Advanced Calculus I F21

MAA 4211: Advanced Calculus I

University of Florida, Fall 2021

Fine Arts Building 105, MWF3 (9:35–10:25)

Instructor information:

Vince Vatter

Office: Little Hall 412
Office hours: M7 (1:55–2:45), T5 (11:45–12:35), and by appointment
Office phone: (352) 294-2338
Email: vatter@ufl.edu

Tentative schedule

Lecture
number
Date Topics
1 Monday 8/23 Introduction and √2
Section 1.1
2 Wednesday 8/25 Sets, functions, and proofs
Section 1.2
3 Friday 8/27 The axiom of completeness (suprema and infima)
Section 1.3
4 Monday 8/30 Consequences of completeness
Section 1.4
5 Wednesday 9/1 Cardinality
Section 1.5
Homework 1 due (before class starts)
6 Friday 9/3 Introduction to sequences and series
Section 2.1
Monday 9/6 Labor day (no class)
7 Wednesday 9/8 Limits of sequences
Section 2.2
8 Friday 9/10 Limit theorems
Section 2.3
9 Monday 9/13 Monotone sequences
Section 2.4
Wednesday 9/15 Quiz 1
10 Friday 9/17 Subsequences and Bolzano–Weierstrass
Section 2.5
11 Monday 9/20 Cauchy sequences
Section 2.6
12 Wednesday 9/22 Numerical series
Section 2.7
Homework 2 due (before class starts)
13 Friday 9/24 The Cantor set
Section 3.1
14 Monday 9/27 Open and closed sets
Section 3.2
Wednesday 9/29 Quiz 2
15 Friday 10/1 Compact sets
Section 3.3
16 Monday 10/4 Perfect and connected sets
Section 3.4
17 Wednesday 10/6 Examples of some exotic functions
Section 4.1
Friday 10/8 Homecoming (no class)
18 Monday 10/11 Limits of functions
Section 4.2
19 Wednesday 10/13 Continuous functions
Section 4.3
Homework 3 due (before class starts)
20 Friday 10/15 Continuous functions on compact sets
Section 4.4
21 Monday 10/18 The intermediate value theorem
Section 4.5
Wednesday 10/20 Quiz 3
22 Friday 10/22 Sets of discontinuity
Section 4.6
23 Monday 10/25 Introduction to derivatives
Section 5.1
24 Wednesday 10/27 Derivatives and the intermediate value property
Section 5.2
Homework 4 due (before class starts)
25 Friday 10/29 The mean value theorems
Section 5.3
26 Monday 11/1 A continuous nowhere-differentiable function
Section 5.4
Wednesday 11/3 Quiz 4
27 Friday 11/5 Uniform convergence (of sequences of functions)
Section 6.2
28 Monday 11/8 Uniform convergence and differentiation
Section 6.3
29 Wednesday 11/10 Series of functions
Section 6.5
Homework 5 due (before class starts)
30 Friday 11/12 Power series
Section 6.6
31 Monday 11/15 Taylor series
Section 6.7
Wednesday 11/17 Quiz 5
32 Friday 11/19 Introduction to integration
Section 7.1
33 Monday 11/22 The Riemann integral
Section 7.2
Wednesday 11/24 Thanksgiving break (no class)
Wednesday 11/26 Thanksgiving break (no class)
34 Monday 11/29 Integrating functions with discontinuities
Section 7.3
35 Wednesday 12/1 Properties of the integral
Section 7.4
Homework 6 due (before class starts)
36 Friday 12/3 The fundamental theorem of calculus
Section 7.5
37 Monday 12/6 Reimann’s original definition
Section 8.1
Wednesday 12/8 Quiz 6 (and last day of class)

Text

Abbott’s Understanding Analysis, 2th edition.

Course content

Advanced treatment of limits, differentiation, integration and series.

In addition to mastery of the course content, course objectives include reading, writing, and discovering proofs and constructing proofs and counterexamples in analysis.

Expectations and grading rubric

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.

Most of the work required in this course will consist of writing proofs. These proofs will be assigned scores of 0–4 points based on the following guidelines.

0 points.
The work contains no original steps toward a correct solution. This includes work that simply consists of relevant definitions or theorems without interpretation.
1 point.
The 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.
2 points.
The 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.
3 points.
The work is 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 “for all” or “implies”, imprecise definitions, or overlooking trivial cases. In general this grade is reserved for work which would receive 4 points with minor revision.
4 points.
The 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.

Evaluation

There will be 6 quizzes and 6 homework assignments throughout the semester, as indicated in the schedule.

All quizzes will be closed-book, closed-note, and in-class. Homework will be collected online, via Canvas. Late homework will not be accepted except by prior agreement.

All assignments will count equally toward your grade.

Final letter grades will be assigned on a curve, which will be no tougher than the 10-point scale: 90%–100% will be some form of A, 80–90% will be at least some form of B, etc.

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.

Grading will be in accordance 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.

Class attendance

Attendance is strongly encouraged but is not a component of grades.

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 requesting accommodations should first register with the Disability Resource Center (352-392-8565, https://www.dso.ufl.edu/drc/) 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.

Online evaluations

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 https://evaluations.ufl.edu/results/.

Complaints

The official UF policy for filing a complaint about the course may be found here.

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

Your well-being is important to the University of Flo­­rida. 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.