{"id":712,"date":"2021-06-02T11:51:17","date_gmt":"2021-06-02T15:51:17","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/vatter\/?page_id=712"},"modified":"2026-03-19T08:16:49","modified_gmt":"2026-03-19T12:16:49","slug":"4212s22","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/vatter\/past-courses\/4212s22\/","title":{"rendered":"Advanced Calculus II S22"},"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<p>University of Florida, Spring 2022<\/p>\n\n\n\n\n\n<p>Little Hall 223, MWF3 (9:35\u201310:25)<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Instructor information:<\/h4>\n\n\n\n<p><a href=\"..\/..\/\">Vince Vatter<\/a><\/p>\n\n\n\n\n\n<p>Office: Little Hall 412<\/p>\n\n\n\n\n\n<p>Office hours:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Monday 1:30\u20132:20 in-person in LIT 412,<\/li>\n<li>Tuesday 5th period (11:45\u201312:35) on Zoom, and<\/li>\n<li>by appointment<\/li><\/ul>\n\n\n\n<p>Office phone: (352) 294-2338<\/p>\n\n\n\n\n\n<p>Email: vatter@ufl.edu<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Text<\/h2>\n\n\n\n<p>We will use the following course notes as a text:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/people.clas.ufl.edu\/vatter\/content-removed\/\" rel=\"attachment wp-att-776\">Chapter 1: Metric spaces<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/vatter\/content-removed\/\" rel=\"attachment wp-att-800\">Chapter 2: Compactness<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/vatter\/content-removed\/\" rel=\"attachment wp-att-803\">Chapter 3: Continuity<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/vatter\/content-removed\/\" rel=\"attachment wp-att-809\">Chapter 4: Sequences of functions<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/vatter\/content-removed\/\" rel=\"attachment wp-att-811\">Chapter 5: Power series<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/vatter\/content-removed\/\" rel=\"attachment wp-att-813\">Chapter 6: Linear algebra<\/a>\n<\/li><li><a href=\"https:\/\/people.clas.ufl.edu\/vatter\/content-removed\/\" rel=\"attachment wp-att-817\">Chapter 7: Multivariable calculus<\/a><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Course content<\/h2>\n\n\n\n<p>From the <a href=\"https:\/\/catalog.ufl.edu\/UGRD\/courses\/mathematics\/\">course catalog<\/a>: Continues the advanced calculus sequence in limits, differentiation, integration and series.<\/p>\n\n\n\n\n\n<p>In addition to mastery of the course content, course objectives include reading, writing, and discovering proofs and constructing proofs and counterexamples in analysis.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Tentative schedule<\/h2>\n\n\n\n<table>\n<tr>\n<th>Lecture<br>number<\/th>\n<th>Date<\/th>\n<th>Topics<\/th>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>Wednesday 1\/5<\/td>\n<td>\n    Metric spaces<br>\n    Section 1.1\n<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>Friday 1\/7<\/td>\n<td>\n    Normed vector spaces<br>\n    Section 1.2\n<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>Monday 1\/10<\/td>\n<td>\n    Convergence and limits<br>\n    Section 1.3\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Wednesday 1\/12<\/td>\n<td>\n    <i>Class canceled<\/i><br>\n    <b>\u2022 Homework 1 due<\/b> (before class)\n<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>Friday 1\/14<\/td>\n<td>\n    Open and closed sets<br>\n    Section 1.4\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Monday 1\/17<\/td>\n<td>\n    <i>Martin Luther King Jr. Day (no class)<\/i>\n<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>Wednesday 1\/19<\/td>\n<td>\n    Interior, exterior, boundary, and closure<br>\n    Section 1.5\n<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>Friday 1\/21<\/td>\n<td>\n    Relative topology<br>\n    Section 1.6<br>\n    <b>\u2022 Homework 2 due<\/b> (before class)<br>\n    <b>\u2022 Quiz 1<\/b> (untimed, on canvas)\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Monday 1\/24<\/td>\n<td>\n    Review\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\n    <br>Wednesday 1\/26\n<\/td>\n<td>\n    <br><b>\u2022 Midterm 1<\/b> (online, during class)<br><br>\n<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>Friday 1\/28<\/td>\n<td>\n    Cauchy sequences and completeness<br>\n    Section 1.7\n<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>Monday 1\/31<\/td>\n<td>\n    Open covers<br>\n    Section 2.1\n<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>Wednesday 2\/2<\/td>\n<td>\n    Sequential compactness<br>\n    Section 2.2<br>\n    <b>\u2022 Homework 3 due<\/b> (before class)\n<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>Friday 2\/4<\/td>\n<td>\n    Heine\u2013Borel<br>\n    Section 2.3\n<\/td>\n<\/tr>\n<tr>\n<td>11<\/td>\n<td>Monday 2\/7<\/td>\n<td>\n    Continuity<br>\n    Section 3.1\n<\/td>\n<\/tr>\n<tr>\n<td>12<\/td>\n<td>Wednesday 2\/9<\/td>\n<td>\n    Limits of functions<br>\n    Section 3.2<br>\n    <b>\u2022 Quiz 2<\/b> (untimed, on canvas)\n<\/td>\n<\/tr>\n<tr>\n<td>13<\/td>\n<td>Friday 2\/11<\/td>\n<td>\n    Continuity and compactness<br>\n    Section 3.3\n<\/td>\n<\/tr>\n<tr>\n<td>14<\/td>\n<td>Monday 2\/14<\/td>\n<td>\n    Uniform continuity and compactness<br>\n    Section 3.4\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Wednesday 2\/16<\/td>\n<td>\n    <i>Class canceled<\/i><br>\n    <b>\u2022 Homework 4 due<\/b> (before class)\n<\/td>\n<\/tr>\n<tr>\n<td>15<\/td>\n<td>Friday 2\/18<\/td>\n<td>\n    Continuity and connectedness<br>\n    Section 3.5\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Monday 2\/21<\/td>\n<td>\n    Review\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\n    <br>Wednesday 2\/23\n<\/td>\n<td>\n    <br><b>\u2022 Midterm 2<\/b> (online, during class)<br><br>\n<\/td>\n<\/tr>\n<tr>\n<td>16<\/td>\n<td>Friday 2\/25<\/td>\n<td>\n    Types of convergence of functions<br>\n    Section 4.1\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Monday 2\/28<\/td>\n<td>\n<\/td>\n<\/tr>\n<tr>\n<td>17<\/td>\n<td>Wednesday 3\/2<\/td>\n<td>\n    The uniform metric<br>\n    Section 4.2<br>\n    <b>\u2022 Homework 5 due<\/b> (before class)\n<\/td>\n<\/tr>\n<tr>\n<td>18<\/td>\n<td>Friday 3\/4<\/td>\n<td>\n    Taylor polynomials<br>\n    Section 5.1\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>\n<br><i>Spring Break<\/i><br><br>\n<\/td>\n<\/tr>\n<tr>\n<td>19<\/td>\n<td>Monday 3\/14<\/td>\n<td>\n    Linear transformations<br>\n    Section 6.1\n<\/td>\n<\/tr>\n<tr>\n<td>20<\/td>\n<td>Wednesday 3\/16<\/td>\n<td>\n    The equivalence of norms<br>\n    Section 6.2<br>\n    <b>\u2022 Quiz 3<\/b> (untimed, on canvas)\n<\/td>\n<\/tr>\n<tr>\n<td>21<\/td>\n<td>Friday 3\/18<\/td>\n<td>\n    The metric space of linear transformations<br>\n    Section 6.3\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Monday 3\/21<\/td>\n<td>\n    Review\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\n    <br>Wednesday 3\/23\n<\/td>\n<td>\n    <br><b>\u2022 Midterm 3<\/b> (online, during class)<br><br>\n<\/td>\n<\/tr>\n<tr>\n<td>22<\/td>\n<td>Friday 3\/25<\/td>\n<td>\n    Invertible matrices<br>\n    Section 6.4\n<\/td>\n<\/tr>\n<tr>\n<td>23<\/td>\n<td>Monday 3\/28<\/td>\n<td>\n    The derivative (for multivariable functions)<br>\n    Section 7.1\n<\/td>\n<\/tr>\n<tr>\n<td>24<\/td>\n<td>Wednesday 3\/30<\/td>\n<td>\n    Directional and partial derivatives<br>\n    Section 7.2<br>\n    <b>\u2022 Quiz 4<\/b> (untimed, on canvas)\n<\/td>\n<\/tr>\n<tr>\n<td>25<\/td>\n<td>Friday 4\/1<\/td>\n<td>\n    The chain rule<br>\n    Section 7.3\n<\/td>\n<\/tr>\n<tr>\n<td>26<\/td>\n<td>Monday 4\/4<\/td>\n<td>\n    The contraction mapping theorem<br>\n    Section 7.4\n<\/td>\n<\/tr>\n<tr>\n<td>27<\/td>\n<td>Wednesday 4\/6<\/td>\n<td>\n    Continuous differentiability<br>\n    Section 7.5<br>\n    <b>\u2022 Homework 6 due<\/b> (before class)\n<\/td>\n<\/tr>\n<tr>\n<td>28<\/td>\n<td>Friday 4\/8<\/td>\n<td>\n    The inverse function theorem<br>\n    Section 7.6\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>Monday 4\/11<\/td>\n<td>\n    Review\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>\n    <br>Wednesday 4\/13\n<\/td>\n<td>\n    <br><b>\u2022 Midterm 4<\/b> (online, during class)<br><br>\n<\/td>\n<\/tr>\n<tr>\n<td>29<\/td>\n<td>Friday 4\/15<\/td>\n<td>\n    The inverse function theorem, continued<br>\n    Section 7.6\n<\/td>\n<\/tr>\n<tr>\n<td>30<\/td>\n<td>Monday 4\/18<\/td>\n<td>\n    The implicit function theorem<br>\n    Section 7.7\n<\/td>\n<\/tr>\n<tr>\n<td>31<\/td>\n<td>Wednesday 4\/20<\/td>\n<td>\n    The implicit function theorem, continued<br>\n    Section 7.7<br>\n    <b>\u2022 Quiz 5<\/b> (untimed, on canvas)\n<\/td>\n<\/tr>\n<\/table>\n\n\n\n<h2 class=\"wp-block-heading\">Expectations and grading rubric<\/h2>\n\n\n\n<p>Work submitted for a grade in this course will be graded in a most rigorous fashion, and thusly, such work should have a good deal of thought and care put into it.<\/p>\n\n\n\n\n\n<p>Most of the work required in this course will consist of writing proofs. These proofs will be assigned scores of 0\u20134 points based on the following guidelines.<\/p>\n\n\n\n\n\n<p><b>0 points.<\/b><br>\nThe work contains no original steps toward a correct solution. This includes work that simply consists of relevant definitions or theorems without interpretation.<br>\n<b>1 point.<\/b><br>\nThe work contains some original steps toward a correct solution but does not contain a workable outline of the full solution. This grade is also used if the student has misunderstood the question or made an unwarranted simplifying assumption that makes the problem trivial.<br>\n<b>2 points.<\/b><br>\nThe work contains an outline of a correct solution and several steps toward this solution. However, the writing may be unclear, or there may be holes in the argument.<br>\n<b>3 points.<\/b><br>\nThe work resembles a full, complete proof, but it has some serious deficiencies. These may include incomplete sentences, abbreviating words with logical symbols such as those for &#8220;for all&#8221; or &#8220;implies&#8221;, imprecise definitions, or overlooking trivial cases. In general this grade is reserved for work which would receive 4 points with minor revision.<br>\n<b>4 points.<\/b><br>\nThe work consists of a full, complete proof and is reasonably well written in complete sentences, without logical symbols. There may be minor typos or clumsy writing that could be improved, but no important steps of the solution are omitted or incorrect.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Evaluation<\/h2>\n\n\n\n<p>There will be 4 midterms, 5 quizzes, and 6 homework assignments throughout the semester, as indicated in the schedule.<\/p>\n\n\n\n\n\n<p>Midterms and homework will be collected online, via Canvas. Quizzes will be conducted in Canvas. All assignments are open-book and open-note. Late assignments will not be accepted except by prior agreement.<\/p>\n\n\n\n\n\n<p>The midterms will collectively count for 50% of your grade, the quizzes for 20%, and the homeworks for 30%. No grades will be dropped.<\/p>\n\n\n\n\n\n<p>Final letter grades will be assigned on a curve, which will be no tougher than the 10-point scale: 90%\u2013100% will be some form of A, 80\u201390% will be at least some form of B, etc.<\/p>\n\n\n\n\n\n<p>If you have a disagreement with the grading of one of your solutions, I ask that you submit a written request for reconsideration within one month.<\/p>\n\n\n\n\n\n<p>Grading will be in accordance with the UF policy stated at <a style=\"color: #243778\" href=\"https:\/\/catalog.ufl.edu\/ugrad\/current\/regulations\/info\/grades.aspx\">https:\/\/catalog.ufl.edu\/ugrad\/current\/regulations\/info\/grades.aspx.<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Honor code<\/h2>\n\n\n\n<p>UF students are bound by The Honor Pledge which states, \u201cWe, 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. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: <b>\u201cOn my honor, I have neither given nor received unauthorized aid in doing this assignment.\u201d<\/b> The <a href=\"http:\/\/www.dso.ufl.edu\/sccr\/process\/student-conduct-honor-code\/\">Honor Code<\/a>\u00a0specifies 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.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Class attendance<\/h2>\n\n\n\n<p>Attendance is strongly encouraged but is not a component of grades.<\/p>\n\n\n\n\n\n<p>Requirements for class attendance and make-up exams, assignments, and other work in this course are consistent with university policies that can be found at <a style=\"color: #243778\" href=\"https:\/\/catalog.ufl.edu\/ugrad\/current\/regulations\/info\/attendance.aspx\">https:\/\/catalog.ufl.edu\/ugrad\/current\/regulations\/info\/attendance.aspx.<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Accommodations for students with disabilities<\/h2>\n\n\n\n<p>Students with disabilities requesting accommodations should first register with the Disability Resource Center (352-392-8565,\u00a0<a style=\"color: #243778\" href=\"https:\/\/www.dso.ufl.edu\/drc\/\">https:\/\/www.dso.ufl.edu\/drc\/<\/a>) by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Online evaluations<\/h2>\n\n\n\n<p>Students are expected to provide feedback on the quality of instruction in this course by completing online evaluations 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\u00a0<a style=\"color: #243778\" href=\"https:\/\/gatorevals.aa.ufl.edu\/\"> https:\/\/gatorevals.aa.ufl.edu\/<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Complaints<\/h2>\n\n\n\n<p>The official UF policy for filing a complaint about the course may be found <a href=\"https:\/\/registrar.ufl.edu\/writtencomplaints\">here<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Counseling and Wellness Center<\/h2>\n\n\n\n<p><a style=\"color: #243778\" href=\"https:\/\/counseling.ufl.edu\/\">https:\/\/counseling.ufl.edu\/<\/a>, 392-1575; and the University Police Department: 392-1111 or 9-1-1 for emergencies.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">U Matter, We Care<\/h2>\n\n\n\n<p>Your well-being is important to the University of Flo\u00ad\u00adrida. The U Matter, We Care initiative is committed to creating a culture of care on our campus by encouraging members of our community to look out for one another and to reach out for help if a member of our community is in need.  If you or a friend is in distress, please contact umatter@ufl.edu so that the U Matter, We Care Team can reach out to the student in distress.  A nighttime and weekend crisis counselor is available by phone at 352-392-1575.  The U Matter, We Care Team can help connect students to the many other helping resources available including, but not limited to, Victim Advocates, Housing staff, and the Counseling and Wellness Center.  Please remember that asking for help is a sign of strength.  In case of emergency, call 9-1-1.<\/p>\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":193,"featured_media":0,"parent":216,"menu_order":202,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-712","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/vatter\/wp-json\/wp\/v2\/pages\/712","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/vatter\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/vatter\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/vatter\/wp-json\/wp\/v2\/users\/193"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/vatter\/wp-json\/wp\/v2\/comments?post=712"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/vatter\/wp-json\/wp\/v2\/pages\/712\/revisions"}],"predecessor-version":[{"id":1143,"href":"https:\/\/people.clas.ufl.edu\/vatter\/wp-json\/wp\/v2\/pages\/712\/revisions\/1143"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/vatter\/wp-json\/wp\/v2\/pages\/216"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/vatter\/wp-json\/wp\/v2\/media?parent=712"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}