### "...so many things are possible just as long as you don't know they're impossible."

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Do only these tasks before our first class:

* Watch this video: Welcome! (We are not using a flipped classroom so some of the material isn't relevant, but most of it is.)

* Read this information on our text that you should have received in an email.

You do not need to do an of the assignments outside of this box until after our first class.

8/30: In Person Learning Today! Live Stream and/or Zoom Links Are On The Help Page - FINALIZED

You are encouraged to use my office hours (Zoom or in person) for help hours on the homework. However, you may not ask questions over homework on the day that the assignment is due.

Do NOT assume that any assignment beyond today's is correct! I often change them the day of class. If you don't see the word in the assignment, the assignment may change!

Introductory Reading and Activities - There is nothing to turn in for reading assignments, but the material could appear on quizzes. **Complete all of these activities before class on Friday!**

* Read the course introduction (syllabus) at this link. This document contains
information that you may need to know. Some of it could appear on
a quiz. (It's also the first 11 pages of our text.)

* Read the Carthage Academic Honesty Guidelines. There is a link at the top of this page.

* Check the blog (see the link on the left side of this page) for updates. You should check the blog every day. I will provide homework hints, comments on how our class went, and more!

Required Videos to View Before Class on 9/1, Which is on Friday

* Watch this video produced by Arizona State University. It could increase your grade significantly! You could also listen to this radio program. You can read the article, or click on the blue "Listen" button on the left side of the page. You can read the text as well, but listening might be more effective.

The Reading and Homework assigned today are due on 9/6.

Reading Assignment

* Read Section 1.0 and Section 1.1 in the notes, filling in all missing proofs, and discussing the results together. Section 1.0 is interesting - why do we take complex numbers seriously?

* In the Schaum's Outline, read bullets 1.1-1.6 together, pages 1-3. Read Solved Problems 1-4 on pages 9-10.

* Start Mathematica, and learn how to manipulate complex numbers. You should be able to add, subtract, multiply, and divide them. Remember that \(\mathtt{I}\) stands for \(\sqrt{-1}\).

* BEFORE OUR NEXT CLASS, Compile a list of at least two questions OVER THE READING MATERIAL that you have for me.

* Start working on the homework (assigned below). You are welcome to work together, but please make sure you understand everything you write on your paper. Remember what I wrote in my e-mail to you in December!

Homework

* From Section 1.1 in the notes, do exercises 1-8.

* From the Schaum's Outline, do Supplemenatary Problems 1.53h, 1.53i, and 1.57.

* Check the blog every day.

9/1: In Person Learning Today! - FINALIZED

The Reading and Homework assigned today are due on 9/8.

Reading Assignment

* Read Section 1.2 in the notes, filling in all missing proofs, up to Vector Representation.

Homework

* From Section 1.2 in the notes, do exercises 1, 2, 3. You may use Mathematica, but you should also know how to do the computations by hand.

* Check the blog every day.

Optional material from the Khan Academy

* Nothing at this time.

Optional: Sign up for your free MAA membership at this link.

9/4: Labor Day - No Class Meeting

9/6: In Person Learning Today! - FINALIZED

The Reading and Homework assigned today are due 9/11. Last day to add or drop a course.

Reading Assignment

* Read the rest of Section 1.2 in the notes.

* Skim Section 1.1 in Fisher. There will be some overlap with the notes.

* Skim Section 1.2 in Fisher, skipping examples 1, 2, and 3.

Homework

* From Section 1.2 in the notes, do exercises 4abce, 5ac, 6ac, 7ab.

* Check the blog every day. I've added some entries.

Optional material

* Nothing at this time.

9/8: In Person Learning Today! - FINALIZED

The Reading and Homework assigned today are due 9/13.

Reading Assignment

* Read Section 1.3 in the notes.

* From Chapter 1 in Schaum's, read solved problems 28, 30, 32, 36, and 37.

Homework

* Do exercises 1, 2, 3, 4, 5 from Section 1.3 in the notes.

* Check the blog every day for new entries.

Optional material

* Nothing at this time.

9/11: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 9/15.

Reading Assignment

* Read Section 1.4 in the notes.

* Skim Section 1.3 in Fisher.

* Review Sections 1.1 and 1.2 and re-work any homework that you didn't get the first time.

Homework

* Do exercises 1-2 from Section 1.4 of the notes. Pictures are fine for 1 - no rigorous proofs needed.

* Check the blog every day for new entries.

Optional material

* None at this time.

9/13: In-Person Instruction Today! - FINALIZED

Here is a Mathematica file for section 1.5

The Reading and Homework assigned today are due 9/18. Last day to add or drop a course.

Reading Assignment

* Read Section 1.5 in the notes.

* Skim Section 1.4 in Fisher.

* Read bullets 2.9-2.13, and 2.15-2.18, in Schaum's, Chapter 2.

* From Chapter 2 in Schaum's, read solved problems 2.23, 2.24, 2.29, 2.33, 2.38.

Homework

* From Section 1.5, do exercises 1, 2, 3, 6, 8, 10.

* Find the real part and the imaginery part of each function below using \(z=x+iy\). (You do not need to do these computations from scratch if we have already done them in class or in the notes!)

(a) \(f(z)=(\overline z)^2\)

(b) \( g(z)=z+|z|\)

* Check the blog every day for new entries.

Optional material

* None yet.

9/15: In-Person Instruction. - FINALIZED

Here is the cobwebs Mathematica file.

The Reading and Homework assigned today are due 9/20.

Reading Assignment

* Read Section 5.1 in the notes. There is a lot of terminology, so you may want to make a list of new terms.

Homework

* Do exercises 1, 3abdf, 4abdf, 5ade, 6ade, 9 from Section 5.1.

* Check the blog every day for new entries.

Optional material

* Iterate many points in \(\mathbb T^1\) using Mathematica. Can you find any that are not periodic or eventually periodic?

9/18: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 9/22.

Here is a Mathematica file for sections 1.6-1.7.

Reading Assignment

* Read Section 1.6 in the notes.

Homework

* Do exercises 1-3 from Section 1.6.

* Check the blog every day for new entries.

Optional material

* Nothing today.

9/20: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 9/25, BUT WILL NOT BE COLLECTED! An answer key will be posted immediately.

Reading Assignment

* Read Section 1.7 in the notes.

Homework

* Do exercises 1-4 from Section 1.7.

* Check the blog every day for new entries.

Optional material

* NorthingToday

9/22: In-Person Instruction. - FINALIZED - Here is a Mathematica file specifically for complex linear functions.

The Reading and Homework assigned today are due 9/29.

Reading Assignment

* Read Section 5.2 in the notes.

Homework

* Do exercises 2abdef (use Mathematica, and sketch in your homework), 5cdg, 6, 8.

* Check the blog every day for new entries.

Optional material

* Nothing today.

9/25: Exam 1 today over Chapter 1 and Section 5.1. You will be able to use Mathematica on the exam. Bring a laptop! - FINALIZED

9/27: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 10/2.

Reading Assignment

* Read Section 2.1 in the notes.

Homework

* Do exercises 1, 2ac, 3, 4, 6, 7 (you may use exercise 5 even though it isn't assigned) from Section 2.1.

* Check the blog every day for new entries.

Optional material

* Nothing yet.

9/29: In-Person Instruction. - FINALIZED

The Reading and Homework assigned today are due 10/4.

Reading Assignment

* Read Section 2.2 in the notes.

Homework

* Do exercises 1 and 4 from Section 2.2. If you want to use Mathematica to help with some of the integrals (once you have parameterized the curve), I think that's reasonable.

* Check the blog every day for new entries.

Optional material

* Note - we'll resume our study of Chapter 5 next week.

10/2: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 10/6.

Reading Assignment

* Read Section 2.3 in the notes.

Homework

* Do exercises 1-3, 5 from Section 2.3.

* Hopefully you are still checking the blog on a regular basis. Just a reminder!

Optional material

* There are some online resources for this section.

10/4: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 10/9. Last day to add or drop a course.

Reading Assignment

* Read 2.4

Homework

* Do exercises 2, 3, and 4 from Section 2.4. Yes, paramaterizing and integrating can be tedious, but use Mathematica when you can.

* Check the blog every day for new entries.

Optional material

* Nothing here.

10/6: In-Person Instruction. - FINALIZED

Today's worksheet - The cobweb file again - For Dr. Snavely

The Reading and Homework assigned today are due 10/11.

Reading Assignment

* Read Section 5.3 in the notes. You may skim the proof of Sarkovskii's Theorem.

Homework

*
From Section 5.3 in the notes, do exercises 2-7 in the notes.

* Check the blog every day for new entries.

Optional material

* Nothing today.

10/9: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 10/13.

Reading Assignment

* Read Section 2.5 in the notes.

Homework

* Do exercises 1-7 except for 6b from Section 2.5 in the notes. You can do 6b for extra credit, but Fisher's answer in the back of the book is not correct, at least in the editions I have.

* Check the blog every day for new entries.

Optional material

* Many more examples in Section 2.3 of Fisher and Chapter 5 of Schaum's. Remember there are answers to the Supplemental Problems at the end of the chapter.

10/11: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 10/18. Last day to add or drop a course.

Reading Assignment

* Read Section 2.6 in the notes.

Homework

* Do exercises 1-2 from Section 2.6 in the notes.

* Check the blog every day for new entries.

Optional material

* There is a lot of material on power series. See Schaum's and Fisher.

10/13: In-Person Instruction. - FINALIZED

The Reading and Homework assigned today are due 10/20.

Reading Assignment

* Skim Section 5.4 in the notes.

Homework

* Do exercises 1, 2c, 3c, and 4 from Section 5.4.

* Check the blog every day for new entries.

Optional material

* I could provide some if you wish!

10/16: NO CLASS - FALL BREAK

10/18: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 10/23. Last day to add or drop a course.

Reading Assignment

* Read Section 2.7 in the notes.

Homework

* Do exercise 1 from Section 2.7 in the notes.

* Are you reading the blog regularly? You should be!

Optional material

* There are many ways to do these integrals on the web, but I want you to use power series!

10/20: In-Person Instruction. - FINALIZED

The Reading and Homework assigned today are due 10/25.

Reading Assignment

* Skim 5.5 in the notes.

Homework

* Do exercise 1 from Section 5.5 in the notes. Have some fun with this! See the Help Page for a link.

Optional material

* I can provide some if requested.

To sign up for the PME undergraduate research conference at St. Norbert, use this form right away!

10/23: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 10/27.

Reading Assignment

* Read 3.1 in the notes.

Homework

* Do exercises 1, 2, 3a, 4, 6 from Section 3.1.

* Check the blog every day for new entries.

Optional material

* Nothing in particular.

10/25: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 10/30, BUT WILL NOT BE COLLECTED. SOLUTIONS ARE POSTED ALREADY!

Reading Assignment

* Read Section 3.2 in the notes.

Homework

* Do exercises 1-4, 6b, 7.

* Check the blog every day for new entries.

Optional material

* Fisher and Schaum's might be helpful for more examples.

10/27: In-Person Instruction. - REVISED AND FINALIZED

No additional homework today. We will review for the exam.

For the exam, I will provide a copy of this sheet to each of you.

10/30: In-Person Instruction Today! - Exam 2 over Chapter 2, Sections 3.1-3.2, and Sections 5.2-5.5. FINALIZED

I will provide a copy of this sheet to each of you.

11/1: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 11/6.

See page 230 of the text!

Reading Assignment

* Read Section 3.3 in the notes.

Homework

*
Do exercise 1 from Section 3.3.

* Check the blog every day for new entries.

Optional material

* This is worth looking up and studying in the other texts.

11/3: In-Person Instruction. - FINALIZED

The Reading and Homework assigned today are due 11/8.

Reading Assignment

* Read Section 3.4 in the notes.

Homework

* Do exercise 1abcd from Section 3.4.

* Check the blog every day for new entries.

Optional material

* Same as last class.

11/6: In-Person Instruction Today! - Residues and Laurent Series - FINALIZED

No additional homework assignment. Practice computing residues!

Optional material

* Same as last class.

11/8: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 11/13.

Reading Assignment

* Read Section 3.5 in the notes.

Homework

* Do exercises 1-9 from Section 3.5 in the notes. Compute residues by hand, and check them with Mathematica.

* Check the blog every day for new entries.

Optional material

* There are many videos about this theorem.

11/10: In-Person Instruction. - FINALIZED

Today pictures: logistic and quadratic

The Reading and Homework assigned today are due 11/15.

Reading Assignment

* Skim Section 5.6 in the notes.

Homework

* Do exercises 1, 3, 4, 6 at the end of Section 5.6 in the notes.

* Check the blog every day for new entries.

Optional material

* Available if you request them!

11/13: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 11/17.

Reading Assignment

* Read Section 3.6 in the notes.

Homework

* Do exercises 1, 2a, 2b, 4a, 5 from Section 3.6 in the notes.

* Check the blog every day for new entries.

Optional material

* Fisher has some *really* hard exercises that I could share.

11/15: In-Person Instruction Today! - Integration Practice - FINALIZED

The Reading and Homework assigned today are due 11/29.

Reading Assignment

* Skim section 5.7 in the notes.

Homework

* Do exercises 2, 3, 4 from Section 5.7, and the exercises below. In Exercise 5, \(\Lambda_n\) is the set of points that never leave the interval \([0,1]\) under iteration by \(f_n(x):= nx(1-x)\).

* How many points of least period 151 does \(f(x):= 5x(1-x)\) have?

* How many points of least period 64 does \(f(x):=5x(1-x)\) have?

* Using exercise 5 from Section 5.7, how many points of least period 151 does \(f(x):= 6x(1-x)\) have?

*
Using exercise 5 from Section 5.7, how many points of least period 64 does \(f(x):= 6x(1-x)\) have?

* Check the blog every day for new entries.

Optional material

* Nothing that you'd want to read.

11/17: In-Person Instruction. - Integration Practice - FINALIZED

No additional homework today.

11/20: No Class - Thanksgiving Break

11/22:No Class - Thanksgiving Break

11/24: No Class - Thanksgiving Break

11/27: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 12/1.

Reading Assignment

* Read Section 4.1 in the notes.

Homework

* Do exercises 1, 3, 4 from Section 4.1 in the notes.

* Check the blog every day for new entries.

Optional material

* Re-read the integration examples!

11/29: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 12/4.

Reading Assignment

* Read Section 4.2 in the notes.

Homework

* Do exercises 1, 2, 3, 5abc, 6a, 7a.

* Check the blog every day for new entries.

Optional material

* Nothing in particular.

12/1: In-Person Instruction - FINALIZED

The Reading and Homework assigned today are due 12/6.

Reading Assignment

* Skim Section 5.9 in the notes.

Homework

* No exercises for this section.

* Check the blog every day for new entries.

Optional material

* You could read the paper I published on the topic!

12/4: In-Person Instruction Today! - FINALIZED

The Reading and Homework assigned today are due 12/8.

This homework will not be collected, but the material will be on the third exam. Solutions will be posted immediately. For the third exam, you will be given a copy of this sheet. You will also be given a copy of this table of conformal mappings. Today's Mathematica File.

Reading Assignment

* Read Section 4.3 in the notes.

Homework

* Do exercises 1-7 from Section 4.3.

* Check the blog every day for new entries.

Optional material

* Both Fisher and Schaum's have tables of conformal mappings.

12/6: In-Person Instruction Today! - FINALIZED

When do you want to take the final exam? Please fill out this form!

-A video for today. Another good video. Today's Mathematica File. Today's pictures: picture1, picture2, picture3, picture4.

The Reading and Homework assigned today are due 12/11.

Reading Assignment

* Read Section 5.8 in the notes.

Homework

* No exercises for this section.

* Check the blog every day for new entries.

Optional material

* Lots of cool pictures out there!

12/8: In-Person Instruction. - Review for the third exam, which will be semi-cululative. I'll say more about exactly which topics from early in the course are on this exam, but think integration! FINALIZED

12/11: Final Exams

12/12: Final Exams

12/13: Final Exams: Our final exam is scheduled for 10:30 today. The exam will cover sections 3.3-3.6, Chapter 4, and sections 5.6.-5.7.

12/14 : WINTER BREAK BEGINS!

Template

Reading Assignment

* Read

Homework

* Do the MyMathLab assignment over today's material. You watched the videos to prepare for today's class.

* Check the blog every day for new entries.

Required Videos to View Before Class on 12/24.

* With the handout available either printed or online, watch these videos and take notes in the handout. If you have access to a printer, print a copy of the handout to use while watching the videos. If you do not have access to a printer, copy the handouts onto a piece of paper to use while watching the videos. Any questions on the videos? Ask them in the blog!

(1)

* While you are watching the videos or immediately after watching the videos, take this video quiz. You should take this quiz before our next class! This will count as a quiz. After you take the quiz, the answers should appear on the screen. You should also receive an email confirmation so you can check your answers.

* The MyMathLab assignment over these videos is officially assigned after our next class, but you should start it now so you can ask questions.

* There is an optional video assignment in MyMathLab over this material.

Optional material from the Khan Academy

* The