Honors Calculus II

Fall 2012

Roughly two-thirds of this course will be about linear algebra, i.e., algorithms and theory related to solving systems of linear equations. Another third will be about selected topics in advanced calculus, mostly sequences and series (with complex numbers). Finally, we will tie it all together to solve certain differential equations using linear algebra and series.

- Douglas Ulmer, Professor and Chair, School of Mathematics
- Office: Skiles 118B
- E-mail: ulmer@math.gatech.edu
- Web site: http://www.math.gatech.edu/~ulmer
- Office hours: Mondays 2:00 - 3:00, Thursdays 3:00 - 4:00, or by appointment. Check my web site for changes.

- Section K1: Philip Benge
- Office: Skiles 149
- E-mail: pbenge3@math.gatech.edu
- Office hours: Tuesdays and Thursdays 11:00 - 12:00, and in the Math lab (Clough 278) on Tuesdays from 12:00-1:00

- Section K2: James Scurry
- Office: Skiles 147
- E-mail: jscurry3@math.gatech.edu
- Office hours: Mondays 12:00 - 1:00 and Wednesdays 12:00 - 1:00

- Title: Honors Calculus II
- Number: 1512-K1 (82100) and 1512-K2 (81874)
- Lectures: TTh 1:35 - 2:55 in Skiles 202
- Recitations: MW 11:05 - 11:55 in Skiles 271 (K1) or Skiles 268 (K2)
- Objectives: Students will learn basic linear algebra and selected topics in calculus at a high level of sophistication. Students will also learn to present complex, multi-step solutions clearly and succinctly.
- Pace: Topics will be covered more quickly and at a higher level of sophistication than in the non-honors version of Calculus II.
- Audience: Students with strong ability, interest, and motivation to master university-level calculus and linear algebra.
- Prerequisites: A score of 5 on the AP Calculus BC exam.
- Topics: See the syllabus for a detailed list of topics.

**Homework**will be assigned regularly, collected, and graded. Normally it will be assigned on Thursday in lecture and will be due at the beginning of lecture the following Tuesday. Assignments will be posted on t-square. Part of each assignment will be done on-line (and graded instantly), part will be traditional, written homework- There will be frequent short
**quizzes**using clickers at the beginning of class. Quiz points will be part of the homework grade - There will be two
**in-class exams: on Tuesday, September 25 and Tuesday, November 6**. - The
**final exam will Tuesday, December 11, 2:50 - 5:40, in Skiles 202.**It is a cumulative exam, covering the whole course. - Grades will be based on the percentage of possible points earned. The-in class exams will each count for 20% of the grade, the final will count for 40%, and homework and quizes will count for 20%.
- Cutoff percentages for A, B, C, D are 90%, 80%, 70%, and 60% respectively.

- Text 1: “Linear Algebra” (fourth edition) by Otto Bretscher
- Text 2: “Calculus” (fourth edition) by Michael Spivak
- Clickers: You will need a ResponseCard NXT clicker from TurningPoint Technologies. See the CETL FAQ for more information about clickers.
- Most homework assignments will include an on-line component. You will have unlimited attempts to solve the problem, with immediate feedback. This routine practice will be an important way to build computational skills. The logon page for on-line homework is https://courses.webwork.maa.org/webwork2/ft-georgiainst-math1512/.

- There will be
**no make-up exams**. If an in-class exam is missed for an*acceptable and documented*reason (severe illness, death in the family, etc.), the score on that exam will be replaced with the score on the corresponding part of the final exam. (What is “corresponding” will be determined by the professor.) A test missed for unacceptable or undocumented reasons will receive a score of 0. - Arrangements for extensive absences (e.g., for extracurricular activities) must be made by the end of the first week of classes. Students requiring arrangements from the ADAPTS-Disability Services Program should consult their information page and make arrangements as soon as possible.
**Collaboration and plagiarism**: Discussing ideas and homework exercises with your peers is not only acceptable, it is a good idea. However, you must write your own solutions in your own words. Copying another's words or otherwise passing off someone else's work as your own is plagiarism and will result in a score of 0 on the entire assignment in question. Egregious cases will be dealt with more harshly.**ASK**if you have**any questions whatsoever about this**- Homework is due at the beginning of lecture, usually on Tuesdays. Late homework is strongly discouraged. It will be accepted up to 24 hours after the due time and will be assessed a 20% penalty.
- Class time will be used to discuss difficult ideas, points of confusion, etc., not to go over basics in the text. Read assignments before class and come prepared with questions.
- The Georgia Tech Honor Code applies 100% without exception. Know it and live it.
- Show some respect for your professor and your classmates---save Facebook, YouTube, and Technique for other times.

- The pace will be very fast and if you fall behind it will be very difficult to catch up.
**Keep up!** **Read**the book. The high school technique of flipping through the section looking for an example like the problem will not work in college. The key is to read**actively**. This means constantly asking yourself questions like “What is the point of this example? What idea does it illustrate?” In a theorem, “why are these assumptions being made? What happens if we relax one of them?”- It is
*very*beneficial to read the relevant parts of the text**before class**. The discussion will be much more meaningful if you already know what the key issues are. - Your goal should be
**active understanding**. This means being able to apply concepts in a new setting. The best way to develop active understanding is to do lots of problems. The texts have far more good problems than can be graded in this class. Doing them is an excellent way to study. **On writing**: The solution to an exercise or the proof of a theorem is a form of communication---it's a conversation between the reader and the author. The goal is to convince the reader that the solution or proof is correct. Doing this well involves all the same skills as writing an essay, in particular, knowing something about the audience (What can be assumed? What is “trivial” and what requires explanation?) and structuring the discussion so that it is easy to follow. Learning to write mathematics well is an important goal for this course.- Good solutions and proofs usually involve more words than formulas. The author should
**explain**what he or she is doing. I'll give some examples in class. - Working in small groups is a great idea. If you can explain the ideas in this course to your friends, then you really know them.
- The TAs and I are
*resources*. We can't learn the material for you, but we can help a lot, by explaining the concepts and clarifying subtle or tricky points. Take advantage, after all, we're why you are going to Tech, not that other, lesser place down the road. **Ask questions**, in class and in office hours. This is how we know what you need help with, and helping you is what we are trying to do.