COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES(CBNST)
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This document provides an overview of computer based numerical techniques (CBNST). It discusses applications of CBNST in fields like signal processing, system monitoring, astrological data analysis, system identification, and quality control. Some key topics covered include solving algebraic equations, interpolation, numerical differentiation and integration, and statistical computation. Specific numerical methods discussed include bisection, Newton-Raphson, regular falsi, and Muller's method. Applications highlighted include using regular falsi for pollution prediction and interpolation for approximating spring load and deflection graphs. Numerical integration is also introduced as the approximate computation of integrals.
COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES(CBNST)
- 2. COMPUTER BASED NUMERICALS TECHNIQUES: It is use to optimize performance and minimize errors in problem
- 3. APPLICATIONS: In Signal Processing that treats signals as stochastic process,dealing with their statistical properties. In regular monitoring to attempt to detect changes in the environment. To analysis and understand the astrological data. In system Identification to build mathematical models of dynamical system for data measurement and for optimal design of experiment. In operational research of applied mathematics and formal science. In quality control system for inspection, testing, analysis to ensure that quality of product is as per requirements.
- 4. TOPICS OF CBNST: SOLUTION OF ALGEBRIC EQUTIONS INTERPOLATION NUMERICAL DIFFERENTIATION AND INTEGRATION STATISTICAL COMPUTATION
- 5. SOLUTION OF ALGEBRIC EQUTIONS BISECTION METHOD NEWTON RAPHSON METHOD REGULAR FALSI METHOD MULLER METHOD ITERATIVER METHOD
- 6. APPLICATION OF REGULAR FALSI It can be used in the prediction of trace quantities of atmospheric pollutants produced by combustion reactions such as those found in industrial point sources.
- 7. INTERPOLATION In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. Interpolation is the approximation of a complicated function by a simple function.
- 9. APPLICATION: A spring is an elastic object used to store mechanical enrgy.In case of mechanical spring there is a spring load and deflection graph.The deflection is in mm and load is in N. The deflection is plotted on axes.Often we have to find the values between the two sets of values . Hence interpolation is the technique used to find the unknown values.
- 10. NUMERICAL INTEGRATION In numerical integration is the approximate computation of an integral using numerical techniques.The numerical computation of an integral is sometimes called quadrature. The basic problem in numerical intrgration is to compute an approximation solution to a definite integral to a given degree of accuracy.