Mathematical Foundations of Electrical Engineering
ECE 18202

Spring 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Problem Set #4 Solution
Spring Semester, 2012
1. (10 points).
(1) (2 points) ode45 numerical integration
Problem 1 is a
Mathematical Foundations of Electrical Engineering
ECE 18202

Spring 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Problem Set #8 Solution
Spring Semester, 2012
1. (20 points).
(a) (5 points) The rank of the matrix is 1 because:
1 2
1
Last (sur)name: _ 18220 Spring 2007
_
TEST #3
_
Last (sur)name: _ First (given) name: _ Lab Section: _ 1. _ 2. _ 3. _ 4. _ 5. _
Closed book, no computers, no calculators, no cell phones. Answers should be numerical if that is possible given the problem s
18220 Fall 2008
_
HW SET #1 (DUE AT THE BEGINNING OF CLASS, SEPT 8)
_ Reading: Chapter 1 in Semiconductor Devices and Technology
Note: All submitted homework must include your full name, first name first, last name last; lab section; and recitation secti
Mathematical Foundations of Electrical Engineering
ECE 18202

Spring 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Problem Set #10 Solution
Spring Semester, 2012
1. (15 points).
(1) (5 points) Eigenvalues of A:
D() = 0 det (A I) = 0
1
Mathematical Foundations of Electrical Engineering
ECE 18202

Spring 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Problem Set #1 Solution
Spring Semester, 2012
1. (20 points) Common birthday probabilities.
Matlab code:
N = 1:50;
p = z
Mathematical Foundations of Electrical Engineering
ECE 18202

Spring 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Problem Set #6 Solution
Spring Semester, 2012
1. (20 points) Prove the matrix identities.
(1) (k A) B = A (k B)
(2) A (
Mathematical Foundations of Electrical Engineering
ECE 18202

Spring 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Problem Set #7 Solution
Spring Semester, 2012
1. (20 points)
(1) Gauss elimination
3
1
15 6
2
5
1
5
2
3
1
R =R +5R
R =3
Mathematical Foundations of Electrical Engineering
ECE 18202

Spring 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Problem Set #2 Solution
Spring Semester, 2012
1. (10 points).
(1) (5 pt)
f (z) = z 4 j4z 2 3 = (x + jy)4 j4(x + jy)2 3
T
Mathematical Foundations of Electrical Engineering
ECE 18202

Spring 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Problem Set #5 Solution
Spring Semester, 2012
1. (20 points) yn+1 3 yn = 1 2 n + 2 n2 , where y0 = 0
(1) (2 points)
yn+1
Mathematical Foundations of Electrical Engineering
ECE 18202

Spring 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Problem Set #3 Solution
Spring Semester, 2012
1. (10 Points) Phasor representation of sinusoids
(1) (5 points) Two perio
Homework 1 Solutions
18202 Mathematical Foundations of Signal Processing
September 1, 2014
1. (a) Not enough information. For example, the statement would be true if X were a power set but
would be false if it were a set of numbers such as R.
(b) True, s
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Fall 2014
P ROBLEM S ET # 5
I SSUED: Monday, September 29, 2014
D UE: Monday, October 6, 2014
Read Chapter 5.
Problems
18220 Spring 2007
_
TEST #1
_
Last (sur)name: _
First (given) name: _
Lab Section: _
1. _
2. _
3. _
4. _
5. _
Closed book, no computers, no calculators, no cell phones. Answers should be numerical if that is possible given the
problem statement. Intermed
Last (sur)name: _ 18220 Spring 2007
_
FINAL EXAM
A
_
Last (sur)name: _ First (given) name: _ Lab Section: _ 1. _ 2. _ 3. _ 4. _ 5. _ 6. _ 7. _ 8. _ Total _
Closed book, no computers, no calculators, no cell phones. Answers should be numerical if that is
18220 Fall 2008
_
HW SET #2 (DUE AT THE BEGINNING OF CLASS, SEPT 15)
_ Reading: Chapter 1 in Semiconductor Devices and Technology
Note: All submitted homework must include your full name, first name first, last name last; lab section; and recitation sect
18220 Fall 2008
_
HW SET #3 (DUE AT THE BEGINNING OF CLASS, SEPT 22)
_ Reading: Chapter 2 in Semiconductor Devices and Technology Chapter 3 in Circuit Analysis and Applications, sections 13.
Note: All submitted homework must include your full name, firs
18220 Fall 2008
_
HW SET #4 (DUE AT THE BEGINNING OF CLASS, SEPT 29)
_ Reading: Chapter 3 in Circuit Analysis and Applications.
Note: All submitted homework must include your full name, first name first, last name last; lab section; and recitation sectio
18220 Fall 2008
_
HW SET #5 (DUE AT THE BEGINNING OF CLASS, OCT 13)
_ Reading: Circuit Analysis and Applications, Chapter 4; Chapter 5 to pg. 63.
Note: All submitted homework must include your full name, first name first, last name last; lab section; and
18220 Fall 2008
_
HW SET #6 (DUE AT THE BEGINNING OF CLASS, OCT 20)
_ Reading: Circuit Analysis and Applications, Chapter 5 to pg. 73.
Note: All submitted homework must include your full name, first name first, last name last; lab section; and recitation
18220 Fall 2008
_
HW SET #7 (DUE AT THE BEGINNING OF CLASS, OCT 27)
_ Reading: Circuit Analysis and Applications, Chapter 5 to end; Chapter 6.
Note: All submitted homework must include your full name, first name first, last name last; lab section; and re
18220 Fall 2008
_
HW SET #8 (DUE AT THE BEGINNING OF CLASS, NOV 10)
_ Reading: Circuit Analysis and Applications, Chapter 7
Note: All submitted homework must include your full name, first name first, last name last; lab section; and recitation section if
18220 Fall 2008
_
HW SET #9 (DUE AT THE BEGINNING OF CLASS, NOV 17)
_ Reading: Circuit Analysis and Applications, Chapter 8
Note: All submitted homework must include your full name, first name first, last name last; lab section; and recitation section if
18220 Fall 2008
_
HW SET #10 (NOT DUE AT THE BEGINNING OF CLASS, ANYTIME)
_ Reading: Circuit Analysis and Applications, Chapter 9
Note: These problems will not be collected and will (obviously) not be graded. Solutions will be posted and they will be dis
18220 Introduction to Electrical Engineering
D.W. Greve dg07@andrew.cmu.edu REH 231 http:/www.ece.cmu.edu/~dwg
Additional staff*
Prof. J. Hoburg (recitations) Jung Yeon Kim (grader) Yunchuan Kong (lab) Steven Mikes (lab) Mingwei Tay (lab) Chen Song (grad
Active devices
B n+ E p C
E n+ E B C
n+ p substrate
B
p n C
BJT
S
G p well n substrate
D
S n+
G
n+
n+
p G
n+
D
MOSFET
D
S
nMOSFET characteristic
1
MOSFET types
depletion
VTn < 0
enhancement
VTn > 0 +
I Dn
n channel
+
I Dn
+
VDS > 0 VGS
+ VDS > 0
VGS
VTp
Why sinusoids?
The method of calculation is considerably simplified. Whereas before we had to deal with periodic functions of an independent variable time, now we obtain a solution through the simple addition, subtraction, etc. of constant numbers Neither
Modulation and demodulation
transmission media
coaxial line twisted pair optical fiber free space (EM wave)
usually more than one stream of information
channel = region of the transmitted frequency spectrum
assigned to particular users or services
Some de
Chapter 4
First Order Ordinary Differential and
Difference Equations
4.1
Introduction
This Chapter introduces linear rst order ordinary differential and difference equations
with constant coefcients. For brevity, we will call a linear ordinary differentia