Math 173, Calculus and Analytic Geometry II
Time: M/W/F 1230-120, 130-220
Location: Univ 117
Office Hours: 700-830 AM, 430-600 Monday PM, 1130-130 Tuesday.
I do not plan on using a specific textbook. All problem sets will be posted here in .pdf format and will not require you to own any specific book. The internet is an amazing resource. I advise find cheap/free references for the material. I find 2-3 good references sufficient. The lectures will be self-contained. I have not decided whether or not I will post the lectures here. It is a bit of a waste of time, giving the volumes written on the topic. Of course, my amazingly lucid and carefully crafted lectures surely warrant typing up for all of humanity to use freely.
I will cover my expectations during the first class meeting. My lectures are brisk, entertaining, and evoke confusion (by construction). My problem sets will not make you feel good. My exams will make you feel worse. Remember, grades are an oddly designed measurement that I am not convinced measure anything useful. If you focus on mastering the material, you will do well. It is more about survival. I will echo this view during the first lecture and likely weekly. Though I am a strong advocate for students, I appreciate my classes are not for everyone. There are other sections of this class not taught by me. If you dislike work or being often confused, then this might not be your cup of tea. Confusion excites me. It means that I have identified something that previously I thought I understood and now no longer do. It means that I am about to discover something amazing. Like a good work out, you should be sore from your learning experience. If you are not sore then likely you are not being pushed. My class will push you. You will be sore. When you finish my class, you should be thoroughly prepared for what comes next as it likely will be easier.
Class News:
- August 19. We decided to have three in class exams with the option of taking either all three exams into account or the best two out of three (which ever is best for your final grade).
- August 21. Set offices hours. 700-830, 430-600 Monday, 1130-130 Tuesday.
- August 23. Pset 1 posted (due September 3rd).
- August 28. Posted scans of the lectures up to present.
- August 29. Added a .pdf with the solution to Problem for on Pset 1. Please note that it is long because I wanted to show every step. As you become more advanced, the length of the solution for a problem like this would decrease.
- September 3. Pset 2 posted (due September 10th)
- September 6. Pset 2 will be due in class on September 11th opposed to in the discussion section on September 10th.
- September 7. Posted scans of lectures 5-7. We did not cover the end of lecture 7 in time. That will be the beginning of lecture 8.
- September 9. First class mid-term is on September 27 (Friday) in class.
- September 11. Class dinner party will be on October 19. Details as the date nears.
- September 12. Reposted Pset 3 (fixed error in problem 4).
- September 16. Reminder. No class this Wednesday and Friday (9-18 and 9-20).
- September 16. Problem sets are due on Wednesday in class. Exception: This week since there will be no class that day. Please turn in the Problem set on Thursday in discussion.
- September 17. Lectures 8-10 posted. Pset 4 posted.
- September 17. Practice Midterm 1 posted. REMEMBER. This is considerably more difficult than your exam. However, the format essentially identical (the real exam has slightly less problems) and the style of questions are similar.
- September 22. Lecture 11 posted.
- September 22. Some notes of proof writing posted. Thank Avi for the find.
- September 25. Formula sheet for Midterm 1 posted.
- September 26. Solution to problem 5 (c) of mid-term posted. Thank Avi please for providing it.
- September 26. I will be in my office (and free) from 8-10 AM on the Friday of the exam for last minute questions.
- September 30. Midterm 1 posted. Midterm 1 solutions posted.
- October 8. Pset 5 posted. Lecture 12 posted.
- October 17. Pset 6 posted.
- October 18. Second mid-term on Module 4 set for 10-25.
- November 3. Lectures 16 and 17 posted.
- November 3. Notes of series tests posted.
- November 3. Pset 7 posted.
- November 3. Exam 2 posted and scanned solutions posted.
- November 13. Pset 8 posted. Note the due date is Friday 11-22.
- Midterm 3 on 11-25.
- November 18. Lectures 18-20 posted.
- November 19. Avi's solutions to Pset 7 posted. The file is doc111913.pdf
- November 21. Exam 3 notes and extra problems posted.
Class Lectures:
- Lecture 0 (8-19). Coarse course overview.
- Lecture 1 (8-21). Introduction to integration theory. Motivation for integration via averaging.
- Lecture 2 (8-23). Definition of upper and lower Riemann integrals. Definition of Riemann integrable. Continuous functions are integrable.
- Lecture 3 (8-26). Mean value theorem for definite integrals. 1st and and 2nd forms of the Fundamental Theorem of Calculus.
- Lecture 4 (8-28). Change of variable formula (substitution method). Symmetric integrals. Even and odd. Area between two curves.
- Lecture 5 (8-30). Computing volumes with slices. Disk, washers, cylindrical shells, .etc.
- Lecture 6 (9-4). Arc length/lengths of curves. Review of basic Riemann sums and integrals via approximating functions by step functions.
- Lecture 7 (9-6). Logs, exponentials, hyperbolic trig functions. Integration by parts. Trig integrals.
- Lecture 8 (9-9). More trig integrals.
- Lecture 9 (9-11). More trig integrals.
- Lecture 10 (9-13). More trig integrals. Trig substitutions.
- Lecture 11 (9-16). Partial fraction decomposition. Students quite clearly do not like my notation. This angered Ben. However, he does agree the notation is complicated but such is life.
- Review for Midterm 1 (9-23).
- Review for Midterm 1 (9-25).
- Midterm 1 (9-27) in class.
- Exam data and exam review (9-30).
- Lecture 12 (10-2). Module 4 begins. Sequences. Convergence.
- Lecture 12, reloaded (10-9). Review Lecture 12.
- Lecture 14 (10-14). Continuous functions and sequences. Monotone convergence theorem.
- Lecture 15 (10-16). Avi filled in. Cauchy sequences. Subsequences.
- Lecture 15, reload (10-18). Gave a formal, intense, dry treatment of Avi's lecture.
- Review for Midterm 2 (10-21).
- Review for Midterm 2 (10-23).
- Midterm 2 (10-25).
- Exam data and exam review (10-28).
- Lecture 16 (10-30). Module 5 on series started.
- Lecture 17 (11-1). "The soul crushing lecture".
- (11-4, 11-6, 11-8). Worked series convergence problems.
- Lecture 18 (11-11). Condition convergence. Rearrangements. Start Module 6. Power series.
- Lecture 19 (11-13). Power series, Taylor series.
- Lecture 20 (11-15). Taylor series. Remainder theorem.