18.014. Calculus with theory. Autumn 2011.
Announcements.
- 4 Dec Problem set X is the last of the semester.
- 27 Nov Problem set IX is seriously fun.
- 16 Nov A cartoon message about Wikipedia.
- 5 Nov Problem set VIII is real (but notice the due date!).
- 28 Oct Problem set VII is accessible.
- 22 Oct Problem set VI is downloadable.
- 14 Oct Problem set V is online.
- 5 Oct Topology is hilarious. Example 1. Example 2 (warning: strong language).
- 30 Sep Problem set IV exists.
- 25 Sep Tim Gowers is writing a fascinating and funny series of blog posts for beginning math students; have a look!
- 23 Sep Problem set III has arrived.
- 18 Sep Erik Waingarten noticed that problem 11 was misstated. The corrected version is here.
- 18 Sep Problem set II is here.
- 12 Sep Prof. Vogan kindly pointed out some silly errors of mine in my questions for the first problem set. In particular, the second half of #8 was wrong, and my statement of Liouville's Theorem left out some key points. I have corrected these errors here. Since these errors may have been pretty confusing, you may have an extra week to do problems #8 and #9.
- Welcome! This semester, we'll develop rigorously the concepts of single-variable calculus, including: the axioms for the real number system; the Riemann integral; limits; continuity; differentiation; the fundamental theorems of calculus; Taylor's theorem; series and power series. This course covers essentially the same material as 18.01, but it does so from a conceptual and rigorous point of view, emphasizing careful reasoning and proofs. Here is the syllabus.
Basic information.
- Lecture times: Tuesday and Thursday, 1-2; Friday, 2-3.
- Lecture location: 2-147
- Rectation time: Monday and Wednesday, 2-3
- Recitation location: 2-147
- Office hours: Tue. 11-1 (Barwick, 2-263) and Wed. and Thu., 3-4 (Vogan, 2-243).
Textbook.
- Apostol, Tom M. Calculus, Volume 1: One-Variable Calculus, with An Introduction to Linear Algebra. Waltham, Mass: Blaisdell, 1967. ISBN: 9780471000051.
Calendar.
- Week #18 Sep. Proofs, sets, and
functions. I 2, 1.3
9 Sep. Number systems. I 3 - Week #213 Sep. Induction. I 4
15 Sep. Functions, compositions, and inverses. 1.1-7
16 Sep. Presentations. Due at 2: Problem set I. - Week #320 Sep. Integrals of step
functions. 1.8-15
22 Sep. The Riemann integral. 1.16-19
23 Sep. Properties of the integral. 1.20-27. Problem set II. - Week #4Quiz 1:
Functions and the Riemann integral.
27 Sep. Limits and continuity I. 3.1-6
29 Sep. Limits and continuity II. 3.7-9,18-20
30 Sep. Presentations. Problem set III. - Week #54 Oct. Limits and continuity III.
6 Oct. Limits and continuity IV.
7 Oct. Presentations. Problem set IV. - Week #611 Oct. Columbus Day; no classes.
13 Oct. Limits and continuity V.
14 Oct. Limits and continuity VI. - Week #718 Oct. Intermediate value
theorem. 3.10-11
20 Oct. Extreme value theorem. 3.16-17
21 Oct. Differentiation. 4.1-9 Problem set V. - Week #8Quiz 2:
Continuity and differentiation.
25 Oct. Chain rule. 4.10-12, 6.20.
27 Oct. Extreme values and mean values. 4.13-15
28 Oct. Fundamental theorems of calculus. 5.1-5 Problem set VI. - Week #91 Nov. Integration techniques I.
5.7-10
3 Nov. Integration techniques II. 6.23-25
4 Nov. Presentations. Problem set VII. - Week #108 Nov. Complex numbers I. 2.5-8
10 Nov. Complex numbers II.
11 Nov. Veteran's Day; no classes. - Week #1115 Nov. The complex exponential and trigonometric functions. 6.1-17
17 Nov. Sequences and series. 10.1-9
18 Nov. Convergence of series I. 10.11-16 Problem set VIII. - Week #1222 Nov. Convergence of series II. 10.17-24.
24 Nov. Thanksgiving; no classes.
25 Nov. Thanksgiving; no classes. - Week #13Quiz 3: Sequences and series
29 Nov. Sequences of functions and uniform convergence. 11.1-7
1 Dec. Taylor series I. 11.8-13
2 Dec. Presentations. Problem set IX. - Week #146 Dec. Taylor series II. 14-15
8 Dec. Taylor series III. 16.
9 Dec. Overflow and review. Problem set X. - Week #1513 Dec. Overflow and review.
- Final Exam20 Dec. 9 AM - 12 Noon in 2-147