1.4. DIVISION ALGORITHM AND THE FUNDAMENTAL THEOREM OF ARITHMETIC13
1.4
Division Algorithm and the Fundamental Theorem of Arithmetic
In the next few pages, we will try to study properties of integers that will be required later. We
start with a lemma, com

8
CHAPTER 1. PROPERTIES OF INTEGERS AND BASIC COUNTING
1.2
Well Ordering Principle and the Principle of Mathematical
Induction
Axiom 1.2.1 (Well-Ordering Principle). Every non-empty subset of natural numbers contains
its least element.
We will use Axiom 1

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NUMERICAL METHODS LAB
IV SEM.
LIST OF EXPERIMENTS
SR.
NO.
1
NAME OF EXPERIMENT
PAGE
NO.
TO FIND THE ROOTS OF NON-LINEAR EQUATION USING
BISECTION METHOD.
3-5
2
TO FIND THE ROOTS OF NON-LINEAR EQUATION USING
NEWTONS METHOD.
69
3
4
CURVE

Chapter 1
Properties of Integers and Basic
Counting
We will use the following notation throughout these notes.
1. The empty set, denoted , is the set that has no element.
2. N := cfw_0, 1, 2, . . ., the set of Natural numbers;
3. Z := cfw_. . . , 2, 1, 0,

1.3. STRONG FORM OF THE PRINCIPLE OF MATHEMATICAL INDUCTION
1.3
11
Strong Form of the Principle of Mathematical Induction
We are now ready to prove the strong form of the principle of mathematical induction.
Theorem 1.3.1 (Principle of Mathematical Induct

UNIT I: QUEUEING THEORY
1. Define a queue and a customer.
Queue: The flow of customers waiting for service in a system rendering some service is
called a queue.
Customer: The arriving unit requires some service to be performed is called a customer.
2. Wha

UNIT-V -
NON-LINEAR PROGRAMMING PROBLEM
PART-A
1. Define general non linear programming problem
2. Define convex and concave functions
3. Define local and global optimum
4. Verify whether the following function is concave or convex f(x1,x2) = 2x13-6x22
5.

UNIT-II: NON MARKOVIAN QUEUES &QUEUE NETWORKS
1. Derive Pollaczek-Khintchine formula
2. A patient goes to a single doctor clinic for a general check up with 4 phases. The doctor
takes on average 4 minutes for each phase of the check up and time taken for

UNIT-III: SIMULATION
1. Define simulation
Simulation is the imitation of the operation of a real world process or system
over time. It is a numerical technique for conducting experiments that involve certain
types of mathematical and system over extended

UNIT IV INTRODUCTION TO LINEAR PROGRAMMING
PART - A
1. What is OR? Give some applications.
Operations Research has been variously described as the Science of Use,
Quantitative Common sense Scientific approach to decision making
problemetc. But only a few