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Differential Equations: An Introduction to Modern Methods and Applications
3rd Edition
ISBN: 9781118531778
Author: James R. Brannan, William E. Boyce
Publisher: WILEY
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Textbook Question
Chapter 8.1, Problem 8P
In each of Problems 5 through 10, draw a direction field for the given differential equation and state whether you think that the solutions are converging or diverging.
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Note: The purpose of this problem below is to use computational techniques (Excelspreadsheet, Matlab, R, Python, etc.) and code the dynamic programming ideas seen inclass. Please provide the numerical answer to the questions as well as a sample of yourwork (spreadsheet, code file, etc.).We consider an N-period binomial model with the following properties: N = 60, thecurrent stock price is S0 = 1000; on each period, the stock price increases by 0.5% whenit moves up and decreases by 0.3% when it moves down. The annual interest rate on themoney market is 5%. (Notice that this model is a CRR model, which means that thebinomial tree is recombining.)(a) Find the price at time t0 = 0 of a (European) call option with strike price K = 1040and maturity T = 1 year.(b) Find the price at time t0 = 0 of a (European) put option with strike price K = 1040and maturity T = 1 year.(c) We consider now, that you are at time t5 (i.e. after 5 periods, which represents 1month later). Assume that the stock…
4. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.024.
Find the approximations Tη, Mn, and S, to the integral
computer algebra system.)
ASK YOUR TEACHER
PRACTICE ANOTHER
4 39
√
dx for n = 6 and 12. Then compute the corresponding errors ET, EM, and Es. (Round your answers to six decimal places. You may wish to use the sum command on a
n
Tn
Mn
Sp
6
12
n
ET
EM
Es
6
12
What observations can you make? In particular, what happens to the errors when n is doubled?
As n is doubled, ET and EM are decreased by a factor of about
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'
and Es is decreased by a factor of about
6. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.001.
ASK YOUR TEACHER
PRACTICE ANOTHER
Let I =
4
f(x) dx, where f is the function whose graph is shown.
= √ ² F(x
12
4
y
f
1
2
(a) Use the graph to find L2, R2 and M2.
42 =
R₂ =
M₂ =
1
x
3
4
Chapter 8 Solutions
Differential Equations: An Introduction to Modern Methods and Applications
Ch. 8.1 - In each of Problems 1 through 4 :
Find approximate...Ch. 8.1 - In each of Problems 1 through 4 :
Find approximate...Ch. 8.1 - In each of Problems 1 through 4: a) Find...Ch. 8.1 - In each of Problems 1 through 4 :
Find approximate...Ch. 8.1 - In each of Problems 5 through 10 , draw a...Ch. 8.1 - In each of Problems 5 through 10, draw a direction...Ch. 8.1 - In each of Problems 5 through 10, draw a direction...Ch. 8.1 - In each of Problems 5 through 10, draw a direction...Ch. 8.1 - In each of Problems 5 through 10 , draw a...Ch. 8.1 - In each of Problems 5 through 10, draw a direction...
Ch. 8.1 - In each of Problems 11 through 14 , use Eular’s...Ch. 8.1 - In each of Problems 11 through 14 , use Eular’s...Ch. 8.1 - In each of Problems 11 through 14 , use Eular’s...Ch. 8.1 - In each of Problems 11 through 14 , use Eular’s...Ch. 8.1 - Consider the initial value problem...Ch. 8.1 - Consider the initial value problem
Use Euler’s...Ch. 8.1 - Consider the initial value problem...Ch. 8.1 - Consider the initial value problem
Where is a...Ch. 8.1 - Consider the initial value problem y=y2t2,y(0)=,...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 1 through 6, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - In each of Problem 7 through 12, find approximate...Ch. 8.2 - Complete the calculations leading to the entries...Ch. 8.2 - Using three terms in the Taylor series given in...Ch. 8.2 - In each of Problems 15 and 16, estimate the local...Ch. 8.2 - In each of Problems 15 and 16, estimate the local...Ch. 8.2 - In each of Problems 17 and 20, obtain a formula...Ch. 8.2 - In each of Problems 17 and 20, obtain a formula...Ch. 8.2 - In each of Problems 17 and 20, obtain a formula...Ch. 8.2 - In each of Problems 17 and 20, obtain a formula...Ch. 8.2 - Consider the initial value problem y=cos5t,y(0)=1....Ch. 8.2 - Using a step size h=0.05 and the Euler method,...Ch. 8.2 - The following problem illustrates a danger that...Ch. 8.2 - The distributive law a(bc)=abac does not hold, in...Ch. 8.2 - In this section we stated that the global...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 1 through 6, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - In each of Problem 7 through 12, find approximate...Ch. 8.3 - Complete the calculation leading to the entries in...Ch. 8.3 - Confirm the results in Table 8.3.2 by executing...Ch. 8.3 - Consider the initial value problem y=t2+y2,y(0)=1....Ch. 8.3 - Consider the initial value problem
Draw a...Ch. 8.3 - In this problem, we establish that the local...Ch. 8.3 - Consider the improved Euler method for solving the...Ch. 8.3 - In each of Problems 19 and 20, use the actual...Ch. 8.3 - In each of Problems 19 and 20, use the actual...Ch. 8.3 - In each of Problems 21 through 24, carry out one...Ch. 8.3 - In each of Problems 21 through 24, carry out one...Ch. 8.3 - In each of Problems 21 through 24, carry out one...Ch. 8.3 - In each of Problems 21 through 24, carry out one...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - In each of Problems 1 through 6, determine...Ch. 8.4 - Consider the example problemwith the initial...Ch. 8.4 - Consider the initial value problem...Ch. 8.P1 - Assume that the shape of the dispensers are...Ch. 8.P1 - After viewing the results of her computer...Ch. 8.P2 - Show that Euler’s method applied to the...Ch. 8.P2 - Simulate five sample trajectories of Eq. (1) for...Ch. 8.P2 - Use the differential equation (4) to generate an...Ch. 8.P2 - Variance Reduction by Antithetic Variates. A...
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