81e013,properties_folder_6cc445026ea84190a05ae2bead81e013,itemcarot_managerecord_6cc445026ea84190a05ae2bead81e013,comments_tool_6cc445026ea84190a05ae2bead81e013,subscriptions_list_6cc445026ea84190a05ae2bead81e013,content_readfile_6cc445026ea84190a05ae2bead81e013,content_overwrite_6cc445026ea84190a05ae2bead81e013,passes_tool_6cc445026ea84190a05ae2bead81e013,permissions_tool_6cc445026ea84190a05ae2bead81e013,content_add_alignment_6cc445026ea84190a05ae2bead81e013,content_tracking_6cc445026ea84190a05ae2bead81e013,content_versions_6cc445026ea84190a05ae2bead81e013,*separator*,*separator*,bookmarkId_6cc445026ea84190a05ae2bead81e013,itemsId_6cc445026ea84190a05ae2bead81e013,packagesId_6cc445026ea84190a05ae2bead81e013,emailId_6cc445026ea84190a05ae2bead81e013,removeContentFolderId_6cc445026ea84190a05ae2bead81e013,*separator*,copyContentId_6cc445026ea84190a05ae2bead81e013,moveContentId_6cc445026ea84190a05ae2bead81e013,*separator*,removeContentId_6cc445026ea84190a05ae2bead81e013,*separator*,Metadata_General_6cc445026ea84190a05ae2bead81e013,Metadata_Dublin_Core_6cc445026ea84190a05ae2bead81e013,Metadata_IMS_6cc445026ea84190a05ae2bead81e013,Metadata_Full_IMS_6cc445026ea84190a05ae2bead81e013,\" bb:overwritenavitems=\"\" bb:beforeshowfunc=\"\"> <a id=\"cmlink_6cc445026ea84190a05ae2bead81e013\" onfocus=\"page.ContextMenu.LI(event, 'cmdiv_6cc445026ea84190a05ae2bead81e013',true);\" onmouseover=\"page.ContextMenu.LI(event, 'cmdiv_6cc445026ea84190a05ae2bead81e013',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_6cc445026ea84190a05ae2bead81e013',true);\"></a> \n  </span> \n<input type=\"hidden\" name=\"76869625_2_fileReadWritePermAvl\" id=\"76869625_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('6cc445026ea84190a05ae2bead81e013');\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> (<span id=\"/xid-76869625_2_fileSize\">283.456 KB</span>) </li></ul></div></div>\n\n    <div class=\"vtbegenerated\"> \n <p>Fleisch, D. (2008). <em>A student's guide to Maxwell's equations</em>. New York: Cambridge University Press.</p> \n <ul> \n  <li>Chapter 2 - <em>Gauss's Law for Magnetic Fields</em><em></em></li> \n </ul> \n <br> \n <p>Nagel, J.R. (2012). Solution to the static charge distribution on a thin wire using the method of moments. Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, UT. </p> \n <ul> \n  <li>Attached as PDF above. <em></em></li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_6258517_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "body": "\n      \n\n    <div> \n <p>Fleisch, D. (2008). <em>A student's guide to Maxwell's equations</em>. New York: Cambridge University Press.</p> \n <ul> \n  <li>Chapter 2 - <em>Gauss's Law for Magnetic Fields</em></li> \n </ul> \n  \n <p>Nagel, J.R. (2012). Solution to the static charge distribution on a thin wire using the method of moments. Department of Electrical and Computer Engineering, University of Utah, Salt Lake City, UT. </p> \n <ul> \n  <li>Attached as PDF above. </li> \n </ul> \n</div>\n  "
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        "body": "\n    <div> \n <p>Please go to the module 8 discussionn area and comment on one of these questions or on another students post:</p> \n <p><span>Questions 1.&nbsp; Discuss the observation that sources of the magnetic field only occur in pairs (north and south poles) but electric charge occurs in separable positive and negative charges.&nbsp; Does this lack of symmetry make sense?&nbsp; Can you site other cases in nature where asymmetry exist?&nbsp; Is it possible that we simply do not yet have to tools to observe isolated sources of static magnetic field?</span></p> \n <p><span>Questions 2.&nbsp; </span><span>Divergence is introduced in this&nbsp;chapter.&nbsp; Can you explain divergence from a point in space?</span></p> \n <p><span> </span></p> \n  \n</div>\n  "
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</li></ul></div></div>\n\n    <div class=\"vtbegenerated\"> \n <p>Complete the exercises at the end of chapter 2 and the additional surface integration problem (attached as PDF above) and check your work and answers with the solutions shown in the textbook companion web site for the textbook problems. Submit any questions on the solution of the surface integration problem to the discussion area of the web site.<br><br>Post questions on the homework problems to the Module 8 Discussion forum if you do not understand the solutions.&nbsp; When you are comfortable with the concepts of the module take the quiz below.</p> \n</div>\n  </div>\n\n <div id=\"_6258520_1previewModule\" class=\"moduleSample\">\n </div>\n",
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Submit any questions on the solution of the surface integration problem to the discussion area of the web site.<br><br>Post questions on the homework problems to the Module 8 Discussion forum if you do not understand the solutions.&nbsp; When you are comfortable with the concepts of the module take the quiz below.</p> \n</div>\n  </div>\n\n <div id=\"_6258520_1previewModule\" class=\"moduleSample\">\n </div>\n",
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</li></ul></div></div>\n\n    <div class=\"vtbegenerated\"> \n <p>This quiz checks your understanding of key concepts and skills covered in this module. 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