# 18.01A - Fall 2010

## 18.01A/18.02A (first half) Syllabus

### Practice Final Exam (2 hours)

(The last problem is based on the 10/20 Tuesday lecture.)
(Sun. 1:15 AM : A typo in Problem 6 is now corrected (the r should be an exponent 2) --
if you printed the practice final Sat. evening instead of gazing at the awesome (used rightly, for once) evening star,
you should reprint page one or just fix the typo.)

### Practice Problems for Exam 1 with solutions

A more easily readable scan of the solutions by Jerry Orloff:

## Problem Set 3

(Sunday 10 PM): Problem 4ab on Part II has been corrected so both (a) and (b) have t=pi/2 at the start (not t=0).
A hint has been added to part (b): Calculate and simplify the integral for s using a general f(t) first, then put f(t)=1/t^p at the end.

## Problem Set 1

In addition to the textbook (Simmons, 2nd ed.), you will need the 18.01A Supplementary Notes, which can be purchased at Copy Tech, in the basement of Building 11, starting Wed. Sept.8. (These differ from the regular 18.01 Notes also on sale there by the addition of 24 pages on Probability.) You can use last year's 18.01A Supplementary Notes: this year's just improve the wording or correct a typo in a few of the exercises.

### Lecturer

Arthur Mattuck 2-241 3-4345 apm@math.mit.edu or mattuck@mit.edu Office: Tues 3-5 in 2-241.

### Recitations: Number, MW Hour, Room, Teacher, Office, MIT phone, E-mail@MATH.mit.edu, Office Hours

1. 11 8-119 Paul Hand 2-390 3-4390 hand@math Tues 12-1, Wed 6-7
2. 12 8-119 Peter Tingley 2-172 3-4470 ptingley@math Tu 10-11 AM, Wed 9-10 AM, 5:20-6:20 PM
3. 1 26-142 Chenyang Xu 2-380 3-6544 cyxu@math Wed 4-5, 7-8 PM
4. 1 8-119 Paul Hand (see above)
5. 2 26-142 Chenyang Xu (see above)
6. 2 66-154 Rafael Oliveira 2-101 rmendes@mit.edu Wed. 8-9 PM (till 9:30 if needed)
7. 2 4-257 Peter Tingley (see above)
8. 3 4-257 Peter Tingley (see above)

## Stellar

Use the Stellar website ( Stellar ) for confirming what recitation you are officially in, after Registration Day. As the information is put onto it, you can use the site to change recitation, or to get into one officially if you were never put in one by the class-scheduling computer. Later you can use it to check your scores on problem sets and exams.

You must present any one of the following. The records of all students who register for 18.01A will be checked during the first few weeks; those who do not present one of these admission criteria will have to drop back to 18.01, regardless of how they have been doing in 18.01A -- sorry. The reason is that 18.01A omits without a review most of the AB topics (roughly, all of differentiation, and elementary integration) and therefore it is fair to ask that students present evidence they have already mastered them.

1. A score of 4 or 5 on the AB Advanced Placement test, or an AB subscore of 4 or 5 on the BC test
2. An equivalent score on the A-level or the IB exam.
3. An equivalent grade in a college calculus subject with syllabus comparable to the AB syllabus. (You must present a college transcript and a copy of the syllabus.)
4. A passing grade on Part I of the M.I.T. 18.01 Advanced Placement exam, given during R/O week. A practice exam and solutions are given by the following links (a description of what it covers is given in the Part I section below them) :

## Solutions to above Practice Exam

(Adobe Acrobat -- pdf file )

# M.I.T. Advanced Placement Exam for 18.01

This exam has two parts.

Part I (90 minutes) is the Exam for Admission to 18.01A, like the practice exam given above; it covers the AB syllabus: definition of derivative, differentiation rules, implicit differentiation, derivatives of the elementary functions (including the inverse functions); standard applications (curve-sketching, max-min problems, related rates); simple antidifferentiation, including substitutions; solving separable first-order differential equations by antidifferentiation; definition of the integral as the limit of Riemann sums; evaluating definite integrals by using the fundamental theorem of calculus, applications to finding areas and volumes of revolution about the x-axis; numerical evaluation of definite integrals by the rectangular and trapezoidal rules. (This should be adequate; a more detailed description of the Calculus AB Syllabus is available on the internet.)

Part II (90 minutes, given immediately afterwards) covers some additional topics in 18.01 on the BC syllabus: linear and quadratic approximation, mean-value theorem, further techniques of antidifferentiation and applications of integration, polar coordinates, parametric equations, L'Hospital's rule, improper integrals, convergence of certain infinite series (geometric series, series whose n-th term gets small like the reciprocal of a fixed k-th power of n, where k is a positive number.)

Part II will not cover the following BC syllabus topics, since they are not included in 18.01: solving first-order differential equations graphically and numerically, second-order differential equations with constant coefficients; ratio test for infinite series.

### Note:

If you want to AP 18.01 by taking the MIT exam, you must take both parts of the exam described above, even if you satisfy one of the other admissions criteria given above for 18.01A.