Fall 2020
Math 2471: Calculus I



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 10 AM - 10:50 AM.

Lab Sessions: TuTh 9:30 AM - 10:50 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.

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, August 26th, 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 August 23.

Important dates

Exam I: (Thursday, October 8, 2020, during lab) Derivatives and applications
Exam II: (Tuesday, October 27, 2020, during lab) Integrals and applications
Final Exam (Monday, December 7, 2020. 11 AM - 1:30 PM) 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

These may be found here. To protect student privacy, these are only accessible via Texas State University NetID.


Notes

At the end of each day's PDF file, there are preparation problems for the next lecture's quiz.
  1. Mon, Aug 24. Slope.
    Lab worksheet for Tuesday.
  2. Wed, Aug 26. Secant lines and tangent lines.
    Lab worksheet for Thursday.
  3. Fri, Aug 28. Derivatives.
  4. Mon, Aug 31. Derivatives of polynomials.
    Lab worksheet for Tuesday.
  5. Wed, Sep 2. Derivatives of sine and cosine. Squeeze theorem.
    Lab worksheet for Thursday.
  6. Fri, Sep 4. Chain Rule.
    Mon, Sep 7. Labor Day. No Class.
    Lab worksheet for Tuesday.
  7. Wed, Sep 9. exp, log, derivatives of inverse functions.
    Lab worksheet for Thursday.
  8. Fri, Sep 11. Derivative of arcsin, and more on e.
  9. Mon, Sep 14. Product and quotient rules.
    Lab worksheet for Tuesday.
  10. Wed, Sep 16. Concavity.
    Lab worksheet for Thursday.
  11. Fri, Sep 18. Max and min
  12. Mon, Sep 21. Mean Value Theorem, I.
    Lab worksheet for Tuesday.
  13. Wed, Sep 23. Mean Value Theorem, II.
  14. Fri, Sep 25. Related Rates.
  15. Mon, Sep 28. Related Rates some more. See notes from last class.
  16. Wed, Sep 30. Implicit differentiation.
  17. Fri, Oct 2. Taylor Polynomials, I.
  18. Mon, Oct 5. Taylor Polynomials, II.
    Wed, Oct 7. Question and Answer session before Midterm.
    Midterm Exam on Thursday, Oct 8, during lab
  19. Fri, Oct 9. Area and Riemann sums.
  20. Mon, Oct 12. Integration and Fundamental Theorem of Calculus.
  21. Wed, Oct 14. Integration technique: u substitution.
  22. Fri, Oct 16. Integration technique: u substitution, II.
  23. Mon, Oct 19. Areas between curves.
  24. Wed, Oct 21. Average values, u substitution practice.
  25. Fri, Oct 23. Practice.
    Mon, Oct 26. Question and Answer session before Exam 2.
    Exam 2 on Tuesday, Oct 27, during lab
  26. Wed, Oct 28. Introduction to limits.
  27. Fri, Oct 30. Limit laws.
  28. Mon, Nov 2. Limit laws and continuity. (For notes, see last class's notes.)
  29. Wed, Nov 4 We discussed what it means for a function to be continuous. This notion is contained in Lecture 27 notes.
  30. Fri, Nov 6. Epsilon-Delta exercises. We had an exercise day and Hiro was attending a conference.
  31. Mon, Nov 9. Continuity, intermediate value theorem, puncture law.
  32. Wed, Nov 11. Limits equaling infinity.
  33. Fri, Nov 13. More limits equaling infinity. See notes from last class.
  34. Mon, Nov 16. Limits at infinity and asymptotes.
  35. Wed, Nov 18. Curve-sketching.
  36. Fri, Nov 20. L'Hopital's Rule.
  37. Mon, Nov 23. Exponential growth and modeling virus outbreaks early on
  38. Mon, Nov 30. Extreme Value Theorem. Differentiable functions are continuous. Review for Final.
  39. Wed, Dec 2. What comes next? Review for Final.
  40. Final Exam (Monday, December 7, 2020. 11 AM - 1:30 PM) Derivatives, integrals, limits, and applications.


Homework

Make sure to fill out the survey by Wednesday, August 26th, 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, August 28, 11:59 PM.
    Writing 1. Revisiting a topic of math you want to learn better. Deadline: Monday, August 31, 11:59 PM.
  2. Extra Credit 2: Proving that derivatives add/scale. Deadline: Friday, September 4, 11:59 PM.
    Writing 2. Proving that derivative of sine is cosine. Deadline: Monday, September 7, 11:59 PM.
  3. Extra Credit 3: Why the chain rule?. Deadline: Friday, September 11, 11:59 PM.
    Writing 3. Finding applications of derivatives. Deadline: Monday, September 14, 11:59 PM.
  4. Extra Credit 4: Miscellaneous questions. Deadline: Friday, September 18, 11:59 PM.
    Writing 4. Arctan. Deadline: Monday, September 21, 11:59 PM.
  5. Extra Credit 5: The power rule. Deadline: Friday, September 25, 11:59 PM.
    Writing 5. Extrema in real life. Deadline: Monday, September 28, 11:59 PM.
  6. Extra Credit 6: A puzzle. Deadline: Friday, October 2, 11:59 PM.
    Writing 6. Word Problem. Deadline: Monday, October 5, 11:59 PM.
    Midterm exam Thursday, October 8, during lab.
  7. Extra Credit 7: Reflecting on your semester so far Deadline: Friday, October 9, 11:59 PM.
    Writing 7: A reflection on derivatives Deadline: Monday, October 12, 11:59 PM.
  8. Extra Credit 8: The smallest and largest Deadline: Friday, October 16, 11:59 PM.
    Writing 8: Applications of integrals Deadline: Monday, October 19, 11:59 PM.
  9. Extra Credit 9: Applying the definition of integral to constant functions Deadline: Friday, October 23, 11:59 PM.
    Writing 9: Average values Deadline: Monday, October 26, 11:59 PM.
  10. Extra Credit 10: A limit at infinity Deadline: Friday, October 30, 11:59 PM.
    Writing 10: Epsilon-delta Deadline: Wednesday, November 4, 11:59 PM. (Deadline extended by two days.)
  11. Extra Credit 11: Addition law Deadline: Friday, November 6, 11:59 PM.
    Writing 11: Limits and epsilon-delta Deadline: Wednesday, November 11, 11:59 PM.
  12. Extra Credit 12: Limit equaling infinity Deadline: Friday, November 13, 11:59 PM.
    Writing 12: Zeno's paradoxes Deadline: Monday, November 16, 11:59 PM.
  13. Extra Credit 13: L'Hopital Deadline: Friday, November 20, 11:59 PM.
    Writing 13: A topic of need Deadline: Monday, November 23, 11:59 PM.
  14. Extra Credit 14 (last one): Book report Deadline: THURSDAY, December 3, 11:59 PM.
    Writing 14 (last one): Reflection Deadline: Monday, November 30, 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.