Introductory Mathematics for Engineering Applications
1st Edition
ISBN: 9781118141809
Author: Nathan Klingbeil
Publisher: WILEY
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Chapter 8, Problem 4P
Repeat problem P8-3 if
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3. Dee Pinckney is married and filing jointly. She has an adjusted gross income of
$58,120. The W-2 form shows the amount withheld as $7124. Find Dee's tax liability
and determine her tax refund or balance due.
4. Jeremy Littlefield is single and has an adjusted gross income of $152,600. His W-2
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1.5. Run Programs 1 and 2 with esin(x) replaced by (a) esin² (x) and (b) esin(x)| sin(x)||
and with uprime adjusted appropriately. What rates of convergence do you observe?
Comment.
Use Taylor Series to derive the entries to the pentadiagonal and heptadiagonal (septadiagonal?) circulant matrices
Chapter 8 Solutions
Introductory Mathematics for Engineering Applications
Ch. 8 - A model rocket is fired horn the roof of a 50 ft...Ch. 8 - Repeat problem P8-1 if H=15m, v(0)=49m/s and...Ch. 8 - The height in the vertical plane of a ball thrown...Ch. 8 - Repeat problem P8-3 if v(0)=161ft/s and...Ch. 8 - The motion of a particle moving in the horizontal...Ch. 8 - The motion of a particle moving in the horizontal...Ch. 8 - The motion of a particle in the vertical plane is...Ch. 8 - The motion of a particle in the vertical plane is...Ch. 8 - The voltage mass an inductor is given by...Ch. 8 - Repeat problem P8-9 if L=0.125H and i(t)=t2etA.
Ch. 8 - The voltage across the inductor of Fig. P8.9 is...Ch. 8 - The current flowing through a capacitor shown in...Ch. 8 - Repeat problem P8-12 if C=40F and...Ch. 8 - The current flowing through the capacitor shown in...Ch. 8 - A vehicle starts from rest at position x = 0. The...Ch. 8 - At time t=0, a vehicle located at position x=0 is...Ch. 8 - At time t=0, a moving vehicle is located at...Ch. 8 - A vehicle starling from rest at position x=0 is...Ch. 8 - A vehicle starting from rest at position x=0 is...Ch. 8 - A vehicle starling from rest at position x=0 is...Ch. 8 - The voltage across the inductor is given by...Ch. 8 - The voltage across the inductor is given in Fig....Ch. 8 - The voltage across the inductor is given in Fig....Ch. 8 - The current applied to a capacitor is given in...Ch. 8 - The current flowing through a capacitor is given...Ch. 8 - The current flowing through a 500F capacitor is...Ch. 8 - A simply supported beam is subjected to a load P...Ch. 8 - A simply supported beam is subjected to a load P...Ch. 8 - A simply supported beam is subjected to an applied...Ch. 8 - A simply supported beam is subjected to a...Ch. 8 - Consider a beam under a linear distributed load...Ch. 8 - A fixed-fixed beam ¡s subjected to a sinusoidal...Ch. 8 - Consider the buckling of a pinned-pinned column...Ch. 8 - Consider the buckling of a pinned-fixed column...Ch. 8 - Consider a beam under a uniform distributed load...Ch. 8 - A cantilever beam is pinned at the end x=L, and...Ch. 8 - Consider a shaft subjected to an applied torque T,...Ch. 8 - The velocity of a skydiver jumping from a height...Ch. 8 - A proposed highway traverses a hill-top bounded by...
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- 1.3. The dots of Output 2 lie in pairs. Why? What property of esin(x) gives rise to this behavior?arrow_forward1.6. By manipulating Taylor series, determine the constant C for an error expansion of (1.3) of the form wj−u' (xj) ~ Ch¼u (5) (x;), where u (5) denotes the fifth derivative. Based on this value of C and on the formula for u(5) (x) with u(x) = esin(x), determine the leading term in the expansion for w; - u'(x;) for u(x) = esin(x). (You will have to find maxε[-T,T] |u(5) (x)| numerically.) Modify Program 1 so that it plots the dashed line corresponding to this leading term rather than just N-4. This adjusted dashed line should fit the data almost perfectly. Plot the difference between the two on a log-log scale and verify that it shrinks at the rate O(h6).arrow_forwardDefine sinc(x) = sin(x)/x, except with the singularity removed. Differentiate sinc(x) once and twice.arrow_forward
- 1.4. Run Program 1 to N = 216 instead of 212. What happens to the plot of error vs. N? Why? Use the MATLAB commands tic and toc to generate a plot of approximately how the computation time depends on N. Is the dependence linear, quadratic, or cubic?arrow_forwardShow that the function f(x) = sin(x)/x has a removable singularity. What are the left and right handed limits?arrow_forward18.9. Let denote the boundary of the rectangle whose vertices are -2-2i, 2-21, 2+i and -2+i in the positive direction. Evaluate each of the following integrals: (a). 之一 dz, (b). dz, (b). COS 2 coz dz, dz (z+1) (d). z 2 +2 dz, (e). (c). (2z+1)zdz, z+ 1 (f). £, · [e² sin = + (2² + 3)²] dz. (2+3)2arrow_forward
- 18.10. Let f be analytic inside and on the unit circle 7. Show that, for 0<|z|< 1, f(E) f(E) 2πif(z) = --- d.arrow_forward18.4. Let f be analytic within and on a positively oriented closed contoury, and the point zo is not on y. Show that L f(z) (-20)2 dz = '(2) dz. 2-20arrow_forward18.9. Let denote the boundary of the rectangle whose vertices are -2-2i, 2-21,2+i and -2+i in the positive direction. Evaluate each of the following integrals: (a). rdz, (b). dz (b). COS 2 coz dz, (z+1) (d). 之一 z 2 +2 dz, (e). dz (c). (2z + 1)2dz, (2z+1) 1 (f). £, · [e² sin = + (2² + 3)²] dz. z (22+3)2arrow_forward
- 18.8. (a). Let be the contour z = e-≤0≤ traversed in the า -dz = 2xi. positive direction. Show that, for any real constant a, Lex dzarrow_forwardf(z) 18.7. Let f(z) = (e² + e³)/2. Evaluate dz, where y is any simple closed curve enclosing 0.arrow_forward18. If m n compute the gcd (a² + 1, a² + 1) in terms of a. [Hint: Let A„ = a² + 1 and show that A„|(Am - 2) if m > n.]arrow_forward
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