{"id":125,"date":"2025-07-06T20:53:23","date_gmt":"2025-07-06T20:53:23","guid":{"rendered":"https:\/\/courses.lsa.umich.edu\/krasny\/?page_id=125"},"modified":"2025-07-13T22:42:06","modified_gmt":"2025-07-13T22:42:06","slug":"math-557","status":"publish","type":"page","link":"https:\/\/courses.lsa.umich.edu\/krasny\/math-557\/","title":{"rendered":"Math 557"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>Math 557, Winter 2020, Applied Asymptotic Analysis<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Instructor: Robert Krasny, 4830 East Hall, (734)-763-3505, krasny@umich.edu<br>Time\/Location: TuTh 1-2:30pm, 3088 East Hall<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_description.pdf\">course description<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_references.pdf\">references<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h4 class=\"wp-block-heading\">Homework<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_hw1.pdf\">hw1<\/a>\u00a0due: Tues Jan 28<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_hw2.pdf\">hw2<\/a>\u00a0due: Thurs Feb 13,\u00a0<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_hw2_sol.pdf\">solution to problem 7<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_hw3.pdf\">hw3<\/a>\u00a0due: Tues Feb 25<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_hw4.pdf\">hw4<\/a>\u00a0due: Tues March 17<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_hw5.pdf\">hw5<\/a>\u00a0due: Thurs April 2<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_hw6.pdf\">hw6<\/a>\u00a0due: Thurs April 16<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_hw7.pdf\">hw7<\/a>\u00a0due: Thurs April 28<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h4 class=\"wp-block-heading\">Lecture Notes<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_chapter_1.pdf\">chapter 1<\/a>\u00a0asymptotic expansions<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_chapter_2.pdf\">chapter 2<\/a>\u00a0Laplace&#8217;s method<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_chapter_3.pdf\">chapter 3<\/a>\u00a0method of steepest descent<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_chapter_4.pdf\">chapter 4<\/a>\u00a0method of stationary phase,\u00a0<a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_superposition.pdf\">mfile<\/a><br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_chapter_5.pdf\">chapter 5<\/a>\u00a0transforms<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_chapter_6.pdf\">chapter 6<\/a>\u00a0differential equations<br><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/math557_chapter_7.pdf\">chapter 7<\/a>\u00a0singular perturbation problems<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h4 class=\"wp-block-heading\">Exams<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">midterm exam, in class, Thursday Feb 27, covers up to 4.1 (method of stationary phase), one page of notes is allowed<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/matlab.pdf\">notes on using MATLAB<\/a><br><a href=\"http:\/\/www.mathworks.com\/academia\/student_center\/tutorials\/launchpad.html\">Matlab resources for students<\/a><br><a href=\"http:\/\/www.mathworks.com\/company\/newsletters\/articles\/the-origins-of-matlab.html\">The Origins of Matlab<\/a>, by Cleve Moler, December 2004<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/courses.lsa.umich.edu\/krasny\/wp-content\/uploads\/sites\/202\/2025\/07\/lax_interview.pdf\">Interview with Peter Lax<\/a>, AMS Notices, February 2006, &#8220;&#8230; the astonishing phenomenon of the interaction of solitons was discovered by numerical calculations &#8230;&#8221;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p class=\"wp-block-paragraph\">Student Data Form&nbsp;<a href=\"http:\/\/instruct.math.lsa.umich.edu\/stu-info\/\">Form<\/a><a href=\"http:\/\/instruct.math.lsa.umich.edu\/stu-info\/faq.html\">FAQ<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/sites.lsa.umich.edu\/krasny\/links\/fellowships\/\">Fellowships, Graduate Study, Internships<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p class=\"wp-block-paragraph\">&#8220;You need the willingness to fail all the time. You have to generate many ideas and then you have to work very hard only to discover that they don&#8217;t work. And you keep doing that over and over until you find one that does work.&#8221; &#8211;&nbsp;<a href=\"http:\/\/en.wikipedia.org\/wiki\/John_Backus\">John Backus<\/a>, lead developer of Fortran<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<p class=\"wp-block-paragraph\">SIAM has a webpage for students;&nbsp;<a href=\"http:\/\/www.siam.org\/students\/\">check it out<\/a>, and don&#8217;t miss the link to&nbsp;<a href=\"http:\/\/www.siam.org\/membership\/individual\/free.php\">free student memberships<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Math 557, Winter 2020, Applied Asymptotic Analysis Instructor: Robert Krasny, 4830 East Hall, (734)-763-3505, krasny@umich.eduTime\/Location: TuTh 1-2:30pm, 3088 East Hallcourse descriptionreferences Homework hw1\u00a0due: Tues Jan 28hw2\u00a0due: Thurs Feb 13,\u00a0solution to problem 7hw3\u00a0due: Tues Feb 25hw4\u00a0due: Tues March 17hw5\u00a0due: Thurs April 2hw6\u00a0due: Thurs April 16hw7\u00a0due: Thurs April 28 Lecture Notes chapter 1\u00a0asymptotic expansionschapter 2\u00a0Laplace&#8217;s methodchapter 3\u00a0method&hellip; <a class=\"more-link\" href=\"https:\/\/courses.lsa.umich.edu\/krasny\/math-557\/\">Continue reading <span class=\"screen-reader-text\">Math 557<\/span><\/a><\/p>\n","protected":false},"author":4973,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"tw-no-title.php","meta":{"footnotes":""},"class_list":["post-125","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/pages\/125","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/users\/4973"}],"replies":[{"embeddable":true,"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/comments?post=125"}],"version-history":[{"count":3,"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/pages\/125\/revisions"}],"predecessor-version":[{"id":162,"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/pages\/125\/revisions\/162"}],"wp:attachment":[{"href":"https:\/\/courses.lsa.umich.edu\/krasny\/wp-json\/wp\/v2\/media?parent=125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}