{"id":534,"date":"2016-08-01T12:01:56","date_gmt":"2016-08-01T16:01:56","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/pilyugin\/?page_id=534"},"modified":"2026-03-19T08:16:38","modified_gmt":"2026-03-19T12:16:38","slug":"map4305_f2016","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/pilyugin\/courses\/map4305_f2016\/","title":{"rendered":"MAP 4305 Intermediate Diff. Equations"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">MAP 4305 Intermediate Diff. Equations<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">MAP 4305 &amp; Intermediate Diff. Equations\u00a0(Section 2E00)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Instructor:\u00a0<a title=\"Sergei S. Pilyugin\" href=\"https:\/\/people.clas.ufl.edu\/pilyugin\/\">Sergei S. Pilyugin<\/a>\u00a0<a title=\"MAP 4305 Intermediate Diff. Eq.\" href=\"https:\/\/people.clas.ufl.edu\/pilyugin\/courses\/map4305_f2016\/\">\u00a0https:\/\/people.clas.ufl.edu\/pilyugin\/courses\/map4305_f2016\/<\/a><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Announcements<\/span><\/span>:\u00a0The second test has been moved to 10\/12\/16. <\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Prerequisites<\/span><\/span>: MAP 2302 (Differential Equations 1) or equivalent.<\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Time and Room<\/span><\/span>: MWF 3 (9:35 a.m &#8211; 10:25 a.m.), FAC 120.<\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Final Exam Time and Room:<\/span><\/span>\u00a0December 15, 3:00-5:00 pm, FAC 120.<\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Literature<\/span><\/span>: R. K. Nagle, E. B. Saff, and A. D. Snider,\u00a0<em>Fundamentals of Differential Equations\u00a0<\/em>, 8th Ed., Pearson Education, ISBN-10: 0-321-74773-9.<\/li>\n<li><span style=\"color: green\"><span style=\"text-decoration: underline\">Critical dates:<\/span><\/span>\u00a0Aug. 22\u00a0(classes begin), Dec. 7\u00a0(classes end). Midterms: M1 09\/16, M2 10\/12, M3 11\/09. <\/li>\n<li><span style=\"color: green\"><span style=\"text-decoration: underline\">Holidays:<\/span><\/span> Sep. 05 (Labor Day), Oct. 14-15 Homecoming, Nov. 11 (Veterans Day), Nov. 23-26 (Thanksgiving).<\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Office Hours<\/span><\/span>: MWF4 (10:40-11:30\u00a0a.m.) in LIT 458, or by appointment. Please, call me at 352- 294-2326 or use e-mail:\u00a0<a href=\"mailto:pilyugin@ufl.edu\">pilyugin@ufl.edu<\/a>\u00a0for communication. For more details, see my\u00a0<a href=\"https:\/\/people.clas.ufl.edu\/pilyugin\/schedule\/\">schedule.<\/a><\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Description and Objectives of the Course<\/span><\/span>:<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"color: #000000\">This course is a continuation of MAP 2302. It covers the power series method, systems of linear ODEs, and the introduction to PDEs.<\/span><\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Weekly Schedule<\/span><\/span>:<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"color: #000000\">W1: Power series method revisited;\u00a0<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W2: Equations with analytic coefficients;\u00a0<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W3: Singular equations, method of Frobenius;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W4: Special Functions;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W5: Review of matrices, linear algebra;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W6: Linear systems of ODEs, variation of parameters;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W7: Systems with constant coefficients, the method of Euler;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W8: The matrix exponential;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W9: Linear PDEs, separation of variables;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W10: Fourier series;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W11: Heat equation;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W12: Wave equation;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W13: Laplace&#8217;s equation;<\/span><br style=\"color: #000000\"><span style=\"color: #000000\">W14: Examples and applications.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Grading System:<\/span><\/span><br>\nExams: 3 midterms (30 points each, best 2 count); 1 (cumulative) final (40 points). Three midterms based on homework assignments. To summarize, 60 points for Midterms, 40 points for Final Exam, and 100 points altogether. The resulting score determines the letter grade according to the following table\n<table id=\"tablepress-grading_scale\" class=\"tablepress tablepress-id-grading_scale\">\n<thead>\n<tr class=\"row-1 odd\">\n<th class=\"column-1\">\n<div>Letter Grade<\/div>\n<\/th>\n<th class=\"column-2\">\n<div>A<\/div>\n<\/th>\n<th class=\"column-3\">\n<div>A-<\/div>\n<\/th>\n<th class=\"column-4\">\n<div>B+<\/div>\n<\/th>\n<th class=\"column-5\">\n<div>B<\/div>\n<\/th>\n<th class=\"column-6\">\n<div>B-<\/div>\n<\/th>\n<th class=\"column-7\">\n<div>C+<\/div>\n<\/th>\n<th class=\"column-8\">\n<div>C<\/div>\n<\/th>\n<th class=\"column-9\">\n<div>C\u2212<\/div>\n<\/th>\n<th class=\"column-10\">\n<div>D+<\/div>\n<\/th>\n<th class=\"column-11\">\n<div>D<\/div>\n<\/th>\n<\/tr>\n<\/thead>\n<tfoot>\n<tr class=\"row-2 even\">\n<th class=\"column-1\">Score<\/th>\n<th class=\"column-2\">100 \u2013 93<\/th>\n<th class=\"column-3\">92 \u2013 88<\/th>\n<th class=\"column-4\">87 \u2013 83<\/th>\n<th class=\"column-5\">82 \u2013 74<\/th>\n<th class=\"column-6\">73 \u2013 69<\/th>\n<th class=\"column-7\">68 \u2013 64<\/th>\n<th class=\"column-8\">63 \u2013 59<\/th>\n<th class=\"column-9\">58 \u2013 54<\/th>\n<th class=\"column-10\">53 \u2013 49<\/th>\n<th class=\"column-11\">48 \u2013 40<\/th>\n<\/tr>\n<\/tfoot>\n<\/table>\n<\/li>\n<li><span style=\"text-decoration: underline\"><span style=\"color: #008000\">Course policies:<\/span><\/span><\/li>\n<li><span style=\"text-decoration: underline\">Closed-book policy<\/span>: No use of graphic calculators, computer algebra systems, or books will be allowed during any in-class tests\/quizzes. Scientific calculators are allowed.<\/li>\n<li><span style=\"text-decoration: underline\">Policy related to make-up exams or other work<\/span>: There will be no opportunities to make up for work not submitted. However, if a student provides a legitimate excuse well in advance, a change of due date may be arranged. Work with due date should be turned in at the beginning of class on the stated due date. Late work will not be accepted and will be deemed work not submitted.<\/li>\n<li><span style=\"text-decoration: underline\">Policy on class attendance<\/span>: Requirements for class attendance and make-up exams, assignments, and other work in this course are consistent with university policies that can be found in the online catalog at: https:\/\/catalog.ufl.edu\/ugrad\/current\/regulations\/info\/attendance.aspx.<\/li>\n<li><span style=\"text-decoration: underline\">University&#8217;s honesty policy<\/span>: UF students are bound by The Honor Pledge which states, &#8220;We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honor and integrity by abiding by the Honor Code&#8221;. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: &#8220;On my honor, I have neither given nor received unauthorized aid in doing this assignment.&#8221; The Honor Code (http:\/\/www.dso.ufl.edu\/sccr\/process\/student-conduct-honor-code\/) specifies a number of behaviors that are in violation of this code and the possible sanctions. Furthermore, you are obligated to report any condition that facilitates academic misconduct to appropriate personnel. If you have any questions or concerns, please consult with the instructor or TAs in this class.<\/li>\n<li><span style=\"text-decoration: underline\">For students with disabilities<\/span>: Students requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to the Instructor when requesting accommodation.<\/li>\n<li><span style=\"text-decoration: underline\">Students&#8217; evaluations of the course<\/span>: Students are expected to provide feedback on the quality of instruction in this course based on 10 criteria. These evaluations are conducted online at https:\/\/evaluations.ufl.edu. Evaluations are typically open during the last two or three weeks of the semester, but students will be given specific times when they are open. Summary results of these assessments are available to students at https:\/\/evaluations.ufl.edu\/results.<\/li>\n<li><span style=\"text-decoration: underline\">Disclaimer<\/span>:\u00a0I reserve the right to change the above policies if situations warrant.<\/li><\/ul>\n\n\n\n<pre>Homework problems for Intermediate Differential Equations Fall 2016  <br> Section 8.1: 1--10, 13, 15--16. <br> Section 8.2: 1--14, 17--34. <br> Section 8.3: 1--28, 32, 34. <br> Section 8.4: 7--19, 21--28. <br> Section 8.5: 1--17. <br> Section 8.6: 1--31, 33, 35, 37. <br> Section 8.7: 1--16, 23--24. <br> Section 8.8: 1--10, 13--20. <br> Section 9.1: all. <br> Section 9.2: all. <br> Section 9.3:  1--14, 17--30, 35--40.<br> Section 9.4: 13--30. <br> Section 9.5: 1--16, 19--24, 31-- 40. <br> Section 9.6: 1--8, 13--14. <br> Section 9.7: 1--16, 21--22.<br> Section 9.8: 1--12, 17--22.<br> Section 10.2: 1--22. <br> Section 10.3: 1--24.<br> Section 10.4: 1--19. <br> Section 10.5: 1--18. <br> Section 10.6: 1--4, 7--9, 13--18. <br> Section 10.7: 1--9, 11--16. <br><br>\nSource files: <a href=\"https:\/\/people.clas.ufl.edu\/pilyugin\/content-removed\/\" rel=\"attachment wp-att-553\">Chapter 8<\/a> <a href=\"https:\/\/people.clas.ufl.edu\/pilyugin\/content-removed\/\" rel=\"attachment wp-att-554\">Chapter 9<\/a> <a href=\"https:\/\/people.clas.ufl.edu\/pilyugin\/content-removed\/\" rel=\"attachment wp-att-555\">Chapter 10<\/a>\n<\/pre>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":311,"featured_media":0,"parent":8,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-534","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages\/534","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/users\/311"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/comments?post=534"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages\/534\/revisions"}],"predecessor-version":[{"id":1590,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages\/534\/revisions\/1590"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/pages\/8"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/pilyugin\/wp-json\/wp\/v2\/media?parent=534"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}