#### Spring 2020: Section 17G4, MWF 3rd hour, Little Hall, room 221

Email: mjury@ufl.edu

Office: Little Hall 484

Office Hours: M 7th, W 6th, F 5th

## As of Friday March 13, the course has transitioned to online delivery. This page will not be maintained, all further course information will be posted in Canvas

Text: There is no required text for the course, all the material may be found in the lecture notes which will be posted below as the course progresses. If you want to look at a book, two that may be helpful are

Introduction to Analysis, by Maxwell Rosenlicht, Dover, 1968.

and

Principles of Mathematical Analysis, by Walter Rudin, McGraw-Hill, 1976.

## Course Content

Topics for this second semester include, uniform convergence; differentiation; Riemann integration; sequences and series of functions; the calculus of functions from R^n→R^m; and the inverse and implicit function theorems. Other topics as time permits. In addition to mastery of the course content, course objectives include reading, writing, and discovering proofs and constructing proofs and counterexamples in analysis.

### Lecture Notes (last updated 9 Feb 2020)

(fixed some typos in Sections 11 and 12)

### Next week’s lectures

### This week’s lectures

### Past lectures

Friday 28 February – more on series, discussion of problems and exercises, finish Section 12

Wednesday 26 February – representing functions by power series, Taylor’s theorem, examples, Section 12.7, homework 7 assigned

Monday 24 February – more on power series; term-by-term differentiation and integration, through end of Section 12.6

Friday 21 February – alternating series test, introduction to power series, radius and interval of convergence, through Lemma 12.17

Wednesday 19 February – root test and ratio test, through Remark 12.10

Monday 17 February – Continue section 12 (Prof. McCullough)

Friday 14 February – Begin section 12, through Proposition 12.3(i), Homework 5 due, homework 6 assigned

Wednesday 12 February – Finish Section 11

Monday 10 February – Continue Section 11, starting with Proposition 11.33

Friday 7 February – Exam 1 (Sections 9.1 through 11.3)

Wednesday 5 February – Review for Exam 1. Exam 1 review page

Monday 3 February – Continue Section 11, the logarithm (Example 11.24) and Section 11.4

Friday 31 January – Continue Section 11, through Theorem 11.25.

Wednesday 29 January – Continue Section 11, Proposition 11.15 through Theorem 11.22. Homework 4 due.

Monday 27 January – Continue Section 11, through Corollary 11.14

Friday 24 January – Begin Section 11, Homework 3 due, Homework 4 assigned

Wednesday 22 January – Finish Section 10, Taylor’s theorem

Monday 20 January – no class (MLK holiday)

Friday 17 January–Section 10 continued, Homework 2 due, Homework 3 assigned

Wednesday 15 January–Section 10 continued, through Proposition 10.10

Monday 13 January–Begin Section 10 (derivatives), through Proposition 10.7 (chain rule)

Friday 10 January–Finish Section 9. Homework 1 due, Homework 2 assigned

Wednesday 8 January –finish Section 9.1, begin 9.2

Monday 6 January–Introduction to the course, begin Section 9.1, through Example 9.5(ii), Homework 1 assigned

## Homework assignments

Homework will be collected and graded roughly once a week; for a total of about 10 to 15 problems. In addition several problems will be assigned each lecture (not to be turned in). Late homework will not be accepted, but the lowest two homework scores will be dropped.

**Homework 7** (due Wednesday 11 March) Problem 12.6 (the integral test)

**Homework 6** (due Friday 21 February) Problems 12.1 and 12.2 (you can appeal to the result of Exercise 12.1 without proving it).

**Homework 5** (due Friday 14 February) Problem 11.5

**Homework 4** (due Wednesday 29 January) Problem 10.4

**Homework 3** (due Friday 24 January) Exercise 10.1 parts (i) and (ii), and Problem 10.1

**Homework 2** (due Friday 17 January) Problem (NOT Exercise!) 9.6

**Homework 1** (due Friday 10 January) Exercises (NOT Problems!) 9.3 and 9.4 (see lecture notes)

## Grading policies

The course grade will consist of the homework average (25% of the final grade) and three midterm exams (25% each). Final grades are assigned according to the standard scale: 90-100 A, 87-89 A-, 84-86 B+, 80-83 B, 77-79 B-, etc.

Tentative exam dates are as follows:

Exam 1: Friday 7 February

Exam 2: Wednesday 18 March

Exam 3: Monday 20 April

The final exam (Tuesday 28 April, 8:30–9:30 AM) will serve as a make-up.

No notes or books will be allowed during exams.

## Additional Information:** **

**Grades:** Grading will be in accord with the UF policy stated at https://catalog.ufl.edu/ugrad/current/regulations/info/grades.aspx.

**Honor Code: “**UF students are bound by The Honor Pledge which states, “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. On all work submitted for credit by students at the University of Florida, the following pledge is either required or implied: “On my honor, I have neither given nor received unauthorized aid in doing this assignment.” The 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.”

**Class Attendance: **“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: https://catalog.ufl.edu/ugrad/current/regulations/info/attendance.aspx.”

**Accommodations for Students with Disabilities:** “Students with disabilities who experience learning barriers and would like to request academic accommodations should connect with the disability Resource Center by visiting https://disability.ufl.edu/students/get-started/. It is important for students to share their accommodation letter with their instructor and discuss their access needs, as early as possible in the semester.”

**Online Evaluations:** “Students are expected to provide professional and respectful feedback on the quality of instruction in this course by completing course evaluations online via GatorEvals. Guidance on how to give feedback in a professional and respectful manner is available at https://gatorevals.aa.ufl.edu/students/. Students will be notified when the evaluation period opens, and can complete evaluations through the email they receive from GatorEvals, in their Canvas course menu under GatorEvals, or via https://ufl.bluera.com/ufl/. Summaries of course evaluation results are available to students at https://gatorevals.aa.ufl.edu/public-results/.”

**Contact information for the Counseling and Wellness Center:** https://counseling.ufl.edu/, 392-1575; and the University Police Department: 392-1111 or 9-1-1 for emergencies.

**U Matter, We Care**: If you or someone you know is in distress, please contact umatter@ufl.edu, 352-392-1575, or visit umatter.ufl.edu/ to refer or report a concern and a team member will reach out to the student in distress.