National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Chapter 2 Maxwells Equations and Plane EM Waves
21 Dielectric and Conductor
Displacement vector: D 0 E P E 0 1 e E 0 r E
nv
Polarization vector:
P
k
P lim
k 1
v
v 0
1
V
4 0
' x
Pa R
2
2
2
2
dv' , R x x' y y ' z z '
v' R 2
1 aR
y
z
x '
y '
z ' ' 2
R
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
Preliminaries
Mehreen Alam
Aug 23, 2013
Contents
Basic Definitions
Languages, String, Words, Concatenation, Length
Palindrome
Kleene Closure
Lexicographic order
Definition
Kleene Closure of null set & set with only null word
Kleene Clos
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
The Chomsky
Hierarchy
Mehreen Alam
Dec 2, 2013
Contents
Type 0
Type 1
Type 2
Type 3
Dec 2, 2013
Mehreen Alam  Theory of
Automata
2
Chomsky Hierarchy
Type0 grammars (unrestricted grammars) include all formal
grammars.
Type1 grammars (
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
Computable Functions
Mehreen Alam
Dec 2, 2013
Contents
Computation
Paradigms
Functions and their computations
Computable and noncomputable functions
Computable Functions
Computer Science Law
TM for Computable Functions
Alonzo Churchs T
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
Turing Machine
Variations
Mehreen Alam
Nov 29, 2013
Contents
The Standard Model
Variations
StayOption
SemiInfinite Tape
OffLine
Multi tape
Multidimensional
Nondeterministic
Nov 29, 2013
Mehreen Alam  Theory of
Automata
2
The Standar
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
18.435 Lecture 13
October 16th , 2003
Scribed by: Eric Fellheimer
This lectured started with details about the homework 3:
Typo in Nielsen and Chuang: If you pick random x such that gcd(x, N) = 1, x < N and N
is the product of m distinct primes raised to
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Lecture 11: Applications of Grovers Search Algorithm
Scribed by: YuanChung Cheng
Department of Chemistry, MIT
October 9, 2003
In this lecture we will cover several applications of Grovers search algorithm, and show that
Grovers search algorithm is optimal
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Lecture 5: Quantum Circuits and a Simple Quantum Algorithm
Scribed by: Dion Harmon
Department of Mathematics, MIT
September 18, 2003
1
Administrativa
On homework 1, the book uses 1 , 2 , and 3 for x , y , and z .
Well go over the homework next lecture.
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Lecture 2: Basics of Quantum Mechanics
Scribed by: Vitaly Feldman
Department of Mathematics, MIT
September 9, 2003
In this lecture we will cover the basics of Quantum Mechanics which are required to under
stand the process of quantum computation. To simpl
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Lecture 14: Cluster States
Scribed by: Ilia Mirkin
Department of Mathematics, MIT
October 21, 2003
A cluster state is a highly entangled rectangular array of qubits. We measure qubits
one at a time. The wiring diagram tells us which basis to measure each
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Lecture 23: FaultTolerant Quantum Computation
Scribed by: Jonathan Hodges
Department of Nuclear Engineering, MIT
December 4, 2003
1
Introduction
Before von Neumann proposed classical faulttolerance in the 1940s, it was assumed that a compu
tational device
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Lecture 16: Quantum Error Correction
Scribed by: DahYoh Lim
October 30, 2003
1
Introduction
Today we are going to look at how one can do error correction in the quantum world. In the
PreShannon days, simple repetition codes were used: to transmit bit 0,
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Lecture 19: How to Build Your Own Quantum Computer
Guest Lecturer: Isaac Chuang
Scribed by: Fen Zhao
Department of Mathematics, MIT
November 13, 2003
1
The DiVicenzo Criteria
The DiVicenzo Criteria list four things required for quantum computing: robust q
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
National University of Computer and Emerging Sciences Islamabad
Electronic and Circuit Design
Assignment No. 2
Deadline: April 22, 2016
QNo.1: Design a MOS Differential pair with active load and constant current source of
Iref=0.75mA.
Apply input signal o
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
Universal Turing
Machine
Mehreen Alam
Dec 2, 2013
Contents
Transition Table for TM
TM Encoding
UTM
Computable Functions
Alonzo Churchs Thesis (1936)
Dec 2, 2013
Mehreen Alam  Theory of
Automata
2
TM instructions in table format
We can
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
Regular Expressions
Mehreen Alam
Aug 30, 2013
Contents
Regular Expressions
Defining Languages by Another New Method
Formal Definition of Regular Expressions
Language Defining Symbols
Alternation, Either/OR, Disjunction, Plus Sign
Produc
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Clock Project
CS 343
Design a digital clock according to the following specifications:
The clock will display time in the standard 12 hour format HH:MM with an indicator for
AM/PM. Your clock will use a 7segment display unit.
The project must include:
1.
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
DenTAL CARIES
In partial fulfillment of the requirement for the award of
MBBS
Submitted by
Alvina lateef
Roll no: 23
Department of Dentistry
North Sichuan medical college
Nanchong, china
DECLARATION
I hereby declare that the work is totally done by me and
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Project
Wireless Garage Door Opener
Weekly Report
Group Members:
22/04/2016
Date
QuestionA
Some of the task which we had done:

The main circuit implantation is already completed.

The switch will decide that what kind of instruction relay is received
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Project
Wireless Garage Door Opener
Weekly Report
Group Members:
22/04/2016
Date
QuestionA
Some of the task which we had done:


The implementation of switch between garage opener and relay Is comleted.
The Bluetooth connection between the garage and
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Project
Wireless Garage Door Opener
Weekly Report
Group Members:
22/04/2016
Date
A. The task which we had done this week are:
 Connection between the garage opener and the relay is completed
 A Relay Board to activate the opener  This acts like a wall
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
186
Ch. 12: Contributed Capital
Chapter 12
Contributed Capital
In this chapter you will learn how contributed capital affects businesses,
how it is controlled, accounted for, and reported in financial statements.
What Is Contributed Capital?
Chapters 10 a
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Project name = Parking
Finder
Second Design
Group Members
Date = 22 april 2016
A. Problem Statement
For the municipality, parking garage administrators and drivers it is very annoying that a
lot of cars have to drive around looking for an available parkin
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Texas Southern University
Department of Engineering
Technologies
Design_and_construction_of_solar_powered_mo
bile_phone_
charger_for_rural_settlement
Weekly Progress Report
Name: Taher
Date: 22042016
Team Members: Taher, Ahmed
Reporting period: Week12
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
PHY3101HW#2
Due:Thursday,May29
9.
An aluminum calorimeter with a mass of 100 g contains 250 g of
water. The calorimeter and water are in thermal equilibrium at
10.0C. Two metallic blocks are placed into the water. One is a 50.0g
piece of copper at 80.0C.
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
Post Machine
Mehreen Alam
Nov 27, 2013
Contents
Post Machine
Examples
Simulating PM on TM
Simulating TM on PM
SHIFTRIGHT CYCLICALLY.
Nov 27, 2013
Mehreen Alam  Theory of
Automata
2
POST Machine
A Post machine denoted by PM is a collec
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
Mehreen Alam
Aug 19, 2013
Acknowledgement
Dr Aftab Maroof
For sharing the course resources and for his
valuable guidance
Aug 19, 2012
Mehreen Alam  Theory of
Automata
2
Contents
Instructor
Outline
Text & reference Material
Grading
Obje
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
Mathematical
Preliminaries
Mehreen Alam
Aug 21, 2013
Mathematical reviews
Sets
Functions and Relations
Graphs and Trees
Proof Techniques
Aug 21, 2013
Mehreen Alam  Theory of
Automata
22
Sets (1)
A set is a collection of elements withou
National University of Computer and Emerging Sciences, Islamabad
Mathematics
ELECTRICAL 4410

Spring 2016
Theory of Automata
Recursive Definitions
Mehreen Alam
Aug 28, 2013
Contents
Recursive Definition
Arithmetic Expression
Examples
Recursive Definition of AE
Theorems
Propositional Calculus
Well Formed Formula
Aug 28, 2013
Mehreen Alam  Theory of
Automata
2