Problem Set 3 Calculus 1
Abdullah Khalid, Hassan Bukhari
December 3, 2010
Thomas Calculus, Exercise 2.6
1. The function is not continuous at x = 2 because the function is not dened at x = 2. Hence the function is not continuous on the internal [-1,3]. 2.
The Analysis and Design of Linear Circuits
5
5.1
Seventh Edition
Signal Waveforms
Exercise Solutions
Exercise 51. Write an expression using unit step functions for the waveform in Figure 56.
The signal has a positive transition with a magnitude of 10 at t
The Analysis and Design of Linear Circuits
14
14.1
Seventh Edition
Active Filter Design
Exercise Solutions
Exercise 141. Develop a second-order low-pass transfer function with a corner frequency of 50 rad/s, a
dc gain of 2, and a gain of 4 at the corner f
The Analysis and Design of Linear Circuits
7
7.1
Seventh Edition
First- and Second-Order Circuits
Exercise Solutions
Exercise 71. Find the time constant TC for circuit C3 in Figure 74.
For an RL parallel circuit, the time constant is the equivalent induct
The Analysis and Design of Linear Circuits
13
13.1
Seventh Edition
Fourier Analysis
Exercise Solutions
Exercise 131. Find the Fourier coecients for the rectangular pulse wave in Figure 131.
Compute each coecient.
a0 =
an =
bn =
1
T0
2
T0
2
T0
T0 /2
f (t)d
The Analysis and Design of Linear Circuits
16
16.1
Seventh Edition
AC Power Systems
Exercise Solutions
Exercise 161. Using the reference marks in Figure 161, calculate the average and reactive power for the
following voltages and currents.
(a). v(t) = 168
The Analysis and Design of Linear Circuits
4
4.1
Seventh Edition
Active Circuits
Exercise Solutions
Exercise 41. Find the output vO in terms of the input vS in the circuit in Figure 45.
Apply Ohms law to compute the source current ix .
ix =
vS
RS + RP
App
The Analysis and Design of Linear Circuits
8
8.1
Seventh Edition
Sinusoidal Steady-State Response
Exercise Solutions
Exercise 81. Convert the following sinusoids to phasors in polar and rectangular form:
(a). v(t) = 20 cos(150t 60 ) V
By inspection, in po
The Analysis and Design of Linear Circuits
6
6.1
Seventh Edition
Capacitance and Inductance
Exercise Solutions
Exercise 61. A 1-F capacitor has no voltage across it at t = 0. A current owing through the capacitor
is given as iC = 2u(t) 3u(t 2) + u(t 4)A.
The Analysis and Design of Linear Circuits
1
Seventh Edition
Introduction
1.1
Exercise Solutions
Exercise 11. Given the pattern in the statement 1 k = 1 kilohm = 1 103 ohms, ll in the blanks in
the following statements using the standard decimal prexes.
(
The Analysis and Design of Linear Circuits
3
3.1
Seventh Edition
Circuit Analysis Techniques
Exercise Solutions
Exercise 31. The reference node and node voltages in the bridge circuit of Figure 33 are vA = 5 V,
vB = 10 V, and vC = 3 V. Find the element vo
The Analysis and Design of Linear Circuits
2
2.1
Seventh Edition
Basic Circuit Analysis
Exercise Solutions
Exercise 21. A 6-V lantern battery powers a light bulb that draws 3 mA of current. What is the resistance
of the lamp? How much power does the lante
1
C+ FUNDAMENTALS
1.1 OBJECT ORIENTED PROGRAMMING PARADIGM
Object oriented programming (oops) treats data as a critical element
in the program development and does not allow it to flow freely around the
system. It ties data more closely to the function th
1
CONTINUOUS-TIME FOURIER SERIES
Professor Andrew E. Yagle, EECS 206 Instructor, Fall 2005
Dept. of EECS, The University of Michigan, Ann Arbor, MI 48109-2122
I. Abstract
The purpose of this document is to introduce EECS 206 students to the continuous-tim
FOURIER SERIES
Continuous-Time Signal Analysis
function) and its harmonics. The magnitudes of
these spikes are the Fourier coefficients. This
series of components are called the wave
spectrum.
The Fourier series is a method of expressing
most periodic, ti
The Analysis and Design of Linear Circuits
9
9.1
Seventh Edition
Laplace Transforms
Exercise Solutions
Exercise 91. Find the Laplace transform of v(t) = 7u(t) V.
Apply the denition of a Laplace transform.
7u(t)est dt
V (s) =
0
=
0
7est dt
7est
s
=
0
=
7
7
The Analysis and Design of Linear Circuits
11
11.1
Seventh Edition
Network Functions
Exercise Solutions
Exercise 111. The network function for a circuit is
T (s) =
10s
s + 100
Find the zero-state response v2 (t) when the input waveform is v1 (t) = cos(50t
The Analysis and Design of Linear Circuits
17
17.1
Seventh Edition
Two-Port Networks
Exercise Solutions
Exercise 171. Find the impedance parameters of the circuit in Figure 173.
Let port 2 have an open circuit so that I2 = 0. Solve for z11 and z21 .
z11 =
The Analysis and Design of Linear Circuits
10
10.1
Seventh Edition
s-Domain Circuit Analysis
Exercise Solutions
Exercise 101. Transform the circuit of Figure 107(a) into the s domain and solve for the voltage vC (t)
if vS (t) = VA et u(t) V and vC (0) = V
The Analysis and Design of Linear Circuits
12
12.1
Seventh Edition
Frequency Response
Exercise Solutions
Exercise 121. A transfer function has a passband gain of 25. At a particular frequency in its stopband,
the gain of the transfer function is only 0.00
Series and Parallel Combinations
Objective of Lecture
Explain how voltage sources in series may be
combined.
Explain how current sources in parallel may be
combined.
Explain under what conditions voltage sources in
parallel and current sources in serie
University of Engineering and Technology Lahore Department of Electrical Engineering
Calculus I
Problem Set #7 R eading: Due date: December 30, 2010
Thomass Calculus Sections 4.4 (till Theorem 5), 4.5, 4.6. Spivak Chapter 13 (pages 250-259)
1. Assume tha
[1] A 5 cm tall object is located 20 cm to the left of a lens whose focal length is 10 cm. (a) Find the position, size, and type of the image. Show a rough sektch. (b) A second lens of 10 cm focal length is placed 40 cm to the right of the rst lens. Find
A half-cylinder of glass has radius R and index of refraction n. A ray of light lies in the plane of the gure as shown, and it is incident on the plane face at an angle . It goes on to hit the curved surface; for what range of incident positions on the at
Problem Set 4 Calculus 1
Abdullah Khalid, Hassan Bukhari
December 8, 2010
Thomas Calculus, Chapter 2 Additional and Advanced Exercises
18. The Dirichlet ruler function, f (x), is discussed in detail in Spivak on pages 97-98 of Chapter 5. Basically he show
Problem Set 2 Calculus 1
Abdullah Khalid, Hassan Bukhari
November 23, 2010
Exercise 2.3
9. We have f (x) = x, xo = 1, L = 1, = 1 . 4 5 We have the graph given in the book. As can be seen L + = 1 + 1 = 4 and L = 4 1 3 9 1 4 = 3 . Consider that when f (x)
Problem Set 1 Calculus 1
Abdullah Khalid, Hassan Bukhari
November 10, 2010
1(a) We have to show that the following statement is true. P (n) 12 + . + n2 = n(n + 1)(2n + 1) 6
Base case: Lets show that P(1) is true. So lets put in n = 1 in P(n). L.H.S = 12 =
University of Engineering and Technology Lahore
Department of Electrical Engineering Calculus I November 2, 2010
It is most useful that the true origins of memorable inventions be known, especially of those which were conceived not by accident but by an e