Spring 2020
Math 2471: Calculus I


Hiro Tanaka
Location: Zoom
Meeting Time: MWF 9 AM to 9:50 AM
Office Hours for Hiro: 5 PM to 6 PM on Mondays. 10 AM to 11 AM on Wednesdays.


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. For a more official description, you can consult the university catalogue.

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.


The syllabus

This is the syllabus.

The survey

Take the survey by class time on Monday, January 27.

Important dates

Thursday, March 5. Exam I: Derivatives, limits, and applications
March 16 - 29. Spring break (no classes)
Monday, March 30. Classes begin again.
Thursday, April 9. Exam II: Integrals and applications
Friday, May 8. Final Exam 8 AM - 10:30 AM.


Writing Assignments

  1. Due Thursday, January 30 at 11:59 PM. Thinking about (instantaneous) rates of change.
  2. Due Thursday, February 6 at 11:59 PM. Thinking about epsilon-delta.
  3. Due Thursday, February 13 at 11:59 PM. The derivative of sine.
  4. Due Thursday, February 20 at 11:59 PM. Thinking about epsilon-delta some more.
  5. Due Thursday, February 27 at 11:59 PM. Real world applications of finding maxima/minima.
  6. Due Thursday, March 5 at 11:59 PM. Problems.
  7. Due Thursday, March 12 at 11:59 PM. Epsilon-Delta or Delta-Epsilon?
  8. Due Thursday, April 2 at 11:59 PM. Why does u substitution work?
  9. Due Thursday, April 9 at 11:59 PM. Reflecting on a hard topic.
  10. Due Thursday, April 16 at 11:59 PM. Exponential growth.
  11. Due Thursday, April 23 at 11:59 PM. Graphs of inverse functions.
  12. Due Thursday, April 30 at 11:59 PM. Reflecting on another hard topic. (Last one!)


Extra Credit

  1. Extra Credit Writing 01: Rational and irrational numbers. Deadline: Wednesday, February 12th, at 11:59 PM.
  2. Extra Credit Quiz Prompt 01: Proving limit laws using epsilon-delta. Deadline: Tuesday, February 18th. (Read instructions carefully, and begin preparation well in advance!)
  3. Extra Credit Writing 02: Functions with repeating derivatives. Deadline: Wednesday, February 26th, at 11:59 PM.
  4. Extra Credit Writing 03: Biochemistry, or continuity questions Deadline: Wednesday, March 11, at 11:59 PM.
  5. Extra Credit Writing 04: Launch angles. Deadline: Wednesday, March 18, at 11:59 PM.
  6. Extra Credit Quizzes for Exam I. Deadline: Wednesday, April 8, at 10:30 AM.
  7. Extra Credit Writing 05: Exploring data of outbreaks. Deadline: Wednesday, April 15, at 11:59 PM.
  8. Extra Credit Writing 06: Carbon dating. Deadline: Wednesday, April 22, at 11:59 PM.
  9. Extra Credit Writing 07: Reflections on your college experience so far. Deadline: Friday, May 1, at 11:59 PM. (Last one! Note the extended deadline.)


Textbook and resources.

The standard reference used by Calculus Courses at Texas State University is the book Calculus, 8th edition, by J. Stewart. We will not follow this textbook too closely. However, if you want to see another author's take on some of these topics, you can check out the free open textbook written by Guichard.



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. Wed, Jan 22. Estimating speed.
  2. Fri, Jan 24. Difference quotients and h approaching zero.
  3. Mon, Jan 27. Introduction to limits.
  4. Wed, Jan 29. Limit laws and continuity.
  5. Fri, Jan 31. Composition law, left and right limits.
  6. Mon, Feb 3. Intermediate Value Theorem.
  7. Wed, Feb 5. Derivatives, power rule, Leibniz rule.
  8. Fri, Feb 7. Derivatives of sine and cosine.
  9. Mon, Feb 10. Chain rule.
  10. Wed, Feb 12. Exp and ln.
  11. Fri, Feb 14. Concavity, local extrema, critical points.
  12. Mon, Feb 17. Infinity and limits, I.
  13. Wed, Feb 19. Infinity and limits, II.
  14. Fri, Feb 21. Implicit Differentiation.
  15. Mon, Feb 24. Related Rates.
  16. Wed, Feb 26. Mean Value Theorem and Logic.
  17. Fri, Feb 28. L'Hopital's Rule.
  18. Mon, Mar 2. Taylor Polynomials.
  19. Wed, Mar 4. Review day.
  20. Fri, Mar 6. Riemann sums.
  21. Mon, Mar 9. The Fundamental Theorem of Calculus.
  22. Wed, Mar 11. u substitution.
  23. Fri, Mar 13. Integration by parts.
  24. Mon, Mar 30. Welcome back, and more on integration by parts.
  25. Wed, Apr 1. Applications of integrals (word problems).
  26. Fri, Apr 3. The area of a circle.
  27. Mon, Apr 6. Average values.
  28. Wed, Apr 8. Review day. (This is the day before Exam II.)
  29. Fri, Apr 10. Exponential growth and viruses.
  30. Mon, Apr 13. Logistic functions and viruses.
  31. Wed, Apr 15. Logistic distributions and viruses.
  32. Fri, Apr 17. Derivatives of inverse trig functions.
  33. Mon, Apr 20. Newton's Method.
  34. Wed, Apr 22. Newton's Method, II.
  35. Fri, Apr 24. Areas between curves.
  36. Mon, Apr 27. Accuracy of Taylor approximations.
  37. Wed, Apr 29. Differentiability implies continuity.
  38. Fri, May 1. Continuation of last lecture. (See last lecture's PDF.)
  39. Mon, May 4. Last Day of Class.
  40. Fri, May 8. Final Exam. 8 AM - 10:30 AM.


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.



Solutions to quizzes

  1. Wednesday, January 22 Quiz.
  2. Friday, January 24 Quiz.
  3. Mon, January 27 Quiz.
  4. Wed, January 29 Quiz.
  5. Fri, January 31 Quiz.
  6. Mon, Feb 3 Quiz.
  7. Wed, Feb 5 Quiz.

Practice Problems

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