Numerical Methods and Application of MATLAB (Theory)

Paper Code: 
DPHY 613(A)
Credits: 
04
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

Course Objectives:

This course will make students learn about the change in properties of materials when subjected to nano-scale dimension. They also learn about basics of Nano-science and Nanotechnology and develop an understanding of various analytical techniques used in Nano science. It will also introduce them to the applications of nano-materials.

Course Outcomes (COs):

Course

Learning outcome (at course level)

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

DPHY613(B)

 

Elements of Nanoscience and Nanotechnology

(Theory)

 

The students will be able to –

CO120: learn basic properties of nanoparticle & applications.

 

CO121: describe various methods for the synthesis/growth of nanomaterials including top down and bottom up approaches.

CO122: analyze the data obtained from the various characterization techniques.

CO123: acquires necessary background to take up higher studies/research in the field of Nano Science & Nano-technology.

Approach in teaching:

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

in tutorials,

 

Learning activities for the students:

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

Additional learning through online Videos, MOOCs Courses.

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

 

CONTENTS

12.00
Unit I: 
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: 
II
Solution of Linear equations: Direct and Iterative methods, Jacobi and Gauss-Seidel   method 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 III: 
III

Integration of a function: Trapezoidal and Simpson's rules. Gaussian quadrature formula, Singular integrals, Double integration.

Integration of Ordinary differential equation: 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: 
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: 
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.
 
Academic Year: 
2023-2024
  • Printer-friendly version
  • PDF version