ECONOMICS S-1010
HARVARD UNIVERSITY
SUMMER SCHOOL
SPRING 2016
PROBLEM SET 1 ANSWERS
due June 29, in class
Show all calculations, explain all answers (up to 5 lines), and fully label graphs. Also:
(a) always acknowledge assistance, (b) highlight final answ
APMTH 21a Problem Set 2 Solutions
Due on Friday, September 19, 2014, before 5pm
Announcements
You may attend as many or as few sections as you like, but please turn in your homework to your assigned TFs dropbox in Pierce 307B.
Problems
Read sections 9.4
APMTH 21a Problem Set 5 Solutions
Due on Friday, October 17, 2014, before 5pm
Announcements
You may attend as many or as few sections as you like, but please turn in your homework to your assigned TFs dropbox in Pierce 307B.
Problems
Read sections 11.4 -
APMTH 21a Problem Set 5
Due on Friday, October 17, 2014, before 5pm
Announcements
You may attend as many or as few sections as you like, but please turn in your homework to your assigned TFs dropbox in Pierce 307B.
Problems
Read sections 11.4 - 11.6 of t
APMTH 21a Problem Set 2
Due on Friday, September 19, 2014, before 5pm
Announcements
You may attend as many or as few sections as you like, but please turn in your homework to your assigned TFs dropbox in Pierce 307B.
Problems
Read sections 9.4 - 9.7 of t
APMTH 21a Problem Set 6 Solutions
Due on Friday, October 24, 2014, before 5pm
Announcements
This weeks problem set looks shorter than usual since it has ten problems instead of
fteen, but youll likely need to spend just as much time (if not more) on this
Miscellaneous Integrals (Answers)
Instructions: For each of the following, you should be able to perform each of the integrations and
dierentiate the result to get back to the original integrand without any errors.
1.
1
dx = 2 tan1 ( x) + C
(1 + x) x
2.
APMTH 21a Problem Set 4 Solutions
Due on Friday, October 10, 2014, before 5pm
Announcements
You may attend as many or as few sections as you like, but please turn in your homework to your assigned TFs dropbox in Pierce 307B.
Problems
Read sections 10.4 -
Applied Mathematics 21a
Mathematical Methods in the Sciences
MWF 11:00am
Northwest Labs B103
Course Description
This class discusses the extension of the single-variable calculus that you have learned to multiple
dimensions. Calculus is the mathematics of
APMTH 21a Problem Set 3 Solutions
Due on Friday, September 26, 2014, before 5pm
Announcements
You may attend as many or as few sections as you like, but please turn in your homework to your assigned TFs dropbox in Pierce 307B.
Problems
Read sections 10.1
APMTH 21a Extra Credit Project
The goal of the extra credit project is for you, in teams of 2 - 4 students, to focus in more
depth on a topic of linear algebra and/or dierential equations that we havent covered at
all or in great detail in class, to learn
APMTH 21a Problem Set 1 Solutions
Due on Friday, September 12, 2014, before 5pm, in Pierce 307B
Announcements
Sections and oce hours begin this Sunday, Sept. 7. Be sure to enter your section
preferences on the website by 5pm on Study Card Day, Sept. 9. F
APMTH 21a Problem Set 4
Due on Friday, October 10, 2014, before 5pm
Announcements
You may attend as many or as few sections as you like, but please turn in your homework to your assigned TFs dropbox in Pierce 307B.
Problems
Read sections 10.4 - 10.5, 11.
APMTH 21a Problem Set 6
Due on Friday, October 24, 2014, before 5pm
Announcements
This weeks problem set looks shorter than usual since it has ten problems instead of
fteen, but youll likely need to spend just as much time (if not more) on this problem
s
APMTH 21a Problem Set 8
Due on Friday, November 14, 2014, before 5pm
Problems
Read sections 12.7 - 12.8, 13.1 - 13.2 of the text, Multivariable Calculus: Concepts and
Contexts, 4th edition, by James Stewart. The following problems are based on ones given
APMTH 21a Problem Set 7
Due on Friday, October 31, 2014, before 5pm
Announcements
The second midterm will be on Thursday, November 6, at 7:30pm, in Geological Museum 100. Because of limited seating in Geological Museum 100, as with the last exam,
some st
APMTH 21a Problem Set 9
Due on Friday, November 21, 2014, before 5pm
Announcements
This is the last graded homework of the semester! Material from 13.6 onwards will
appear on an ungraded homework 10.
If you plan to do an extra credit project, you must s
APMTH 21a Problem Set 1
Due on Friday, September 12, 2014, before 5pm
Announcements
Sections and oce hours begin this Sunday, Sept. 7. Be sure to enter your section
preferences on the website by 5pm on Study Card Day, Sept. 9. For this week, please go
to
APMTH 21a Problem Set 3
Due on Friday, September 26, 2014, before 5pm
Announcements
You may attend as many or as few sections as you like, but please turn in your homework to your assigned TFs dropbox in Pierce 307B.
Problems
Read sections 10.1 - 10.3 of
Applied Mathematics 21b
Mathematical Methods in the Sciences
MWF 1:00pm
Northwest Labs B103
Course Description
Engineering and the sciences rely heavily on many mathematical topics and techniques. In
this course we will study the two arguably most prevale
APMTH 21b Homework 2
Due: February 13, 2013 at 5pm
1. Determine if this system has a nontrivial solution.
possible.
2x1 4x2 + 9x3
x1 2x2 + 3x3
2x1 3x2 4x3
Try to use as few row operations as
=0
=0
=0
2. Describe all solutions of Ax = 0 in parametric vecto