EBK DIFFERENTIAL EQUATIONS
5th Edition
ISBN: 9780321974235
Author: Calvis
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 7.6, Problem 21P
(a)
Program Plan Intro
Program Description: Purpose of the problem is to show that current in the
(b)
Program Plan Intro
Program Description: Purpose of the problem is to solve the differential equation
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2. calculates the trajectory r(t) and stores the coordinates for time steps At as a nested list trajectory that contains [[xe, ye,
ze], [x1, y1, z1], [x2, y2, z2], ...]. Start from time t = 0 and use a time step At = 0.01; the last data point in the
trajectory should be the time when the oscillator "hits the ground", i.e., when z(t) ≤ 0;
3. stores the time for hitting the ground (i.e., the first time t when z(t) ≤ 0) in the variable t_contact and the corresponding positions
in the variables x_contact, y_contact, and z_contact. Print
t_contact = 1.430
X_contact = 0.755
y contact = -0.380
z_contact =
(Output floating point numbers with 3 decimals using format (), e.g., "t_contact = {:.3f}" .format(t_contact).) The partial
example output above is for ze = 10.
4. calculates the average x- and y-coordinates
1
y =
Yi
N
where the x, y, are the x(t), y(t) in the trajectory and N is the number of data points that you calculated.
Store the result as a list in the variable center = [x_avg, y_avg]…
Electromagnetic Pulse propagating at oblique angle to a dielectric interface
Consider a gaussian wave pulse propagating along the z-axis from region 1 with refractive index n1 and onto a dielectric interface y = m z (for all x). To the left of this dielectric interface, the refractive index is n2.
Devise an initial value computer algorithm to determine the time evolution of the reflected and transmitted electromagnetic fields for this pulse.
e.g., n1 = 1 , n2 = 2
initial profile (t = 0, with z0 < 0) Ex = E0 exp[-a (z-z0)^2] By = n1 * Ex Choose parameters so that the pulse width is at least a fact of 8 less than the z- domain of integration ( -L < z < L).
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3. You have seen how Kirchhoff's laws were used in your lectures to obtain a 2nd
order differential equation where we solved for the current. This time we will
use an even simpler concept: principle of conservation of energy to derive the
2nd order differential equation where we will solve for the charge. Take a look
at the circuit below.
IHE
2F
In the circuit above, we have a capacitor with capacitance 2 F, an inductor of
inductance 5 H and a resistor of 32
(a) The total energy that is supplied to the resistor is
LI?
E =
2
Q?
20
where L is the inductance, I is the current, C is the capacitance and Q
is the charge.
Write down the total energy supplied E in terms of Q and t only.
OP
Remember that I =
dt
(b) Now you know that the power dissipation through a resistor is -1R.
Use the conservation of energy (energy gain rate = energy loss rate) to
derive the differential equation in terms Q and t only.
(c) Solve the differential equation for initial charge to be Qo with a initial
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Chapter 7 Solutions
EBK DIFFERENTIAL EQUATIONS
Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Prob. 5PCh. 7.1 - Prob. 6PCh. 7.1 - Prob. 7PCh. 7.1 - Prob. 8PCh. 7.1 - Prob. 9PCh. 7.1 - Prob. 10P
Ch. 7.1 - Prob. 11PCh. 7.1 - Prob. 12PCh. 7.1 - Prob. 13PCh. 7.1 - Prob. 14PCh. 7.1 - Prob. 15PCh. 7.1 - Prob. 16PCh. 7.1 - Prob. 17PCh. 7.1 - Prob. 18PCh. 7.1 - Prob. 19PCh. 7.1 - Prob. 20PCh. 7.1 - Prob. 21PCh. 7.1 - Prob. 22PCh. 7.1 - Prob. 23PCh. 7.1 - Prob. 24PCh. 7.1 - Prob. 25PCh. 7.1 - Prob. 26PCh. 7.1 - Prob. 27PCh. 7.1 - Prob. 28PCh. 7.1 - Prob. 29PCh. 7.1 - Prob. 30PCh. 7.1 - Prob. 31PCh. 7.1 - Prob. 32PCh. 7.1 - Prob. 33PCh. 7.1 - Prob. 34PCh. 7.1 - Prob. 35PCh. 7.1 - Prob. 36PCh. 7.1 - Given a0, let f(t)=1 if 0__1a,f(t)=0 if t__a....Ch. 7.1 - Given that 0ab. Let f(t)=1 if a__tb,f(t)=0 if...Ch. 7.1 - Prob. 39PCh. 7.1 - Prob. 40PCh. 7.1 - Prob. 41PCh. 7.1 - Given constants a and b. define h(t) for t__0 by...Ch. 7.2 - Prob. 1PCh. 7.2 - Prob. 2PCh. 7.2 - Prob. 3PCh. 7.2 - Prob. 4PCh. 7.2 - Prob. 5PCh. 7.2 - Prob. 6PCh. 7.2 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 10PCh. 7.2 - Prob. 11PCh. 7.2 - Prob. 12PCh. 7.2 - Prob. 13PCh. 7.2 - Prob. 14PCh. 7.2 - Prob. 15PCh. 7.2 - Prob. 16PCh. 7.2 - Prob. 17PCh. 7.2 - Prob. 18PCh. 7.2 - Prob. 19PCh. 7.2 - Prob. 20PCh. 7.2 - Prob. 21PCh. 7.2 - Prob. 22PCh. 7.2 - Prob. 23PCh. 7.2 - Prob. 24PCh. 7.2 - Prob. 25PCh. 7.2 - Prob. 26PCh. 7.2 - Prob. 27PCh. 7.2 - Prob. 28PCh. 7.2 - Prob. 29PCh. 7.2 - Prob. 30PCh. 7.2 - Prob. 31PCh. 7.2 - Prob. 32PCh. 7.2 - Prob. 33PCh. 7.2 - Prob. 34PCh. 7.2 - Prob. 35PCh. 7.2 - Prob. 36PCh. 7.2 - Prob. 37PCh. 7.3 - Prob. 1PCh. 7.3 - Prob. 2PCh. 7.3 - Prob. 3PCh. 7.3 - Prob. 4PCh. 7.3 - Prob. 5PCh. 7.3 - Prob. 6PCh. 7.3 - Prob. 7PCh. 7.3 - Prob. 8PCh. 7.3 - Prob. 9PCh. 7.3 - Prob. 10PCh. 7.3 - Prob. 11PCh. 7.3 - Prob. 12PCh. 7.3 - Prob. 13PCh. 7.3 - Prob. 14PCh. 7.3 - Prob. 15PCh. 7.3 - Prob. 16PCh. 7.3 - Prob. 17PCh. 7.3 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 23PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 27PCh. 7.3 - Prob. 28PCh. 7.3 - Prob. 29PCh. 7.3 - Prob. 30PCh. 7.3 - Prob. 31PCh. 7.3 - Prob. 32PCh. 7.3 - Prob. 33PCh. 7.3 - Prob. 34PCh. 7.3 - Prob. 35PCh. 7.3 - Prob. 36PCh. 7.3 - Prob. 37PCh. 7.3 - Prob. 38PCh. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.3 - Problems 39 and 40 illustrate Iwo types of...Ch. 7.4 - Find the convolution f(t)g(t) in Problems 1...Ch. 7.4 - Prob. 2PCh. 7.4 - Prob. 3PCh. 7.4 - Prob. 4PCh. 7.4 - Prob. 5PCh. 7.4 - Prob. 6PCh. 7.4 - Prob. 7PCh. 7.4 - Prob. 8PCh. 7.4 - Prob. 9PCh. 7.4 - Prob. 10PCh. 7.4 - Prob. 11PCh. 7.4 - Prob. 12PCh. 7.4 - Prob. 13PCh. 7.4 - Prob. 14PCh. 7.4 - Prob. 15PCh. 7.4 - Prob. 16PCh. 7.4 - Prob. 17PCh. 7.4 - Prob. 18PCh. 7.4 - Prob. 19PCh. 7.4 - Prob. 20PCh. 7.4 - Prob. 21PCh. 7.4 - Prob. 22PCh. 7.4 - Prob. 23PCh. 7.4 - Prob. 24PCh. 7.4 - Prob. 25PCh. 7.4 - Prob. 26PCh. 7.4 - Prob. 27PCh. 7.4 - Prob. 28PCh. 7.4 - Prob. 29PCh. 7.4 - Prob. 30PCh. 7.4 - Prob. 31PCh. 7.4 - Prob. 32PCh. 7.4 - Prob. 33PCh. 7.4 - Prob. 34PCh. 7.4 - Prob. 35PCh. 7.4 - Prob. 36PCh. 7.4 - Prob. 37PCh. 7.4 - Prob. 38PCh. 7.4 - Prob. 39PCh. 7.4 - Prob. 40PCh. 7.4 - Prob. 41PCh. 7.5 - Prob. 1PCh. 7.5 - Prob. 2PCh. 7.5 - Prob. 3PCh. 7.5 - Prob. 4PCh. 7.5 - Prob. 5PCh. 7.5 - Prob. 6PCh. 7.5 - Prob. 7PCh. 7.5 - Prob. 8PCh. 7.5 - Prob. 9PCh. 7.5 - Prob. 10PCh. 7.5 - Prob. 11PCh. 7.5 - Prob. 12PCh. 7.5 - Prob. 13PCh. 7.5 - Prob. 14PCh. 7.5 - Prob. 15PCh. 7.5 - Prob. 16PCh. 7.5 - Prob. 17PCh. 7.5 - Prob. 18PCh. 7.5 - Prob. 19PCh. 7.5 - Prob. 20PCh. 7.5 - Prob. 21PCh. 7.5 - Prob. 22PCh. 7.5 - Prob. 23PCh. 7.5 - Prob. 24PCh. 7.5 - Prob. 25PCh. 7.5 - Prob. 26PCh. 7.5 - Let g(t) be the staircase function of Fig. 7.5.15....Ch. 7.5 - Suppose that f(i) is a periodic function of period...Ch. 7.5 - Suppose that f(t) is the half-wave rectification...Ch. 7.5 - Let g(t)=u(tk)f(tk), where f(t) is the function of...Ch. 7.5 - Prob. 31PCh. 7.5 - Prob. 32PCh. 7.5 - Prob. 33PCh. 7.5 - Prob. 34PCh. 7.5 - Prob. 35PCh. 7.5 - Prob. 36PCh. 7.5 - Prob. 37PCh. 7.5 - Prob. 38PCh. 7.5 - Prob. 39PCh. 7.5 - Prob. 40PCh. 7.5 - Prob. 41PCh. 7.5 - Prob. 42PCh. 7.6 - Prob. 1PCh. 7.6 - Prob. 2PCh. 7.6 - Prob. 3PCh. 7.6 - Prob. 4PCh. 7.6 - Prob. 5PCh. 7.6 - Prob. 6PCh. 7.6 - Prob. 7PCh. 7.6 - Prob. 8PCh. 7.6 - Prob. 9PCh. 7.6 - Prob. 10PCh. 7.6 - Prob. 11PCh. 7.6 - Prob. 12PCh. 7.6 - Prob. 13PCh. 7.6 - Prob. 14PCh. 7.6 - This problem deals with a mass in on a spring...Ch. 7.6 - Prob. 16PCh. 7.6 - Prob. 17PCh. 7.6 - Prob. 18PCh. 7.6 - Prob. 19PCh. 7.6 - Repeat Problem 19, except suppose that the switch...Ch. 7.6 - Prob. 21PCh. 7.6 - Prob. 22P
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