Numerical Methods in Physics

Paper Code:

24PHY222

Credits:

Contact Hours:

60.00

Max. Marks:

100.00

Objective:

This course will enable the students to –

explore the key principles and applications of Numerical Methods and their relevance to current developments in physics.
make the students learn the numerical solution of different kinds of equations.

Course Outcomes:

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

24PHY222

Numerical Methods in Physics

(Theory)

CO45: develop knowledge about the Error in Numerical Analysis

CO46: Solve Linear equations and develop a deep understanding of various methods.

CO47: Determine the solution of non-linear equations and mathematical problems related to it.

CO48: Develop a better understanding of Numerical Differentiation and Integration.

CO49: Explain the Numerical Solution Of Ordinary Differential Equations by the help of various examples.

CO50: Contribute effectively in

course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Power point presentation, Problem Solving

Learning activities for the students:

Self-learning assignments, Effective questions, Seminar presentation, Solving numerical, Additional learning through online videos

Class test, Semester end examinations, Quiz, Solving problems , Assignments, Presentations

12.00

Unit I:

Errors in Numerical Analysis

Source of Errors, Round off error, Arithmetic error, error analysis, Condition and stability, method of undetermined coefficients, use of interpolation formula, iterated interpolation, inverse interpolation, Hermite interpolation and Spline interpolation (linear method).

12.00

Unit II:

Solution of Linear equations

Need and Scope, Existence of Solutions, Solution by Elimination, Basic Gauss Elimination Method, Gauss- Jordan Method, Matrix Inversion Method, Jacobi Iteration Method, Gauss-Seidel Method.

12.00

Unit III:

Solution of Nonlinear equation

Bisection method, Newton-Raphson method, Generalized Newton-Raphson method, method of iteration, Newton-Raphson method for the case of nearly equal roots, double root and multiple roots.

12.00

Unit IV:

Numerical Differentiation and Integration

Numerical Differentiation: Need and Scope, differentiating continuous functions, Differentiating tabulated functions, Difference tables, Numerical Integration: Trapezoidal Rule, Simpson’s1/3Rule, Simpson’s 3/8 Rule, Higher Order Rules.

12.00

Unit V:

Numerical Solution Of Ordinary Differential Equations

Need and Scope, Tailor Series Method – Improving accuracy, Picard’s method, Euler’s Method – accuracy of Euler’s method, Heun’s Method–Error analysis, Polygon Method, Runge-Kutta Methods- Determination of weights, Fourth order Runge-Kutta methods.

Essential Readings:

· Numerical methods in Science and Engineering-M.K.Venkataraman National PublishingCo. Madras, 1996.

· Numerical methods for scientific and engineering computations -Jain and

· Iyengar. New Age International, 2003

· NumericalMethods, E. Balagurusamy, Tata McGraw-Hill, India,1999

References:

· IntroductoryMethodsofNumericalAnalysis-S.S.Sastry-Prentice Hall, 2005.

· NumericalMethodsforEngineers, Steven C. Chapra and Raymond P. Canale, McGraw Hill International editions, 2ndedtion, 1990.

E- Content:

·https://freecomputerbooks.com/Numerical-Methods-with-Applications.html

·https://www.e-booksdirectory.com/listing.php?category=407

·https://open.umn.edu/opentextbooks/textbooks/741