Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
Problem 8)
Is the following equation an ordinary function? If so, give the answer. Otherwise, give an
explanation.
2
lim
 
Solution:
Let z = x + jy
For the numerator:
z2 = (x+jy)2 = x2 + 2jy + (jy)2 = x2 + 2jy y2
Hence, Re(2z2) = Re(2 (x2 +
Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
18202 Mathematical Foundations of Electrical Engineering
Quiz
October 16, 2012
You are given the two natural frequencies 1,2 = 1 j of a secondorder continuoustime ODE.
1. Write the ODE in the canonical form.
Answer:
( 1 )( 2 ) = 2 2 + 2 x(t) 2x(t) + 2x
Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Fall 2011
Exam # 1
Wednesday, September 19, 2012
The exam lasts for 110 min, i.e., it is from 9:30 AM to 11:20AM.
Be s
Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
18202 Homework 1 Solutions
September 3, 2012
1. Let X be a set and the empty set. For each of the statements below,
which one holds: true, false, or not enough information to decide.
(a) X
Answer: Not enough information to decide because not every set has
Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Fall 2012
P ROBLEM S ET # 6
I SSUED: Monday, October 8, 2012
D UE: Monday, October 15, 2012
Read Chapter 5 and start re
Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Fall 2012
P ROBLEM S ET # 5
I SSUED: Monday, October 1, 2012
D UE: Monday, October 8, 2012
Read Chapter 5 of the Notes.
Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Fall 2012
P ROBLEM S ET # 3
I SSUED: Wednesday, September 12, 2012
D UE: Tuesday, September 18, 2012
Read Chapters 2 an
Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Fall 2012
P ROBLEM S ET # 4
I SSUED: Monday, September 24, 2012
D UE: Monday, October 1, 2012
Read Chapter 4 of the Not
Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Fall 2012
P ROBLEM S ET # 2
I SSUED: Wednesday, September 5, 2012
D UE: Wednesday, September 12, 2012
Read Chapter 2 of
Mathematical Foundations of Electrical Engineering
ECE 202

Fall 2012
Carnegie Mellon University
Department of Electrical and Computer Engineering
18202 Mathematical Foundations of Electrical Engineering
Fall 2012
P ROBLEM S ET # 1
I SSUED: Monday, August 27, 2012
D UE: Wednesday, September 5, 2012
Read carefully the Syll