SCIENTIFIC METHOD IN OPERATIONS RESEARCH

1.Judgement Phase :
This phase includes -
(1)Identification of the real-life problem,
(2)Selection of an appropriate goal and the value of various variable related to the goals,
(3)Appropriate scale of measurement,and
(4)Formulation of an appropriate model of the  problem, abstracting the essential information so that a solution at the decision-maker's goal can be sought.

2.Research Phase :
This phase is the largest and longest among the other two.
However,the remaining two are also equally important as they provide the basis for a scientific method.
This phase utilizes-
(1)Observations and data collection for a better understanding of what the problem is,
(2)Formulation of hypothesis and models,
(3)Observation and experimentation to test the hypothesis on the basis of additional data,
(4)Analysis of the available information and verification of the hypothesis using pre-established measures of
effectiveness,
(5)Predictions of various results from the hypothesis, and
(6)Generalization of the results and consideration of alternative methods.

3.Action Phase : This phase consists of making recommendations for decision process by those who first posed the problem for consideration, or by anyone in a position to make a decision influencing the operation in which the problem occurred.

ORIGIN AND DEVELOPMENT OF OPERATION RESEARCH

The term, Operational Research, was first coined in 1940 by McClosky
and Trefthen in a small town,Boxesey,of the United Kingdom.

This new science came into existence as a result of research on military operations during World War II. During the was there were strategic and tactical problems which were greatly complicated,to expect
adequate solutions from individuals or specialists was
unrealistic.

Therefore, the military management called on scientists from various disciplines and organised them into teams to assist in solving strategic and tactical  problems,i.e. ,to discuss,evolve and suggest ways and means to improve the execution of various military projects.

By their their joint efforts,experience and deliberations,they suggested certain approaches that showed remarkable progress.This new approach to systematic and scientific study of the operations of the system was called the Operations Research or Operational Research.

MONTE CARLO METHODS

These involve the use of probability and sampling concepts.

The various steps associated with a Monte
Carlo Method are as follows:

(a) For appropriate model of the system,make sample observations and
determine the probability distribution for the variables of interest.

(b) Convert the probability distribution to cumulative distribution.

(c) Select the sequence of random numbers with the help of random tables.
(d) Determine the sequence of values of variables of interest with the sequence of random numbers obtained in the above step.
(e)Fit an appropriate standard mathematical function to the values
obtained in step-(d) The Monte Carlo Method is essentially a simulation technique in which statistical  distribution functions are created by generating a series of random numbers.

METHODOLOGY OF OPERATIONS RESEARCH

The Operations Research approach to problem solving consists of the following seven steps:

1. Formulate the problem.
2. Construct a mathematical model.
3. Acquire the input data.
4. Derive the solution from the model.
5. Validate the model.
6. Establish control over solution.
7. Implement the final results.

Financing System -Income and Saving

Financing system:
When our income is more than our need,we need financing institutions
to save that money and to earn profit from that.Thus the financing
institutions keep our surplus income or saving as deposits and lend it
to the persons who need money.Therefore the process of collecting
money as deposits and providing loans, is known as financing system.
Thus the process of maintaining balance between demand and supply of
wealth or capital in the economy is called financing system.

M.P.BOARD 10th Class Syllabus

1.Linear Equations in Two Variables
2.Polynomials & Rational Expression
3.Ratio and Proportion
4.Quadratic Equations
5.Commercial Maths
6.Similar Triangles
7.Circles
8.Constructions
9.Trigonometry
10.Height and Distance
11.Mensuration
12.Statistics & Probability

M.P.BOARD 12th Class Syllabus

12th Class Syllabus
1.Partial Fraction
2.Three Dimensional Geometry
3.The Plane
4.Straight Line & Sphere
5.Vectors
6.Vector Products
7.Application of Vectors in three Dimensional Geometry
8.Inverse Trigonometric Functions
9.Functions,Limits & Continuity
10.Differentiation
11.Harder Differentiations
12.Applications of Derivatives
13.Integration
14.Harder Integration
15.Definite Integrations
16.Differential Equations
17.Correlation
18.Regression
19.Probability
20.Numerical Methods

M.P.Board Syllabus

11th Class Syllabus
1.Complex Numbers
2.(A)Special Simultaneous equations in three Variables and their Solutios
(B)Theory of Quadrctic Equations
3.Arithmetic Progression and Harmonic Progression
4.Geometric Progression and Special Series
5.Determinants
6.Matrices
7.Cartesian Co-ordinates of Points
8.Straight Lines
9.Pair of Lines
10.Circle
11.Conic Section
12.Trigonometric Functions
13.Trigonometricall Identities,Graphs and Equations
14.Properties of triangle and solution of Triangles
15.Height and Distance
16.Statistics
17.Permutations and Combinations
18.Mathematical Induction and Binomial Theorem
19.(A)Linear Inequalities(B)Linear Programming
20.Exponential and Logarithmic Series

Taylor's Theorem

Taylor's Theorem
Suppose we're working with a function f(x) that is continuous and has n + 1 continuous
derivatives on an interval about x = 0. We can approximate f near 0 by a polynomial Pn(x)
of degree n:

For n = 0, the best constant approximation near 0 is
P0(x) = f(0)
which matches f at 0.

For n = 1, the best linear approximation near 0 is
P1(x) = f(0) + f0(0)x:
Note that P1 matches f at 0 and P01 matches f0 at 0.

For n = 2, the best quadratic approximation near 0 is
P2(x) = f(0) + f0(0)x +
f00(0)
2!
x2: