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 9:00 AM - 9:50 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 website for the last time Hiro taught this course. There, you will find all the class notes and homework from the previous incarnation 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 this Wednesday, January 20th, at 11:59 PM. It should take no more than 45 minutes. Names will be removed from the survey responses, but all other results of the survey will be shared.

The syllabus

Here is the course syllabus as of January 16.

Important dates

Exam I: (Thursday, Mar 4, during lab) Derivatives and applications
Exam II: (Tuesday, Mar 30, during lab) Integrals and applications
Final Exam (Friday, May 7, 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. Tue, Jan 19. Slope.
2. Wed, Jan 20. Secant lines, tangent lines, and derivatives.
   Lab worksheet for Thursday.
3. Fri, Jan 22. Derivatives.
4. Mon, Jan 25. Derivatives of polynomials.
   Lab worksheet for Tuesday.
5. Wed, Jan 27. Derivatives of sine and cosine. If you are uncomfortable with sine and cosine (and other trigonometry ideas) make sure to look at the trigonometry review material at the bottom of the course website.
   Lab worksheet for Thursday.
6. Fri, Jan 29. Chain rule.
7. Mon, Feb 1. Derivatives of exp and ln.
   Lab worksheet for Tuesday.
8. Wed, Feb 3. Derivatives of inverse functions.
   Lab worksheet for Thursday.
9. Fri, Feb 5. Product and quotient rules.
10. Mon, Feb 8. Concavity.
    Lab worksheet for Tuesday.
11. Wed, Feb 10. Local extrema.
12. Fri, Feb 12. Mean Value Theorem.
    Mon, Feb 15. Snowpacolypse.
    Wed, Feb 17. Snowpacolypse.
    Fri, Feb 19. Snowpacolypse.
    Mon, Feb 22. Snowpacolypse.
13. Wed, Feb 24. Related Rates.
14. Fri, Feb 26. Implicit Differentiation.
15. Mon, Mar 1. Exercise Day with practice problems for the midterm. Substitute (Anton Dochtermann).
16. Wed, Mar 3. Exercise Day with more practice problems for the midterm. Substitute (Cody Patterson).
    Thu, Mar 4. MIDTERM ONE during lab.
17. Fri, Mar 5. Area and Riemann sums.
18. Mon, Mar 8. Fundamental Theorem of Calculus.
    Lab worksheet for Tuesday.
19. Wed, Mar 10. Properties of integration, indefinite integrals, and u substitution
    Lab worksheet for Thursday.
20. Fri, Mar 12. Practice with u substitution.
    Spring Break Mar 15 - Mar 19.
21. Mon, Mar 22. Areas between curves.
    Lab worksheet for Tuesday.
22. Wed, Mar 24. Applications and interpretations of integration.
    Lab worksheet for Thursday.
23. Fri, Mar 26. Average Values. More practice with integration.
24. Mon, Mar 29. Practice Day for Midterm.
    Tue, Mar 31. Second midterm.
25. Wed, March 31. Introduction to limits and one-sided limits.
    Lab worksheet for Thursday.
26. Fri, Apr 2. Limit laws.
27. Mon, Apr 5. Epsilon-Delta.
    Lab worksheet for Tuesday.
28. Wed, Apr 7. Practice with epsilon-delta and some notation.
    Lab for Thursday will be a continuation of practicing the lecture notes problems.
29. Fri, Apr 9. We ended up discussing more epsilon-delta problems; see previous notes.
30. Mon, Apr 12. IVT and limit laws from continuity. (Note these are entitled "Lecture 29" because they were meant to be covered Friday.)
    Lab worksheet for Tuesday will be the same as for Thursday, so people have more opportunities to practice epsilon-delta problems.
31. Wed, Apr 14. Limits involving infinity.
    Lab worksheet for Thursday.
32. Fri, Apr 16. Limits at infinity.
33. Mon, Apr 19. Curve sketching.
    Lab worksheet for Tuesday.
34. Wed, Apr 21. L'Hopital's Rule.
    Lab worksheet for Thursday.
35. Fri, Apr 23. Exponential growth.
36. Mon, Apr 26. Taylor polynomials and more on exponential functions (see notes from last time).
    Lab worksheet for Tuesday: Practice for the final.
37. Wed, Apr 28. Taylor polynomials, continued. See notes from last class.
    Lab worksheet for Thursday is the same worksheet at Tuesday. Here is a key.
38. Fri, Apr 30. Review day. Come with questions.
39. Mon, May 3. Last day of class.

Homework

Make sure to fill out this survey by this Wednesday, January 20th, at 11:59 PM.
All homework assignments will be 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, January 22, 11:59 PM.
   Writing 1. Revisiting a topic of math you want to learn better. Deadline: Monday, January 25, 11:59 PM.
2. Extra Credit 2: Verifying some derivative rules. Deadline: Friday, January 29, 11:59 PM.
   Writing 2. Derivative of sine. Deadline: Monday, February 1, 11:59 PM.
3. Extra Credit 3: Chain rule. Deadline: Friday, February 5, 11:59 PM.
   Writing 3. Applications of derivatives. Deadline: Monday, February 8, 11:59 PM.
4. Extra Credit 4: (Ir)rational numbers. Deadline: Friday, February 12, 11:59 PM.
   Writing 4. Arctan. Deadline: Monday, February 15, 11:59 PM. (Pushed back to Friday, February 26 due to snow.)
   MIDTERM Thursday, May 4, 8 AM - 9:20 AM (during lab).
5. Writing 5: Reflecting on derivatives. Deadline: Monday, March 8, 11:59 PM.
   Extra Credit 5: Various fun things to think about. Deadline: Friday, March 12, 11:59 PM.
6. Writing 6: Your own derivative word problem. Deadline: Wednesday, March 24, 11:59 PM. (Note this is due on a Wednesday, not a Monday. This is to give you extra time to get back into school after Spring Break.)
   Extra Credit 6: Various fun things to think about. Deadline: Friday, March 26, 11:59 PM.
7. Extra Credit 7: Estimating ln(2) using Riemann sums. Deadline: Friday, April 2, 11:59 PM.
   Writing 7: Reflecting on a topic you want to learn better. Deadline: Monday, April 5, 11:59 PM.
8. Extra Credit 8: Addition law. Deadline: Friday, April 9, 11:59 PM.
   Writing 8:Epsilon-Delta for a friend. Deadline: Monday, April 12, 11:59 PM.
9. Extra Credit 9: Limits of infinity. Deadline: Friday, April 16, 11:59 PM.
   Writing 9: Intermediate value theorem. Deadline: Monday, April 19, 11:59 PM.
10. Extra Credit 10: Big fences. Deadline: Friday, April 23, 11:59 PM.
    Writing 10:Undefined. Deadline: Monday, April 26, 11:59 PM.
11. Exam Make-up (Extra Credit): Deadline: Friday, April 30, 11:59 PM.
    Extra Credit 11: Reflections. Deadline: Friday, April 30, 11:59 PM.
    Writing 11: A collection of calculus problems. Deadline: Monday, May 3, 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.