MAE 305
Engineering Mathematics Fall 2005
Mikko Haataja
MIDTERM EXAM #1 11:00am-11:50 Friday, October 28 A single hand-written sheet and a pocket calculator are allowed. 3 problems; 20 points each. Please hand in this question sheet at the end of
Chapter 3: Modern portfolio theory
Self test questions
1. The disadvantage(s) of using variance as risk measure is(are):
(a) It ignores higher moments (skewness)
(b) It gives equal weight to upward and downward deviations from the expectation
(c) It can b
Math 308 Differential Equations, Fall 2003
Exercise Set 3 Solutions
2.5/ 3.
0.6
f(y)
0.4
0.2
0
0.5
1
0.2
2
1.5
y
0.4
0.6
The equilibrium points are y = 0, y = 1 and y = 2. y = 0 is unstable; y = 1 is asymptotically stable; and
y = 2 is unstable.
2.5/ 4.
3
Calculus IV - HW 4
Due 7/20
Section 3.7
1. (Problems 2,3 from B&D) For each of the following, determine 0 , R, and to write
the given expression in the form u = R cos(0 t ).
(a) u = cos(t) +
3 sin(t)
(b) u = 4 cos(3t) 2 sin(3t)
Solution:
(a) q
We can imme
CHAPTER 18
18.1 RISK-ADJUSTED RETURNS
Performance Evaluation
and Active Portfolio
Management
Introduction
Complicated subject
Theoretically correct measures are difficult to
construct
Different statistics or measures are appropriate
for different types of
Technische Universitat M
unchen
Institut f
ur Informatik
Dr. Miriam Mehl
Dr. Michael Bader
WT 2004/2005
November 12, 2004
Introduction to Scientific Computing
Exercise 2: Harvesting a renewable resource Solution
Suppose that the population p(t) of a certa
Math 266, Practice Midterm 2
Part I: Multiple Choice (5 points) each. For each of the following questions
circle the letter of the correct answer from among the choices given. (No partial
credit.)
1. Find the general solution of the equation y 00 2y 0 + 2
The Journal of Portfolio Management 1997.23.2:45-54. Downloaded from www.iijournals.com by Teresa Lo on 08/09/14.
It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permis
Math 201 (Fall 2009)
Differential Equations
Solution #3
1. Find the particular solution of the following differential equation by variation of parameter
(a) y 00 + y = csc t
(b) t2 y 00 + ty 0 y = t ln t,
t>0
Solution:
(a) The corresponding homogeneous eq
MAE 305 Ordinary Differential Equations, Fall 2005
Midterm Exam #2
r r rt x = e
(a)
H ( s) = a a 1 1 = 2- 2 2 s 2 (s 2 + a 2 ) as a s + a2
(
t t r A - rI = 0
t 1 - sin(at ) a a2
)
h (t ) =
(b)
s 2Y ( s ) - sY ( s ) - 2Y ( s ) =
1 s+2
Y ( s
Please report typos to LM (20) 1. Solve the following initial value problem: z - tan(x)z = sec(x) The integrating factor is (x) = e Thus the equation is reduced to
- tan(x)dx
Page
1
;
z(0) =
= eln(cos(x) = cos(x)
d (cos(x) z) = 1 dx z= x+c cos
Name: (20) 1. Solve the following initial value problem: z - sin(x)z = x2 The Integrating factor is : (x) = e- therefore the equation can be written as d ecos(x) z = x2 ecos(x) dx and integrating we obtain: ecos(x) z = Hence z = e-cos(x) but z(0) = 1
MAE 305
Engineering Mathematics I
Princeton University
Tips on the Second Mid-Term to be held on
November 26, 1997
PMI lecture room, 11:00AM
1. The Second Mid-Term covers Chapter 9 (nonlinear dierential equations and stability), Chapter 6 (Laplace Transfo
MAE 305
Engineering Mathematics I
Princeton University
Second Mid-Term, Closed-book, 50 minutes
November 27, 1996
State your strategy of attack in English whenever appropriate.
1. Give succinct answers.
a. What is meant by an ODE system is autonomous? (5
MAE 305
Engineering Mathematics I
Princeton University
Assignment # 1
September 12, 1997
Due on Friday, 2PM, September 19, 1997
1. Teaching Sta. Professor Harvey Lam is the lecturer, supported by
six TAs. Outside my oce at D302c Equad, there are three MAE
MAE 305
Engineering Mathematics I
Mid-Term, Fall 1996
50 minutes, closed book.
1. Given an ODE for a single dependent variable:
(a) What is the order of the ODE? (5 points)
(b) How to identify it as linear, nonlinear, or quasi-linear? (5
points)
(c) For a
MAE 305
Engineering Mathematics I
Princeton University
First Mid-Term, Closed-book, 50 minutes
October 24, 1997
The approximate number of minutes you should spend on each
problem should be about half the number of points allocated to
that problem.
Do the
MAE 305
Engineering Mathematics I
Princeton University
Final Exam, Closed-book, 2 hours and 50 minutes
January 21, 1997
It is a good idea to rst look through all the questions, and do the easy
ones rst, the harder ones later. Whenever appropriate, always
MAE 305
Engineering Mathematics I
Princeton University
Tips on the FINAL EXAM to be held on
January 20, 1998
CS 104, 1:30PM
Please arrive about 1:20PM so that you can do the course evaluations just
before the exam. Thanks.
The best preparation for the nal