Course format

This course will be primarily instructed face-to-face. On rare occasions we may switch to an online format.

Class Meetings: MW 2 PM - 3:20 PM. Derrick Hall 331.

Lab Sessions: TuTh 2 PM - 3:20 PM. Derrick Hall 328.

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 18th, at 11:59 PM. It should take no more than 45 minutes. Names will be removed from the survey responses, but other results of the survey will be shared. Do not include private information.

The syllabus

Here is the course syllabus.

Important dates

Exam I: (Thursday, Mar 2, during lab) Derivatives and applications
Exam II: (Tuesday, April 4, during lab) Integrals and applications Note the exam has been pushed back to April. (The exam used to be Tuesday, March 28th.)
Final Exam (Mon. May 8, 2:00-4:30 PM, as dictated by the university schedule.) 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.

Notes

1. Tue, Jan 17. Slope.
2. Wed, Jan 18. Secant and tangent lines
   Lab worksheet for Thu, Jan 19. Topic: Computing derivatives by hand.
3. Mon, Jan 23. Derivatives. Derivatives of polynomials.
   Lab worksheet for Tue, Jan 24 coming soon. Topic: Derivatives of polynomials.
4. Wed, Jan 25. Drawing derivatives. Derivatives of sine and cosine.
   Lab worksheet for Thu, Jan 26 coming soon. Derivatives of sine and cosine, and of polynomials, added together.
5. Mon, Jan 30. Chain rule; review of exp and ln.
   Lab on Tue, Jan 31 was cancelled due to icy weather.
   Wed, Feb 1. Class was cancelled due to icy weather.
   Lab worksheet for Thu, Feb 2. Topic: Chain rule.
6. Mon, Feb 6. Exp, log, and inverse functions.
   Lab worksheet for Tue, Feb 7. Derivatives of exp, log, and all adding all functions we've studied.
7. Wed, Feb 8. Product and quotient rules.
   Lab worksheet for Thu, Feb 9. Practice with product and quotient rules.
8. Mon, Feb 13. Concavity, second derivatives, and local extrema.
   Lab worksheet for Tue, Feb 14. Concavity, second derivatives, and local extrema.
9. Wed, Feb 15. More exercises on concavity, second derivatives, and local extrema.
   Lab worksheet for Thu, Feb 16. More exercises on concavity, second derivatives, and local extrema.
10. Mon, Feb 20. Related rates.
    Lab worksheet for Tue, Feb 21. Related rates.
11. Wed, Feb 22. Implicit differentiation.
    Lab worksheet for Thu, Feb 23. Implicit differentiation.
12. Mon, Feb 27. Review problems for Exam One.
13. Wed, Mar 1. Review day for Exam One. No notes.
    Thu, Mar 2. Exam One.
14. Mon, Mar 7. Mean Value Theorem. Guest lecture by Dr. Lee.
15. Wed, Mar 9. Riemann sums and sigma notation.
16. Mon, Mar 20. Integration, Antiderivatives, Fundamental theorem of calculus, Indefinite integrals, applications.
    Lab worksheet for Tue, Mar 21. Integration and antiderivatives.
17. Wed, Mar 22. u substitution. Guest lecture by Dr. Lee.
    Lab worksheet for Thu, Mar 23. u substitution.
18. Mon, Mar 27. Areas between curves, average values.
    Lab for Tuesday: Start doing the practice problems for the exam.
19. Wed, Mar 29. Practice problems and review for exam.
    Lab for Thursday: More practice for the exam.
20. Mon, Apr 3. More review for exam.
    Lab for Tuesday: The Exam.
21. Wed, Apr 5. Limits, one-sided limits, and continuity.
    Lab worksheet for Thursday, April 6: Limit law practice.
22. Mon, Apr 10. Applications of continuity (Intermediate Value Theorem and Extreme Value Theorem). The derivative of absolute value.
    Lab for Tuesday: Intermediate Value Theorem and computing limits.
23. Wed, Apr 12. Limits involving infinity
    Lab for Tuesday: Asymptotes.
24. Mon, Apr 17. L'Hopital's Rule.
    Lab for Tuesday: Computing limits.
25. Wed, Apr 19. Taylor Polynomials
    Lab for Thursday: Taylor Polynomials.

Homework

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.)
Your homework assignments are posted on the Canvas website.

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.