Math 20 Midterm Review
Carolyn Stein October 4, 2011
Systems of Equations and the Leontief Model
Example: Table 1: A Farming Economy Input for 1 unit Input for 1 unit Input for 1 unit of tomatoes of t
Answers to even-numbered problems in Mathematics for Economic Analysis
Knut Sydster Peter Hammond
Preface
Mathematics for Economic Analysis, Prentice Hall, 1995 has been out for a long time, and over
Homework 11 Solutions
Math 18
Fall, 2016
1. Evaluate the given integral by converting to polar coordinates. Please draw the region of integration
in each part.
ZZ
(a) (Stewart 12.4 #8 )
(x+y) dA, wher
Homework 6 Solutions
Math 18
Fall, 2016
Quadratic Polynomials and Quadric Surfaces
widget price
1. The Wadzooks company makes widgets and gidgets. Widgets and gidgets are tools that must be used
toget
Math 18
Homework 13 Solutions
Fall, 2016
0. Read section 12.8 in Stewart up to page 885. You do not need to read the section on spherical
coordinates that follows. Write down one question or key idea.
Homework 1 Solutions
Math 18
Fall, 2016
0. Skim 9.1, pages 634635, and read 9.6, pages 673675, and 11.1, pages 738743, in Stewart. If
anything confuses you, write a question. If not, write two key ide
Math 18
Homework 2 Solutions
Fall, 2016
0. Skim 9.6, pages 675677 and read 11.1, pages 744745 in Stewart. If anything confuses you, write
a question. If not, write two key ideas that you want to remem
Math 18
Homework 3 Solutions
Fall, 2016
0. Read 11.3, pages 756763 in Stewart. You can skim the first couple of pages, but look carefully at
the figures on page 760 and make sure you understand them.
Homework 12 Solutions
Math 18
Fall, 2016
0. Read section 12.7 in Stewart up to page 877. You do not need to read the section on applications
that follows. Write down one question or key idea.
1. Evalu
Distances and Projections Answers and Solutions
1. (a) Here
compv u = |
and
projv u =
(b) Here
uv
h1, 1, 2i h 2, 3, 1i
2+3+2
3
|=|
| = |p
|= p
|v|
|h 2, 3, 1i|
4+9+1
14
uv
h1, 1, 2i h 2, 3, 1i
3
v=
h
Math 18
Homework 4 Solutions
Fall, 2016
Economic Interpretations of Derivatives and Elasticity
1. Read this article on marginalism.
(a) Using the information in the eighth paragraph (Other studies hav
Homework 5 Solutions
Math 18
Fall, 2016
Linear Approximation and Tangent Planes
0. Read 11.4, pages 770-776 in Stewart. We have not talked about differentials in class, so dont
get too bogged down wit
Harvard University
Math 20: Algebra & Multivariable
Mathematics for Social Sciences
Syllabus
Fall 2011
MWF 9:00-10:00 a.m. Science Center 507
Rachel Epstein Science Centre 525 (617) 495-2334
repstein
Proposal Essay on The Owl
Abdulla Khan
Student Number: 7715027
University of Manitoba
Course Number: FAAH 1040
Dr. Oliver Botar
February 6th 2017
This essay will be a discussion and an elaborate analy
1. True. The constraint is a circle, which is a closed, bounded set. The EVT says the functions on closed bounded sets have a max and min. 2. False. This constraint is a parabola, which is unbounded.
Math 20 Final Exam Review
Carolyn Stein Exam Date: December 13, 2011
Unconstrained Optimization
Finding Stationary Points
To find the stationary points or critical points, set fx = 0, fy = 0 and find
Name:
Math 20 Fall 2010 Final Exam
1
(1) (10 points) For a system of linear equations in 2 variables x and y, how many solutions could it have? For each case, give an example of a system of linear equ
Harvard University, Math 20 Fall 2011, Instructor: Rachel Epstein
1
Notes on Vector Spaces, Bases, and Dimension
Definition 0.1. A vector space is a set of vectors V Rn that satisfies the following pr
Harvard University, Math 20 Fall 2011, Instructor: Rachel Epstein
1
Practice & Review of Single Variable Calculus
Fall, 2011
We are about to begin our study of multi-variable calculus. Here are some s
Harvard University, Math 20 Fall 2011, Instructor: Rachel Epstein
1
Lines and Planes
September 16, 2011
Find the following line and planes, using either parametric form or an equation. Let P = (1, 2,
Math 20 Midterm 2 Review
Carolyn Stein Exam Date: November 9, 2011
Eigenvectors and Eigenvalues
What are Eigenvectors and Eigenvalues?
"Eigen" is German for "own" or "characteristic" If A~ = ~ , we sa
Math 20 Midterm 2 Review (Solutions)
Carolyn Stein Exam Date: November 9, 2011
Eigenvectors and Eigenvalues
What are Eigenvectors and Eigenvalues?
"Eigen" is German for "own" or "characteristic" If A~
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Here is a list of topics that may be covered on the first midterm, and problems to help you prepare. The intention is not that you will do all the problems, but that you will use this to identify the
Harvard University, Math 20 Fall 2011, Instructor: Rachel Epstein
1
Review for Final Exam
You should review all the material for the midterms, as well as the following new material below. 1. Optimizat