LAB #1 CSI - Time of Death
Goal: Approximate parameters in a dierential equation using calculus; approximate the solution of a dierential equation using direction elds; solve the dierential equation;
MA 36600 FINAL EXAM SOLUTIONS
Problem 1.
(a) Sketch the direction eld for the dierential equation y = 1+y 4 . Are there any equilibrium solutions?
Explain.
(b) Sketch the direction eld for the dierent
LAB #2 Escape Velocity
Goal: Determine the initial velocity an object is shot upward from the surface of the earth so as to never return; illustrate scaling variables to simplify dierential equations.
MA 36600
GOINS
SAMPLE MIDTERM EXAM #2
This exam is to be done in 50 minutes in one continuous sitting. Collaboration is not allowed,
but you may use your own personal notes; the lecture notes posted o
MA 366 Spring 2011 Assignments
For Wednesday 1/12: Read 1.21.3. Do: p. 25: 7, 9, 16 p. 360, The answer to Exercise 8 is given in the back of the text. Substitute the given functions x1 and x2 into the
LAB #12 Linearization
Goal: Investigate the local behavior of a nonlinear system of dierential equations near its equilibrium points by linearizing the system. Required tools: Matlab routine pplane ;
LAB #10 SIR Model of a Disease
Goal: Model a disease and investigate its spread under certain conditions. Use graphs generated by pplane (and its many options) to estimate various quantities. Required
LAB #5 Population Models
Goal: Compare various population models for the population of New York over the last 200 years. Required tools: Matlab routines plot, norm, fplot; separable dierential equatio
MA 36600 MIDTERM #1 SOLUTIONS
Problem 1. For a xed real number r, solve the initial value problem
y + r y = r,
y (0) = 0.
Solution: First we nd the general solution to the dierential equation. Multipl
LAB #6 The Swaying Building
Goal: Determine a model of the swaying of a skyscraper; estimating parameters Required tools: Matlab routines pplane , ode45, plot; M-les; systems of dierential equations.
LAB #4 First Order Linear Differential Equations
Goal: Introduction to symbolic routines in Maple to solve dierential equations; dierences in linear and nonlinear dierential equations; solutions to ho
2.
dP/dt = r dP = rdt P = rt + c P(0) = c = 379 P(1) = r + c = r + 379 = 423 r = 44 P(t) = 44t + 379 P(23) = 44*23+379 = 1391
3. dP/dt = rP dP/P = rdt ln(P) = r t + c P = e^(rt+c) = ce^(rt) P(0) = c =
1.
y '=v v ' = - 0.25 y 2
1.5
1
0.5
v
0
-0.5
-1
-1.5
-2 -5 -4 -3 -2 -1 0 y 1 2 3 4 5
y '=v v ' = - 0.25 y 3 2 1 y 0 -1 -2 -3 -20 -10 0 t 10 20 30
Period: about 10s
I'd consider this a slow oscillation
LAB #7 Resonance
Goal: Observe the phenomenon of resonance; nd numerical approximations of solutions to non-autonomous systems of dierential equations. Required tools: Matlab routines pplane , ode45 ;
LAB #9 Predator-Prey Problems
Goal: Investigate the interaction of species via a particular predator-prey problem. Required tools: Matlab routines pplane , deld and fplot. Discussion You will examine
MA 36600 HOMEWORK ASSIGNMENT #6 SOLUTIONS
Problem 1. Sec. 3.2, pg. 156; prob. 31
In each of Problems 15 through 18 nd the Wronskian of two solutions of the given dierential equation
without solving th
MA 36600 HOMEWORK ASSIGNMENT #5 SOLUTIONS
Problem 1. Sec. 3.1, pg. 144; prob. 21
Solve the initial value problem y y 2 y = 0, y (0) = , y (0) = 2. Then nd so that the solution
approaches zero as t .
S
MA 36600 HOMEWORK ASSIGNMENT #4 SOLUTIONS
Problem 1. Sec. 2.7, pg. 110; prob. 8
In each of Problems 5 through 10 draw a direction eld for the given dierential equation and state
whether you think that
MA 36600 HOMEWORK ASSIGNMENT #3 SOLUTIONS
Problem 1. Sec. 2.5, pg. 88; prob. 3
Problems 1 through 6 involve equations of the form dy/dt = f (y ). In each problem sketch the graph of
f (y ) versus y ,
MA 36600 HOMEWORK ASSIGNMENT #9 SOLUTIONS
Problem 1. Sec. 7.1, pg. 359; prob. 7
Systems of rst order equations can sometimes be transformed into a single equation of higher order.
Consider the system
Spring 2014
MA 266
Study Guide - Exam # 1
(1) Special Types of First Order Equations
I
dy
+ p(t)y = g(t)
dt
First Order Linear Equation (FOL):
Method of Solution :
y=
1
(t)
[
]
II Separable Equation (
Undetermined Coefficients
Method to find a particular solution yp (t) to a linear nonhomogeneous equation with constant coefficients
L[y] = g(t), where g(t) has a very special form.
2nd Order Nonhomog