Mathematic calculation in over life

U                        HEAT AND THERMODYNAMICS        Thermodynamics deals with various phenomena of energy and related properties of matter, especially the transformation of heat into other forms of energy. An example of such transformation is the process converting heat into mechanical work. Thermodynamics thus plays central role in technology, since almost all the raw energy available for our use is liberated in the form of heat. in this topic we shall their significance and applications.               KINETIC THEORY OF GASES       The behavior of gases is well accounted for by the kinetic theory based on microscopic approach. Evidence in favor of the theory is exhibited in diffusion of gases and Brownian motion of smoke particles etc.      The following postulates help to formulate a mathematical model of gases.      A finite volume of gas consists of very large number of molecules.      The size of the molecules is much smaller then the separation between molecules.

                                             SETS       INTRODUCTION           We often speak some words in daily life which represent a collection of things, for example, a team of players, a bunch of flowers, a cluster of trees, a group of friends, a swarm of birds and so on. But in mathematics, we can use a single word "set" to denote all such type of words that show the collection of things such as, a set of players, a set of flowers, a set of trees, a set of friends and a set of birds, etc. Thus we can define a set as:     "A collection of distinct and well-defined objects is called a set. "  The objects of a set are called its members or elements.          In 19th century George  Cantor was the first mathematician who gave the proper idea of sets that we are using now in various branches of mathematics.     Well- defined sets         We-defined means a specific property of an object that enables it to be an element of a set or not. To make it clear

                                        PROBABILITY                          INTRODUCTION                                                                   The word probability has two meaning:(1) a quantitative measure of uncertainty and (2) a measure of degree of belief in a particular or problem.                                Probability and statistic are fundamentally interrelated. probability is often called the vehicle of statistics. the area of inferential statistics in which we are mainly concerned with drawing inferences from experiments or situations involving an element of uncertainty, leans heavily upon probability theory. Uncertainty is also an inherent part of statistics inference as inferences are based on a sample, and a sample being a small part of larger population, contains incomplete information. A similar type of uncertainty occurs when we toss a coin, draw a card or throw dice,etc. The uncertainty in all these cases is measured in terms of probability.

                CURVE FITTING BY LEAST SQUARES           INTRODUCTION            Let us suppose that we wish to approximate (describe) a certain type of function that best expresses that association that exists between variables. A scatter plot of the set of values of the variables makes it possible to visualize a smooth cure that effectively approximates the given data set. A more useful way to represent this sort of approximating curve is by means of an equation or a formula. A term applied to the process of determining the equation and/or estimating the parameters appearing in the equation of approximating curve, is commonly called curve fitting .            It is relevant to point out that the relationship between the variables may be functional or regression. In functional relationship, a variable Y, has a true corresponding to each possible value or of another variable X, i.e. there is no question of random variation in the values of Y, and we make no relationship, i.

Introduction                 A time series consists of numerical data collected observed or recorded at more or less regular intervals of time each hour, day, month, quarter or year, More specifically, it is any set of data in which observation are arranged in a chronological order, Examples of time series are the hourly temperature recorded at a locality for a period of year, the weekly prices of wheat in Lahore, the monthly consumption of electricity in a certain town, the monthly total of passengers carried by rial,the quarterly sales of a certain fertilizer, the annual rainfall at Karachi for a number of year, the enrollment of students in a college or university over a number of year and so forth.               The analysis of a time series is a process by which a set of observation in a time series in analyses.Time series analysis is rather a difficult topic but we shall limit our discussion to the basics of time series analysis          The observation in a time series, d