Math 21 : Calculus - Spring 2008

Last updated: April 2nd, 2008.

Math 21 : Calculus - Spring 2008

This is the combined webpage for both sections. The teaching assistant, grading, office hours and such will be combined for the two sections.

Text: Stewart, Calculus: Concepts and Contexts, 3rd ed.
Instructor: Ben Lee, blee at math dot stanford dot edu (midfield at stanford dot edu), Sloan 381-C

Section 01: TTh 9:30AM-10:45AM in 380D
Section 02: TTh 11:00AM-12:15PM in McCullough 122

Teaching Assistant: Isidora Milin, milin at math dot stanford dot edu, Sloan 380-S

TA sections:

Monday: 10-10:50AM in 381U
Monday: 1:15-2:05PM in McCull 122
Wednesday: 11-11:50AM in 380F
Wednesday: 2:15-3:05PM in 300-300

You are free to go to whichever section. Isidora will answer questions and give supplemental explanations.

Office Hours:

Tuesday 1-2PM and 3:40-4:40PM Ben 381C
Wednesday 12-1PM and 5-7PM Isidora 380S
Thursday 1-2PM and 3:40-4:40PM Ben 381C

HW Grader: Grading for both classes:
Tamara Alexander, talex at stanford dot edu

I've been told that tutoring resources can be found at http://tutoring.stanford.edu.

Course diary and Homework assignments

Homework is assigned every day. Homework assigned Tuesday is due on the following Friday at 5PM. Homework assigned Thursday is due in 8 days time, the next Friday at 5PM. Homework should be turned in during class or in the manilla envelope in front of my office.

Any questions regarding homework and homework grading (late homework, missing homework) should be directed towards the homework graders (email addresses above.)

* - indicates a "challenging problem" which is "for fun."

4/1: Outline of course; Taylor series begets infinite series begets infinite sequences; definition and example of sequences and limits. HW due 4/4: 8.1: 2, 4, 10, 12, 14, 16, 18, 28*.
4/2: Convergence of sequences, MST and examples. HW due 4/11: 8.1: 24, 38a, 38c, 42, 44, 48*, 52*; 8.2: 1, 2, 4, 6, 8. For 8.2: 4, 6, 8, don't worry about graphing.
4/8: More properties of convergent sequences, BCT. Series, sigma notation, convergence, examples: geometric, harmonic, telescoping. HW due 4/11: 8.2: 10, 12, 14, 18, 24, 28, 28, 34, 36*.
4/10: Properties of series. Integral test, comparison test, p-series. HW due 4/18: 8.2: 16, 20, 22, 30, 38*, 42, 44, 49, 50-53*, 55*.
4/15: Limit comparison and Ratio tests; testing methodology; alternating series; non-positive series and absolute convergence. HW due 4/18: 8.3: 2, 4, 5, 6, 8, 10, 12, 14, 18, 20, 22, 24, 27*, 37-40*. HW due 4/25 (but use these for practice for the midterm) 8.4: 1, 2, 4, 6, 20, 22, 24.
4/17: Examples, examples; testing methodology; error terms; power series. HW due 4/25: 8.4: 8, 12, 26, 28, 30, 33, 34*; 8.3: 28, 32.
4/22: Midterm 1 (in class.)
4/24: Midterm post-morteum; remainder / error formulas.
4/29: Power series; radius of convergence; centering power series; representation as power series; differentiation and integration of power series. HW due 5/2: 8.5: 2, 4, 6, 8, 14, 16, 20, 21*, 26*, 27*, 28*; 8.6: 2, 4, 8, 12, 14.
5/1: Two different questions: where does a power series converge, and what does a power series converge to? Taylor / MacLaurin series, Taylor's inequality. HW due 5/9: 8.5: 10, 12; 8.6: 10, 12, 24, 28, 36; 8.7:4, 6, 8, 10, 12, 14.
5/6: How to use Taylor's inequality. Exponential and sin, cos are equal to their Taylor series. HW due 5/9: 8.7: 2, 18, 20, 24, 26*, 32, 34, 38, 50, 52, 56*.
5/8: More on Taylor series; estimating via Taylor polynomials. Differential equations, separable equations. HW due 5/16: 8.7: 12, 36, 40. 7.1: 2, 4; 7.3: 2, 4, 6.
5/13: More on separable differential equations. Examples: mixing, exponential growth, Newton's law of cooling, continuously compounding interest. HW due 5/16: 7.1: 10; 7.3: 10, 12, 16, 34, 36; 7.4: 2, 6, 12, 16, 18.
5/15: Logistic equation and other examples of (separable) differential equations. Graphical / numerical solutions; Euler's method. HW due 5/23: 7.2: 3-6, 8; 7.3: 22; 7.5: 6-8.
5/20: Midterm 2.
5/22: Midterm 2 post-morteum.
5/27: More on Euler's method. Solving differential equations with power series. Handout on power series solutions to differential equations. HW: handout problems 2, 4, 6, 8.

Important dates

Course Drop Deadline: Sunday, April 27th
Course Withdraw Deadline: Monday, May 26th (Memorial day)

The test dates will NOT be changed for any reason except dire emergency. I'm publishing the exam dates now, plan accordingly.

Midterm 1: Tuesday, April 22nd
Midterm 2: Tuesday, May 20th
Final: Friday, June 6th, 7-10PM, location TBA

Repeat: the test dates will NOT be changed for any reason except dire emergency. If you have special circumstances please let me know well, well in advance.

Policies

Required reading: the Honor Code.

Grades: Homework 5%, Midterm 1 25%, Midterm 2 25%, Final 45%. Homework, however, is the best way to prepare for the exams.

On test regrading: occasionally we make errors in grading. The policy is: 1) If you submit your test for regrading, we reserve the right to completely regrade your test, including deducting points; and 2) We will accept regrade requests only basically immediately after the midterms have been returned. So if they come back in class, check over it carefully in class, and if you think we've made a mistake, make a note of it on the FRONT of your test, and hand it back at the end of class. If you get your test from me in office hours or otherwise, check over it right then and there.

Here are conversations you can expect if you ask about what is going to be on the exam:

Student: What's going to be on the exam?
Teacher: Do your homework.
Student: Is XXX going to be on the exam?
Teacher: It is now.

One side of half a sheet of paper of scribbles will be allowed during exams, otherwise no notes.

No graphing calculators are allowed during the examinations. Using graphing calculators for the homework is not recommended, since you won't have them during the exams. A non-graphing calculator will be provided during the exams, but should not be necessary.

No late homework. To be lenient, your 2 lowest homework scores are dropped automatically. Cooperation is encouraged on homework, but write up your assignments on your own after discussing with other students; to do so otherwise is cheating and will be treated seriously. Repeat: No Late Homework. If you must turn in something late, contact the graders -- it is up to them whether or not to accept late homework.

Send me an email with your name, where you live, when you like to work, etc, and I'll make a web page for people looking for people to work with.

Your questions, comments and suggestions are welcome: ask in class, drop by office hours, or send email anytime.

Syllabus

The goal for the year is to finish most of the book; the goal for this quarter is chapters 8 and 7, and some additional topics.

Should I take Math 21?

If you're worried that you might not be prepared, you are welcome to ask me about it, after class or in office hours, or on email. My experience is that as long as you have time for office hours (maybe every week) and a lot of homework (maybe even a little extra), anyone can do well in this class. However if you don't have that kind of time it might be a problem if you need extra help.

If you're worried this might be too slow you can look try Math 42.

I would recommend contacting Brian White (white at math dot stanford dot edu) or Greg Brumfiel (brumfiel at math dot stanford dot edu) if you have further questions.

"Mathematics begins in bewilderment, and ends in bewilderment."