Syllabus

Module-1 ( 6 lectures)

Uncertainties in Measurements, Errors as Uncertainties, Inevitability of Uncertainty, Importance of Knowing the Uncertainties, Estimating Uncertainties When Reading Scales, Estimating Uncertainties in Repeatable Measurements. How to Report and Use Uncertainties,
Best Estimate and Uncertainty, Significant Figures, Discrepancy Comparison of Measured and Accepted Values, Comparison of Two Measured Numbers, Checking Relationships with a Graph, Fractional Uncertainties, Significant Figures and Fractional Uncertainties, Multiplying Two Measured Numbers
Numerical Methods: Programmings with Python/Fortran 90/95,
Polynomial Interpolation, Roots of Nonlinear equation,


Module-2 (6 lectures )

Propagation of Uncertainties , Uncertainties in Direct Measurements, The Square-Root Rule for a Counting Experiment, Sums and Differences Products and Quotients, Independent Uncertainties in a Sum, Arbitrary Functions of One Variable, Propagation Step by Step with examples. General Formula for Error Propagation
Numerical Methods: Differentiation, Integration


Module-3 (8 lectures )

Statistical Analysis of Random Uncertainties: Random and Systematic Errors, The Mean and Standard Deviation , The Standard Deviation as the Uncertainty in a Single Measurement, The Standard Deviation of the Mean, Systematic Errors.
The Normal Distribution, Histograms and Distributions, The Standard Deviation as a 68% Confidence Limit, Direct Application of the Maximum­ Likelihood Method, Justification of the Mean as Best Estimate, Justification of Addition in Quadrature, Standard Deviation of the Mean, Acceptability of a Measured Answer
Numerical Methods: Solution of Simultaneous Equations by Determinants, Matrix Inversion)

Module-4 (6 lectures)

Rejection of Data, Weighted Averages, Least-Squares Fitting The Binomial Distribution, Probabilities in Dice Throwing, The Poisson Distribution, Definition of the Poisson Distribution, Applications, The Chi-Squared Test for a distribution.
Numerical Methods: Solving differential equations by Euler and Runge­ Kutta methods, Data smoothing

Course Objectives
To impart knowledge on
1. The importance of error analysis in theoretical and experimental analysis
2. Calculating the propagation of error
3. Analyze the random data set using statistical methods
4. learn and understand different distributions
5. Apply numerical techniques to solve problems in physics

At the end of the course, students will be able to:
CO1: Understand the importance of error analysis
CO2: Apply methods of error propagation in experimental and theoretical analysis
CO3: Perform statistical analysis of random data sets
CO4: Perform a chi-squared test for various distributions
CO5: Develop algorithms and codes for solving problems for which exact solutions can’t be obtained.

Philip Bevington and D. Keith Robinson, Data Reduction and Error Analysis for the Physical Sciences., McGraw Hill Education (India) Private Limited , 3rd Edition, 2015

Steven C. Chapra and Raymond P. Canale, Numerical Methods for Engineers, McGraw Hill Education (India) Private Limited , 6th Edition, 2010

V. Rajaraman, Computer Programming in Fortran 90 and 95, Prentice Hall of India private Limited , 7th Edition, 2006

H. M. Antia, Numerical Methods for Scientists and Engineers, Hindustan Book Agency (India) , 3rd Edition, 2012