Course format

This class will be offered entirely online. We will meet live during class time over Zoom, where (on top of traditional lecturing activities) we will engage in group work and you will be able to ask questions. To the extent possible, instructor will upload lecture videos and class notes after every class. Office hours will take place online.

If you are taking this class, but have any concerns about accessibility--including to fast-enough internet, to technology (such as a laptop), and to a quiet location where you can attend lecture--let Hiro know as soon as possible.

Class Meetings: MWF 8:00 AM - 8:50 AM.

Lab Sessions: TuTh 8:00 AM - 9:20 AM.

Course description

This course is usually called "Calculus I." My goal in this course is to teach you brand new ways to study functions. How does the value of a given function change? (Derivatives.) Does a function approach some value in the long run? (Limits and asymptotes.) How do we compute the average value of a function, or the area under the graph of a function? (Integrals.) These are incredibly difficult topics that took hundreds of years of human history to make precise--the Greeks knew they needed these ideas (700 BC - 400 AD), Newton and Leibniz developed our modern foundations (1600s to early 1700s), and we now use the tools of calculus throughout quantitative sciences.

Beyond a fluency with the above topics, another goal of this class is for you to become familiar with mathematical thinking---questioning and understanding why definitions exist, identifying when you or another communicator is being precise or imprecise (and for what purpose), developing tastes that are rooted in practice and informed experience, exploring the mathematical landscape on your own.

Prerequisites: MATH 2417 (Precalculus) with a grade of "C" or better, ACT Mathematics score of 27 or higher, SAT Mathematics score of 580 or higher, SAT Math Section score of 600 or higher, Accuplacer College Mathematics score of 103 or higher, Compass Trigonometry score of 46 or higher.

Textbook and resources.

Math CATS, sponsored by the Department of Mathematics, provides free drop-in and by-appointment math tutoring.

While the standard reference used by calculus courses at Texas State University is the book Calculus, 8th edition, by J. Stewart, you will have no pedagogical need for this particular textbook, as there are many similar, freely available textbooks out there. You do not need to buy a textbook for this course. The following are freely available resources:

1. The course websites from when Hiro taught this course in Spring 2021 and Fall 2020. There, you will find all the class notes and homework from the previous incarnations of this course.
2. A free calculus textbook, by the openstax project.
3. The free, open textbook Calculus: Early Transcendentals written by Guichard.
4. The freely available APEX Calculus textbook.
5. A freely available online textbook, Active Calculus by Matthew Boelkins.

The survey

Fill out this survey by Wednesday, August 25th, at 11:59 PM. It should take no more than 45 minutes. As part of the survey, I will ask you for your mathematical autobiography, so you should write one out and have it ready to be copy-pasted. Names will be removed from the survey responses, but all other results of the survey will be shared with the rest of the class.

The syllabus

Here is the course syllabus as of August 19.

Important dates

Exam I: (Thursday, Oct 7, during lab) Derivatives and applications
Exam II: (Thursday, Oct 28, during lab) Integrals and applications
Final Exam (Friday, December 10, 8 AM - 10:30 AM) Derivatives, integrals, limits, and applications.

Collaboration policy

I strongly encourage all of you to collaborate. Please do so. If you do, you must indicate clearly on every assignment that you have collaborated, and indicate with whom. However, write solutions on your own. It is fine to think through problems and find solutions with each other, but when it comes to the act of writing your homework, you must do so without assistance from another. This is because the act of solving something and writing a mathematical proof are two different skills, and I want you to also hone the latter. As an extreme anti-example, copying and pasting solutions/proofs will not be tolerated. To reiterate, you may not write solutions together.

Recordings of Zoom Lectures

Can be found here.

Notes

1. Mon, Aug 23. Slope and speed.
   For Tuesday's lab, we'll be doing the exercises at the end of Monday's class notes.
2. Wed, Aug 25. Secant lines, tangent lines, and derivatives.
   Lab worksheet for Thursday.
3. Fri, Aug 27. Derivatives.
4. Mon, Aug 30. Derivatives of polynomials
   Lab worksheet for Tuesday.
5. Wed, Sep 1. Derivatives of sine and cosine
   Lab worksheet for Thursday.
6. Fri, Sep 3. Chain rule
   Mon, Sep 6. No class, Labor Day.
   Lab worksheet for Tuesday.
7. Wed, Sep 8. Derivatives of inverses--exp and ln
   Lab worksheet for Thursday.
8. Fri, Sep 10. Derivatives of inverses, II
9. Mon, Sep 13. Product and Quotient Rules
   Lab worksheet for Tuesday.
10. Wed, Sep 15. Concavity
    Lab worksheet for Thursday.
11. Fri, Sep 17. Extrema
12. Mon, Sep 20. Mean value theorem
    Lab worksheet for Tuesday.
13. Wed, Sep 22. Related rates
    Lab worksheet for Thursday.
14. Fri, Sep 24. Implicit differentiation
15. Mon, Sep 27. Logic, converses, and differentiability
    Lab worksheet for Tuesday.
16. Wed, Sep 29. Taylor polynomials
    Lab worksheet for Thursday.
17. Fri, Oct 1. Practice problems for Exam on Oct 7.
18. Mon, Oct 4. More practice problems for Exam on Oct 7.
    Lab worksheet for Tuesday coming soon.
19. Wed, Oct 6. Review and questions day. You come in with questions.
    Thu, Oct 7. Exam One.
20. Fri, Oct 8. Riemann sums.
21. Mon, Oct 11. The Fundamental Theorem of Calculus
    Lab worksheet for Tuesday.
22. Wed, Oct 13. u substitution
    Lab worksheet for Thursday.
23. Fri, Oct 15. Areas between curves.
24. Mon, Oct 18. Applications
    Lab worksheet for Tuesday.
25. Wed, Oct 20. Average value and some practice
    Lab worksheet for Thursday.
26. Fri, Oct 22. More practice
27. Mon, Oct 25. More more practice.
    Lab worksheet for Tuesday coming soon.
28. Wed, Oct 27. More more more practice.
    EXAM II (Integration) during Thursday lab.
29. Fri, Oct 29. Limits.
30. Mon, Nov 01. Limit laws
    Lab worksheet for Tuesday .
31. Wed, Nov 03. Epsilon-delta
    Lab worksheet for Thursday .
32. Fri, Nov 05. Epsilon-delta practice
33. Mon, Nov 08. Continuing with last lecture's notes.
    No new lab worksheet for Tuesday.
34. Wed, Nov 10. Guest lecture: The squeeze theorem.
    Lab worksheet for Thursday.
35. Fri, Nov 12. Guest lecture: Proving that the derivative of sin is cos.
36. Mon, Nov 15. Differentiability implies continuity
    Lab worksheet for Tuesday .
37. Wed, Nov 17. Limits involving infinity
    Lab worksheet for Thursday .
38. Fri, Nov 19. Limits at infinity
39. Mon, Nov 22. L'Hopital's Rule and curve-sketching
    Lab worksheet for Tuesday .
    No class Wednesday (Thanksgiving break).
    No lab Thursday (Thanksgiving).
    No class Friday (Thanksgiving break).
40. Mon, Nov 29. Intermediate Value Theorem
    Lab worksheet for Tuesday .
41. Wed, Dec 1. Exponential Growth.
42. Thu, Dec 2. Hiro will lecture for lab. Exponential Growth. (Last day of class. What's next?)

Homework

Make sure to fill out the survey above by the first Wednesday of the semester, at 11:59 PM.
All homework assignments will be potentially shared with your classmates, so you may remove your names from your scanned/typed/written assignments. (When you upload your homework, I will know which assignments belong to whom, thanks to Canvas.)

1. Extra Credit 1: Rational numbers. Deadline: Friday, August 27, 11:59 PM.
   Writing 1. Revisiting a topic of math you want to learn better. Deadline: Monday, August 30, 11:59 PM.
2. Extra Credit 2: Verifying a derivative law. Deadline: Friday, September 3, 11:59 PM.
   Writing 2. Derivative of sine. Deadline: Tuesday, September 7, 11:59 PM. (Delayed a day due to Labor Day.)
3. Extra Credit 3: Why the chain rule? Deadline: Friday, September 10, 11:59 PM.
   Writing 3. Examples of derivatives in real life. Deadline: Monday, September 13, 11:59 PM.
4. Extra Credit 4: (Ir)rational Deadline: Friday, September 17, 11:59 PM.
   Writing 4. arctan. Deadline: Monday, September 20, 11:59 PM.
5. Extra Credit 5: Some fun things to think about Deadline: Friday, September 24, 11:59 PM.
   Writing 5. Your problems. Deadline: Monday, September 27, 11:59 PM.
6. Extra Credit 6: Breaking the mean value theorem Deadline: Friday, October 1, 11:59 PM.
   Writing 6. Reflecting on derivatives. Deadline: Monday, October 4, 11:59 PM.
7. Extra Credit 7: Reflections on life/school Deadline: Friday, October 8, 11:59 PM.
   Writing 7. Revisiting a topic of math you want to learn better, again. Deadline: Monday, October 11, 11:59 PM.
8. Extra Credit 8: ln(2) Deadline: Friday, October 15, 11:59 PM.
   Writing 8. Integrating velocity. Deadline: Monday, October 18, 11:59 PM.
9. Extra Credit 9: A pattern Deadline: Friday, October 22, 11:59 PM.
   Writing 9. This one's different from the others Deadline: Monday, October 25, 11:59 PM.
10. Writing 10. Epsilon-delta Deadline: Monday, November 8, 11:59 PM.
    Extra Credit 10: Addition law Deadline: Friday, November 12, 11:59 PM.
    Midterm make-ups Deadline: Friday, November 19, 11:59 PM.
11. Writing 11. Some standard "calculus problems" for some review Deadline: Monday, November 15, 11:59 PM.
    Extra Credit 11: None. Just focus on Midterm make-ups Deadline: Friday, November 19, 11:59 PM.
12. Writing 12. Another standard "calculus problem" for some review Deadline: Monday, November 22, 11:59 PM.
    Extra Credit 12: None. Just focus on Midterm 2 make-ups Deadline: Wednesday, November 24, 11:59 PM.
13. Writing 13. Review of your choice Deadline: Monday, November 29, 11:59 PM.
    Extra Credit 13: Reflections Deadline: Thursday, December 2, 11:59 PM. (No late penalty for handing it in by Sunday, December 5, 11:59 PM.)

Practice Problems from past classes

1. Practice Problems on Derivatives (this topic will be on Exam I).
2. True/False Practice Problems.
3. Related Rates and Implicit Differentiation Practice Problems (this topic will be on Exam I).
4. Exam I Practice Problems from another class (these problems are courtesy of Sean Corrigan).
5. Practice Problems on Limits.
6. Practice Problems on Integrals.

Trigonometry review

1. Chapter 1.3 of Guichard. There are practice problems at the very end of the PDF file.
2. Chapter 7, Chapter 8, and Chapter 9 of the OpenStax Precalculus Book. These are links to websites, not a PDF file.