November 30, 2015
Due at the beginning of class on Monday December 7.
Line Integrals
1. Draw the curve C and evaluate each integral.
(a)
2xy dx + (x2 + y 2 ) dy, where C is the counterclockwise oriented arc of the circle (of
radius 1 centered at the origi
September 25, 2015
1. Find the angle between the given vector and the plane:
(a) (2, 3, 5) and 2x + 3y 4 = 2z
(b) The vector parallel to the line given by the symmetric equations
4y + 2
z1
=
3
2
3x 5 =
and the plane containing the points (1, 1, 1), (1, 2,
September 28, 2015
1. Find the equations of the lines in parametric and symmetric forms.
(a) passing through (2, 3, 5) and parallel to the vector (1, 2, 7)
(b) passing through (1, 3, 5) and perpendicular to the plane 3x 5y + 2z = 9
(c) passing through the
September 18, 2015
1. Find the equation of the plane that is perpendicular to the plane 2x + 3y 4z = 1 and
intersects it along the line parallel to the vector v = (1, 2, 2). Find, also, the equation of the
line of intersection.
2. Find the intersection of
September 2t, 2015
1. For each of the following, nd the domain and graph the domain.
(a) f (x, y) =
x2 + y 2 4
(b) f (x, y) =
4 x2 y 2
(c) f (x, y) =
(d) f (x, y) =
2x+y
x+y2
2x+y
x+y2
(e) f (x, y) = sin(x + y 2)
2. For each of the following, nd 3 element
November 23, 2015
Due at the beginning of class on Wednesday after break.
Lengths of curves and areas of surfaces
1. Find the arc length of each curve. Draw each curve and describe in words its shape.
(a) r(t) = (4 + 3t, 2 2t, 5 + t), 3 t 4
(b) r(t) = (t,
November 18, 2015
Due at the beginning of class on Monday November 16.
Integrating.
1. For each of the following, nd the volume given by the integral and draw the region over
which you are integrating. Then, write the integral by switching the order of in
October 23, 2015 (Due Friday October 30)
There are lots of topics on this one. Be sure to read through and ask me questions.
1. Find the directional derivatives of the given function f at the point p in the direction v. Also,
write the spaces X and Y so t
October 7, 2015
1. For each of the functions below, nd the rst and second partial derivatives.
(a) f (x, y) =
x2 + y 2 4
(b) f (x, y) =
4 x2 y 2
(c) f (x, y) =
(d) f (x, y) =
2x+y
x+y2
2x+y
x+y2
(e) f (x, y) = sin(x + y 2)
2. Given the parameterizations b
October 19, 2015 (Due Friday October 23)
1. I dont want you to forget old material. So, here are some review problems.
(a) Find the equation of the line passing through p = (1, 2, 1, 4) and normal to the hyperplane 3x 4y + 2z + 7w = 15. (Hint: a hyperplan
November 2, 2015 (Due Friday November 6)
1. Find and use the Hessian to classify the critical points for each of the functions:
(a) f (x, y) = 5x2 + 6y 2
(b) f (x, y) = 2y 2 + x3 12x + 12y
(c) f (x, y) = x2 5y 2 + 2x + 10y
(d) f (x, y) = x3 4y 3 + 16y 2 +
Solutions to OddNumbered Problems
Chapter 3
1. a. 800 caps
b. $10
c. $20
3. b. P = $4.00
5. a. QD = 61,000 200P
b, 0, 26,000, 31,000, 36,000
c. $80
7. Supply curve shifts to right and demand curve shifts to left. The combined shifts drastically reduced th
Econ 155, Spring 2015
Name _ _
Dr. Mahua Barari Mitra
Seat # _
Reminder: Put your name and seat # on the test. Write your name on the answer sheet with
last name first and seat number again. Make sure to use a pencil.
Read all the choices carefully and se
Econ 155, Spring 2015
Name _
Dr. Mahua Barari Mitra
Seat # _
Reminder: Put your name and seat # on the test. Write your name on the answer sheet with last name
first and fill in the bubbles. Make sure to use a pencil.
Read all the choices carefully and se
ECO 155 - Principles of Macroeconomics
Dr. Barari Mitra
HANDOUT # 9
Ch. 15 - Short Run Fluctuations - Aggregate Demand and Aggregate Supply
Model
Here we will develop the model of aggregate demand and aggregate supply (AD-AS
model) to explain short run ec
ECO 155, Spring 2015
Dr. Mitra
Extra Credit Assignment 5 bonus points
To get the bonus points, you will need to do the following.
Attend one session of your choice at the Public Affairs Conference in PSU April 15-17,
2015. You can check out the schedule o
Eco 155 - Principles of Macroeconomics
Dr. Barari Mitra
HANDOUT # 10
Ch: 16: Influence of Monetary and Fiscal Policy on AD
I.
Effect of Monetary Policy on AD in Short Run
II.
Effect of Fiscal Policy on AD in Short Run
I.
Monetary Policy and AD
Question: W
Eco 155 - Principles of Macroeconomics
Dr. Mahua Barari Mitra
HANDOUT # 2 Ten Principles
Ch. 1 - Mankiw
Ten Principles ten building blocks
Ten Principles at a glance grouped into 3 categories
I.
How People Make Decisions
Principle # 1: People face tradeof
Eco 155 - Principles of Macroeconomics
Dr. Mahua Barari Mitra
HANDOUT # 1
Ch. 2 - Mankiw
Scope of economics:
i) Microeconomics: study of behavior of individual decision making units (e.g. the
individual household, the single firm, the specific industry) h
Eco 155 - Principles of Macroeconomics
Dr. Mahua Barari Mitra
HANDOUT # 2A Graphing: A Brief Overview
(Appendix to Chapter 2, Mankiw)
Graphs pictures are worth thousand words
Let us look at a few graphs as a starter.
Q: Why do economists frequently use gr
Eco 155 - Principles of Macroeconomics
Dr. Mahua Barari Mitra
HANDOUT # 4
Chapter 4: Market Forces of Supply and Demand
Question: what is a market?
Markets are institutions through which buyers and sellers of a particular good or
service interact and tran
Eco 155 - Principles of Macroeconomics
Dr. Mahua Barari Mitra
HANDOUT # 3 - PPF, Specialization and Trade (Ch. 2 & 3)
PPF (Production Possibility Frontier) Chapter 2
Scarcity gives rise to the notion of costs. Remember?
We model this cost with the help of