## Schedule

The schedule below is a record of what we have actually done as well as an approximate projection of what we will do. Readings, homework assignments, and worksheets will be posted as they are assigned. Most homework problems will come from Basic Analysis: Introduction to Real Analysis by Jiří Lebl (freely available online; click on the title for a link). Homework sets are due by 4:00 PM on the date indicated. Harder problems are marked with a * and are counted separately from normal homework problems. You must complete at least 15 starred problems over the course of the semester.

- Week 1
- 1/12: Discuss the syllabus and Chapter 0.
- 1/14: Section 1.1 basic properties and the start of a worksheet (due 1/19; .tex version).

- Week 2
- 1/17: MLK Day; no class.
- 1/19: Section 1.1.
- 1/21: Section 1.2 the set of real numbers.
**Homework due today:**- 0.3: 8, 13, 20
- 1.1: 1, 3, 10*, 12* (use earlier parts of prop 1.1.8 in 1 and 3)

- Week 3
- 1/24: Section 1.2 the set of real numbers.
- 1/26: Section 1.2 the set of real numbers.
- 1/28: Discuss 1.3 absolute values and start a worksheet (due 1/31; .tex version).
**Homework due today:**- 1.1: 9, 14 (for part a, just try to understand the ordering).
- 1.2: 2, 7*, 8, 9, 13*, and prove part (iii) of prop. 1.2.6.

- Week 4
- 1/31: 1.5 decimal representations and 2.1 sequences and limits.
- 2/2: 2.1 Sequences an limits.
- 2/4: 2.1.
**Homework due today:**- 1.3: 1-4, 8, 9.
- 1.4: 2, 5*.
- One more starred problem: the challenge from the worksheet on bounds and bijections.

- Week 5
- 2/7: 2.1.
- 2/9: 2.2 Facts about limits of sequences. Start a worksheet (.tex version).
- 2/11: 2.2.
**Homework due today:**- 2.1: 2, 5, 6, 7, 10, 15, 16*, 22*. Be sure to provide proofs for problems 2-6 (proofs may use the definition and/or propositions of the section).
- 2.2: 5, 7, 8*.

- Week 6
- 2/14: 2.2.
- 2/16: 2.3 Limit superior, limit inferior, and Bolzano-Weierstrass.
- 2/18: 2.4 Cauchy sequences. Start a worksheet (.tex version).
**Homework due**~~today~~Wednesday?- 2.2: 9, 12, 15*.
- 2.3: 1, 2, 3, 5, 6, 7*.

- Week 7
- 2/21: Presidents' Day; no class
- 2/23: 2.5 Series.
- 2/25: 2.5.

- Week 8
- 2/28: Chapter 2 wrap up.
**Homework due today:**- 2.3: 9*, 14ac, 16*.
- 2.4: 3*, 4, 5, 7.
- 2.5: 1, 3, 4, 8*.

- 3/2: 3.1 Limits of functions.
**Take home exam runs today through Friday.**Exam covers 1.1-2.4. - 3/4: 3.1.

- 2/28: Chapter 2 wrap up.
- Spring break
- Week 9
- 3/14: 3.1 and 3.2 Continuous functions.
- 3/16: 3.2. Start a worksheet (.tex version).
- 3/18: 3.2.
**Homework due today:**- 2.5: 9, 10, 11, 15*.
- 3.1: 1, 3, 5, 7, 8, 9*.

- Week 10
- 3/21: Finish 3.2.
- 3/23: 3.3 Min-max and IVTs, and start 3.4 Uniform continuity.
- 3/25: 3.4 continued
**Homework due today:**- 3.2: 2, 5, 6 (i and iii only), 7, 9*, 10*, 11.
- 3.3: 2, 3*.

- Week 11
- 3/28: 3.4. continued.
- 3/30: 3.5 Limits at infinity and a general wrap up of chapter 3.
- 4/1: 4.1 The Derivative. Start a worksheet (.tex version).
**Homework due**~~today~~Monday:- 3.3: 7, 10*, 11, 13.
- 3.4: 3, 4, 8*, 10a, 10b*, 12, 14*.
- 3.5: 4, 5.

- Week 12
- 4/4: 4.1 continued.
- 4/6: 4.2 The MVT. Start a worksheet (.tex version).
- 4/8: 4.3,4 Taylor's theorem and the inverse function theorem.

- Week 13
- 4/11: 5.1 the Riemann integral.
**Homework due today:**- 4.1: 2, 5, 6*, 9, 10*, 11.
- 4.2: 3, 4, 6, 7*, 8.

- 4/13: 5.1 continued.
- 4/15: Good Friday; no class.

- 4/11: 5.1 the Riemann integral.
- Week 14
- 4/18: Easter Monday; no class.
- 4/20: 5.2 Properties of the integral.
- 4/22: 5.2 continued.

- Week 15
- 4/25: 5.3 Fundamental theorem of calculus. Start proving the FTC (.tex version).
**Homework due today**(last homework):- 4.3: 3.
- 5.1: 1, 2, 5, 7, 9, 11*.
- 5.2: 2, 4, 7*, 14*.

- 4/27: 5.3 continued.
- 4/29: 5.4 The logarithm and the exponential (briefly).

- 4/25: 5.3 Fundamental theorem of calculus. Start proving the FTC (.tex version).
- Final exam week
**Final: 8-10 Thursday**- Approximately 10 problems
- Solve 8 problems during the final time
- Turn in the final 2 solutions Friday
- You may bring 2 pages of notes (front and back; 4 total surfaces)

- Office hours:
- Monday 3-4
- Tuesday 11:00-12:30
- Wednesday 11:00-12:30
- Thursday 10:15-11:15
- Friday 10:00-12:00
- Or by appointment.

- Final exam schedule.

### Links and class resources

- Basic Analysis: Introduction to Real Analysis by Lebl (our textbook)
- Elementary Real Analysis by Thompson, Bruckner, and Bruckner
- Introduction to Real Analysis by Trench
- Syllabus
- WolframAlpha
- Geogebra
- Desmos
- Overleaf

### Office hours

In person in Herak 307A unless otherwise specified, or via Zoom by request.

- Monday 9-10 in the Math Learning Center and 2:30-3:30
- Wednesday 2:30-3:30
- Friday 9:30-10:30
- Or by appointment

Logan Axon

Department of Mathematics

MSC 2615

Gonzaga University

Spokane, WA 99258

Office: Herak 307A

Phone: 509.313.3897

Email: axon@gonzaga.edu

Last updated 4/29/2022