Numerical Methods and Application of MATLAB (Theory)

Paper Code: 
24DPHY613(A)
Credits: 
04
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 
Course Objectives: 
This course will enable the students to-
• develop their knowledge of basic Numerical methods and programming. 
• acquire knowledge of MATLAB extension and will be able to apply these techniques to problem-solving in the basic research field.
 
Course Outcomes: 

Course Outcomes (COs):

Course

Learning outcome

(at course level)

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24DPHY613(A)

Numerical Methods and Application of  MATLAB

(Theory)

CO130: Identify the sources of error Perform error analysis to understand the impact of errors on numerical solutions and also Evaluate the condition and stability of numerical algorithms.

CO131: Find numerical solutions of the systems of linear  and Non-linear equations with accuracy and obtain numerical solutions of algebraic transcendental equations.

CO132: Solve initial and boundary value problems in differential equations using numerical methods and apply various numerical methods in real-life problems.

CO133:Evaluate the accuracy and suitability of different curve fitting, interpolation, and extrapolation techniques for different types of data sets and applications.

CO134: Develop the knowledge of MATLAB extension and will be able to apply these techniques to problem-solving in basic research field.

CO135: Contribute effectively in Course specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Power point presentation,  Demonstration, problem solving  in tutorials

 

Learning activities for the students:

Self learning assignments, Effective questions, Seminar presentation, Solving numericals

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 and Nonlinear equations:
Direct and Iterative methods, Jacobi and Gauss-Seidel method.
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 III: 
Integration of a function and Ordinary differential equation:
Trapezoidal and Simpson's rules. Gaussian quadrature formula, Singular integrals, Double integration.
Predictor-corrector methods, Runga-Kutta method. Simultaneous and Higher-order equations.
Numerical differentiation of Data, Least-Squares Approximations, Fast Fourier Transformation.
 
12.00
Unit IV: 
Curve fitting using MATLAB:

Least square line, Methods of curve fitting, Interpolation by Spline functions, Fourier series and trigonometric polynomials, Bezier curve.

12.00
Unit V: 
Numerical Integration using MATLAB:

Introduction to Quadrature, Composite trapezoidal and Simpson’s Rule, Recursive rules, Adaptive Quadrature, Gauss-Legendre Integration.

Essential Readings: 
• “Mathematical Methods”, Potter and Goldberg, Prentice Hall of India (1998).
• “Mathematical methods in Physics”, D. Biswas, New Central Book Agency (P) Ltd.
• “Mathematical Physics”, M.P. Saxena, P.R. Singh, S.S. Rawat, P.K. Sharma, CBH, Jaipur.
• “A First Course in Numerical Analysis”, A Ralston and P. Rabinowitz, McGraw Hill (1985). 
• “Introductory Methods of Numerical Analysis”, S.S. Sastry, Prentice-Hall of India (1979). 
• “Numerical Methods using MATLAB.”, John H. Mathews and Kurtis D. Fink, PHI
 
References: 
• “Applied Maths for Engineers and Physicists”, Pipes and Harvill, McGraw Hill.
• “Advanced Engineering Mathematics”, Ervin Kreyzig 5th Edition, Wiley Eastern Ltd. 
• “Numerical Methods”, S. Balachandra Rao, C.K. Shantha, University Press, 1992.
• “Mathematical Physics”, Ellgnine Butkon, Addison Wiesley.
• “Mathematical Physics”, Gupta, Vikas Publishing House.
 
E-Content:
 
 
 
 
 
Academic Year: 
2024-2025
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