APPM 2360: Final Exam
10:30am 1:00pm, May 3, 2014.
ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number, (3) lecture
section, (4) your instructors name, and (5) a grading table for eight questions. Text books, class notes, and
ca
APPM 2360
FINAL EXAM SOLUTIONS
FALL 2015
INSTRUCTIONS: Books, notes, and electronic devices are not permitted. Write your (1) name, (2) instructors name,
(3) recitation number on your bluebook. Work all problems. Show and explain your work clearly. Note t
APPM 2360 Exam 3
Wednesday, April 13, 2016, 7:00pm 8:30pm
ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number,
(3) recitation section, (4) your instructors name, and (5) a grading table. Books, class notes,
cell phones, and calc
APPM 2360 Final Exam Solutions
Wednesday December 17, 7:30am 10:00am
ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number, (3)
recitation section (4) your instructors name, and (5) a grading table. Text books, class notes, and
ca
Symbolic Solution for Generalized Quantum Cylindrical Wells
using Computer Algebra
Edward Yesid Villegas Pulgarin
Logic and Computation Group, Department of Physical Engineering, EAFIT University
Medellin, Antioquia, Colombia
[email protected]
Abstrac
APPM 2360 Summer 2017
Lab #1: Fish Population
1
Instructions
Labs may be done in groups of 2 or 3 (i.e., not alone). You may use any programming language
you wish but MATLAB is highly suggested. One report must be turned in for each group and must
be in P
H
(5) FYOWI 'XIZ] , yzz 323, we, tiling! that by: gay?
n  
W
H cw 7C+37+28 :1 Lemmas l'57+\)+3 +2 +239 =
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We Hum 4t VIN; Stauclnkcl cfw_bywp
f,
__mAme_z;gLLz_. Humm
lum H w 5/;
n gin 26 a m Wm
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Applied Math 5600
Bengt Fornberg
Final
December 15, 2016
7.30  10.00 pm
Return this problem set as the first part of your solution set.
Name: _

1.
The figure to the right illustrates (and
gives some facts about) the cubic Bspline for a unitspaced gri
Homework 8 Solutions APPM 4440 Fall 2016
1. (4.4.3) (a) Using f (t) = t2 and g(t) = t3 , then
f (1) f (0)
f 0 (c)
2c
2
=1= 0
= 2 = c1
g(1) g(0)
g (c)
3c
3
Thus c = 23 .
(b) On the other hand for f (1) f (0) = 1 = f 0 (c)(1 0) = 2c, we have c = 21 uniquely
Homework 9 Solutions APPM 4440 Fall 2016
1. Problem 1: Go over the statements of your definitions and theorems one more time. Then assign
yourself 10 points for this problem.
2. (6.1.1c) Since f (x) = x2 is monotone decreasing on [0, 1], the infima occur
Homework 7 Solutions APPM 4440 Fall 2016
1. (4.1.7) We assume f : R R is differentiable at x0 = 1, and the result of problem 4.1.6
(a) Let g(x) = x + 1, and x0 = 0 then
A = lim
h0
(b) Let g(t) =
f (1 + h) f (1)
f (g(h) f (g(0)
= lim
= f 0 (g(0) = f 0 (1).
Homework 1 Solutions APPM 4440 Fall 2016
Directions: Grade your homework and turn in the graded homework in class on Friday, Sept 2.
Each problem is worth 5 points, so this hw is worth 50 points total. Use a different color pen for
your grading and be sur
Homework 5 Solutions APPM 4440 Fall 2016
1. (3.1.1) These problems are very close to 2.1.1.
(a) FALSE. Consider the functions f, g : R R defined by f (x) = 1, x 0, and f (x) = 1, x <
0, and g(x) = f (x). Then f + g = 0, but neither f nor g is continuous.
Homework 6 Solutions APPM 4440 Fall 2016
1. (3.4.7) We are given f : D R and g : D R are uniformly continuous and bounded. We need
to show that the product, f g : d R is also uniformly continuous.
Proof Assume that cfw_un and cfw_vn are sequences in D w
Homework 10 Solutions APPM 4440 Fall 2016
1. Suppose a function E : R R is defined as the solution of the ODE
E 0 (x) = xE(x),
E(0) = 1.
We will assume that this equation has a solution, and that E(x) 6= 0 for all x R. For this
problem, you are to answer
Homework 2 Solutions APPM 4440 Fall 2016
Directions: Grade your homework and turn in the graded homework in class on Friday, Sept 9. (If
you need extra time, thats fine. You can put your graded homework under my office door later
on Friday or sometime on
Homework 3 Solutions APPM 4440 Fall 2016
1. (2.1.1) (Grading: 1 point each for parts a, b, and d. 2 points for part c.)
(a) FALSE. Consider the sequence an = (1)n . Since cfw_a2n = cfw_1 this converges to 1,
but cfw_an does not converge, recall Example
Homework 4 Solutions APPM 4440 Fall 2014
1. Copy the definitions from the text. There are many possible examples for each definition. (Grading: This problem is worth 5 points. If you have questions about your examples, please ask.)
2. (2.3.1)
(a) FALSE. O
APPM/MATH 4/5520
Exam II Review Problems
The exam will be on Thursday, November 10th from 6:30 to 9:00pm in FLMG 155.
Optional Extra Review Session: will be on Wednesday, November 9th from 6 to 8 pm in MUEN
E113.
1. Let X1 , X2 be a random sample from the
APPM 4/5520
Problem Set Ten (Due Wednesday, November 9th)
1. Let X1 , X2 , . . . , Xn be a random sample from the exp(rate = ) distribution. Verify that
P
S = ni=1 Xi is a sufficient statistic from the definition of sufficiency. (ie: do not use the
Factor
APPM/MATH 4/5520
Solutions to Problem Set One
c
1. (a) F (x) = 1 e(x)
on [0, ) and is 0 otherwise So,
c
f (x) = F 0 (x) = 0 [c(x)c1 e(x) ]
c)
= cc xc1 e(x)
and f is zero otherwise.
All together,
c
f (x) = cc xc1 e(x) I(0,) (x).
This is the pdf for the
Wei
APPM/MATH 4/5520
Exam I Review Problems
Exam I: Thursday, September 9th from 6:30 to 9pm in a room TBA.
Optional Extra Review Session: Wednesday, September 28th from 6 to 8 pm in a room TBA.
(Note: I reserved these rooms a long time ago but just discovere
APPM/MATH 4/5520
Problem Set Two (Due Wednesday, September 7th)
1. Suppose that U is a continuous random variable that is uniformly distributed on the interval
(1, 1). That is, U unif (1, 1).
Let > 0 and let
Y =
2
1U
1.
Find the distribution of Y . (Name
APPM 4/5520
Problem Set Seven (Due Wednesday, October 19th)
1. (a) On HW 5, Problem 1, we saw that for a random sample X1 , X2 , . . . , Xn from a distribution with continous and invertible cdf F ,
2
n
X
ln F (Xi ) 2 (2n).
i=1
Recall that the proof was ba
APPM/MATH 4/5520
Problem Set Four (Due Wednesday, September 21st)
1. Let X1 , X2 , . . . , Xn be a random sample from the P areto() distribution. (By default, the
Pareto distribution refers to the continuous Pareto distribution.)
(a) Find the distribution
APPM 4/5520
Problem Set Eight (Due Wednesday, October 26th)
1. Let X1 , X2 , . . . , Xn be a random sample from the distribution with pdf
f (x; ) =
(2) 1
x (1 x)1 I(0,1) (x).
[()]2
Find the method of moments estimator (MME) of .
2. Let X1 , X2 , . . . , X