AMATH 383: Assignment #2 Solution
Due on Thursday, January 29, 2015
Yuan Gao 1:00pm
1
Problem 1
Right-handed snails
D Arcy Wentworth Thompson, a noted scientist of natural history, asked in his book On Growth and Form
(1917): But why, in the general run o
AMATH 383 Autumn 2016
Homework 2
Due: Thursday, Oct 13, 2016, 2:00PM in class
0. Nonlinear models
x 0 and y 0 represent populations of two different species. For the following problem,
find the equilibrium points. For each equilibrium point, find the eige
Homework 3 Solution
Problem 1
Right-handed snails
D Arcy Wentworth Thompson, a noted scientist of natural history, asked in his book On Growth and Form
(1917): But why, in the general run of shells, all the world over, in the past and in the present, one
Homework 1 Solution
Problem 1
(a)(4pts)
2
Calculate the derivative of e1/x at x = 0.
2
2
2
Solution: The derivative of e1/x is 2e1/x /x3 . The limit of 2e1/x /x3 as x 0 is 0.
(b)(4pts)
Calculate the Taylor series of ln(x) at x = 2.
Solution:
1
d2 lnx
d3 l
AMath 383, Autumn 2012
Assignment 2.
Due Thursday, Apr. 12.
Reading: Chs. 2-3.
1. Exercise 4 of Chapter 2. Please note that there is a typo in the formula in part c: An
exponent of 1 is missing. It should say
4
a
dR
=
R.
dt
4M 1/4
2. Exercise 7 of Chapter
AMATH 383 Autumn 2016
Homework 3
Due: Thursday, Oct 20, 2016, 2:00PM in class
1. Harvest Model-Allee effect
In class we discussed the logistic model with constant effort harvesting, modeled by
dN
N
= rN 1
hN,
dt
K
where N (t) was the abundance of fish,
AMATH 383 Spring 2016
Homework 2 Due Thurs Apr 14th in class
Show work for full credit! The grader will subtract points for poor presentation.
Any problem that has a Matlab component can alternatively be programmed in the software of your choice (with
the
AMATH 383: Assignment #3 Solution
Due on Thursday, February 5, 2015
Yuan Gao 1:00pm
1
AMATH 383 (Yuan Gao 1:00pm): Assignment #3 Solution
PROBLEM 1
Problem 1
Two-sex models (5pts)
Remember in the last homework you derived a population model
dN
= N (B D),
Homework 3 Solutions
k
1
Problem 1. (5 pts. total) For the reaction A
B
(a) (1 pt.) Determine the order of the reaction.
Solution:
As we did in class, take the ratio of trial 1 to trial 2:
n
Trial 1
4.0 102
k1 1n
1
:
=
,
1=
,
n = 0,
2
n
Trial 2
4.0 10
Dark Matter Astrophysics
arXiv:0907.1912v1 [astro-ph.CO] 10 Jul 2009
Guido DAmico, Marc Kamionkowski and Kris Sigurdson
Abstract These lectures are intended to provide a brief pedagogical review of dark
matter for the newcomer to the subject. We begin wit
AMATH 383 Spring 2016
Homework 3 Due Thurs Apr 21st in class
Show work for full credit! The grader will subtract points for poor presentation.
Any problem that has a Matlab component can alternatively be programmed in the software of your choice (with
the
AMATH 383 Spring 2016
Homework 1 Due Thurs Apr 7th in class
Show work for full credit! The grader will subtract points for poor presentation.
1. Getting a feel for Fermi problems: Come up with an estimate of the answer for the following problems. For each
AMATH 383 Spring 2016
Homework 0 Not graded; complete by end of first week
We will be using differential equations frequently throughout the course, so it is extremely important that you know
how to solve them! If these questions seem foreign or rusty, yo
Homework 5
The physical dynamics of a pendulum can be described as the following ODE
= asin b
where is the angle of the pendulum (the angle between its natural rest position and current position),
is the angular velocity and is the angular acceleration.
AMATH 383 Spring 2016
Homework 4 Due Thurs Apr 28th in class
Show work for full credit! The grader will subtract points for poor presentation.
Any problem that has a Matlab component can alternatively be programmed in the software of your choice (with
the
Homework 2
Financial Planning
Charles has a set of financial goals that he wants to achieve in his life, like buying a car next year, or
maintaining the standard of living after retirement, etc. In this homework were going to answer the following
question
AMATH 383 Lecture Notes
Analysis of Nonlinear 2D Autonomous
Dynamical Systems
Oct. 31st, 2013
(Covering chapter 9 from the book)
So far, we have only been looking at models where one variable changes in time. This
variable could represent a variety of thi
AMATH 383 Lecture Notes
Review
Sept. 26th, 2013
Ordinary Dierential Equations (ODEs) such as AMATH 351, is a prerequisite for AMATH 383. A standard textbook reference is Boyce & DiPrimas Elementary Dierential
Equations and Boundary Value Problems. All top
Homework 4 Solutions
AMATH 383
due 7/18/2008 by 5pm
(65 Points Possible)
Problem 1. (5 pts.) Problem 5.7.3 from the text:
If you want to put a satellite in a geosynchronous orbit (so that the satellite will always
appear to be above the same spot on earth
Homework 5 Solutions
AMATH 383
due 7/25/2008 by 5pm
(65 Points Possible)
Problem 1. (15 pts. total) Disease Spread Models, Part 1:
Which of the following are reasonable models for the spread of a disease among a
finite number of people? Let N be the numbe
Homework 1 Solutions
AMATH 383
Due Friday 6/27/2008 by 5pm
(60 PointsPossible)
Problem 1. (7 pts.)
xy 2 y 0 x2 = 0
Solution:
(a) First Order
(b) Nonlinear because of y 2
(c) This is a separable first order ODE, so first rewrite, then separate and integrat
Homework 8 Solutions
AMATH 383
due 8/15/2008 by 5pm
(55 Points Possible)
This homework is meant to be short. There are only 3 problems. At this point, you should
use more of your time to work on your final projects.
Problem 1. (25 pts. total) Blackbird Po
AMATH 383 Lecture Notes
Units and Dimensional Analysis
Nov. 21st, 2013
(Covering sections of Part 1 in Mathematical Models by Richard Haberman)
1
Introduction
Whenever we derive a continuous model for a physical, biological, chemical or other process,
it
Homework 2
AMATH 383
Due Thursday 7/3/2008 by 5pm
(80 Points Possible)
Problem 1. (10 pts. total)
2
y 0 y = x2 cos x,
x
y() = 1
(1)
(a) (5 pts.) Solve the initial value problem in (1) by hand. (Note that this is the
example from Integrating Factors, Revis
Homework 6 Solutions
AMATH 383
due 8/1/2008 by 5pm
(70 Points Possible)
Problem 1. (6 pts. total) (There is one equilibrium point for this system)
dx
= ex 1
dt
dy
= 21 yex
dt
(1)
(a) (1 pt.) Solution:
You can find the equilibrium point by solving the x-eq
Homework 7 Solutions
AMATH 383
due 8/8/2008 by 5pm
(60 Points Possible)
This homework is meant to be short. There are only 3 problems. Problems 1 and 2 have
several parts, but this is just to be sure that no one loses points for not seeing/following all
o
Homework 1
Problem 1
(a)(4pts)
2
Calculate the derivative of e1/x at x = 0.
(b)(4pts)
Calculate the Taylor series of ln(x) at x = 2.
(c)(4pts)
Calculate the partial derivative of f (x, y) = ln(xy) + xy 2 with respect to x at the point (1, 2).
Problem 2
So