21-115: Differential Calculus
Homework: Week #12
Due at the start of class on Monday, November 8.
Read:
Section 3.1.
Exercises:
Section 3.1: #4, 5, 18, 32, 43, 53.
Due at the start of class on Wednesday, November 10.
Read:
Section 3.1
Section 3.2
Exercise

Class Notes - Sigma
Let
be a series which converges by the integral test, with
satisfying
for all
series. First approximate
given by the remainder
. We wish to estimate the actual sum
with a partial sum
of the
, with error
(1)
As shown in the text,
(2)
Le

Class Notes Harmonic
We shall show that the alternating harmonic series,
converges to
. Also, almost immediately, we will deduce that the harmonic
series
diverges to
. (In the text, the harmonic series is shown to
diverge directly, by the argument in sect

Class Notes Converges
Let
be a series which converges by the integral test, with
satisfying
for all
series. First approximate
given by the remainder
. We wish to estimate the actual sum
with a partial sum
of the
, with error
(1)
As shown in the text,
(2)

Andruy Tynyuk
21-256 Solutions to Sample Exam 2
Section A
A1. Find the partial derivatives of
h(x, y, z) =
x2 y 2 z 2 + (x2 y + y 2 z + z 2 x)2 + x3 y 3 z 3 sin(x2 y + y 2 z + z 2 x)
with respect to x, y and z.
Solution. Substituting u = xyz and v = x2 y

21-115: Differential Calculus
Homework: Week #13
Due at the start of class on Monday, November 15.
Read:
Section 3.5.
Exercises:
Section 3.5: #1, 4, 13, 23, 24, 38.
Due at the start of class on Wednesday, November 17.
Read:
Section 3.6, Implicit Different

21-115: Differential Calculus
Homework: Week #14
Due at the start of class on Monday, November 22.
Read:
Section 3.10, Related Rates.
Exercises:
Section 3.10: #7, 12, 14, 21, 30.
Due dinner time on Thursday, November 25.
Eat a lot of turkey.
Unless you ar

21-115: Differential Calculus
Homework: Week #8
Due at the start of class on Friday, October 15.
Read:
A Preview of Calculus
Section 1.1.
Exercises:
Section 1.1: #2, 5, 7, 46, 53, 58.

21-115: Differential Calculus
Homework: Week #11
Due at the start of class on Monday, November 1.
Read:
Section 2.7.
Exercises:
Section 2.7: #2, 6, 11, 19, 20.
Due at the start of class on Wednesday, November 3.
Read:
Review your notes.
Exercises:
Study f

21-115: Differential Calculus
Homework: Week #9
Due at the start of class on Monday, October 18.
Read:
Section 1.2.
Section 1.3.
Exercises:
Section 1.2: #4, 10.
Section 1.3: #3, 6, 30.
Due at the start of class on Wednesday, October 20.
Read:
Section 2.2.

21-115: Differential Calculus
Homework: Week #10
Due at the start of class on Monday, October 25.
Read:
Section 2.3, pp. 107-9.
Section 2.4.
Exercises:
Section 2.3: #35.
Section 2.4: #3, 5, 13, 16, 21.
Due at the start of class on Wednesday, October 27.
R

21-115: Differential Calculus
Homework: Week #15
Due at the start of class on Monday, November 29.
Read:
Section 3.11, Linear Approximations and Differentials.
Exercises:
Section 3.11: #15, 19, 27, 31, 40.
Due at the start of class on Wednesday, December

21-115: Differential Calculus
Exams
The course will have two exams. The First Exam will be given in class
on Wednesday November 3. The Second Exam will be given during the finals
period, on Tuesday December 14. There will be an opportunity for students to

21-256 Exam 3: Lagrange multipliers and integration
(sample)
Andruy Tynyuk
Friday 27th June, 10:3011:20am
Instructions (please read carefully)
This test is split into two sections of ve questions each:
Section A: Lagrange multipliers
Section B: Integrat