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 tomato seeds of labor 0 0.33 0.2 0.5 0 0 0.5 0.2 0
Exter
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 the years we have had many request for supplying soluti
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. The EVT only holds for closed, bounded sets. 3. False.
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 areas that you need to study and try to do some problem
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Name: Linear Algebra and Multivariable Calculus Math 20 Fall 2011 Midterm 2 Please write neatly and show all your work, using proper notation. Don't hesitate to ask me questions if anything isn't clear. There are 100 points total. The point values of each
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~ = ~ , we say ~ is an eigenvector of matrix A with an a
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 say ~ is an eigenvector of matrix A with an associated ei
Harvard University, Math 20 Fall 2010, Instructor: Rachel Epstein
1
Review sheet 2
1. Vector spaces, bases, and dimension (from supplement) (a) Know the definitions of vector space, basis, and dimension. Be able to identify when something is or is not a v
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, 3, 4), Q = (2, 3, 4, 4), and R = (0, 0, 2, 0). 1. Find
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 single-variable calculus topics and exercises for you to
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 properties: 1. If v, w are in V , then v + w is in V . 2.
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 equations in two variables with that many solutions.
2
(2)
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 all x, y that satisfy the system of equations. A statio
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. Optimization without constraints (Chapter 17.4-9): (a) Know what
Object 1
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