Numerical Analysis

Paper Code: 
CMAT 411
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Understand different numerical methods to obtain approximate solutions to mathematical problems. 
  2. learn numerical methods to solve interpolation based problems, ordinary differential equations, various numerical root finding problems.

Course Outcomes (COs):

 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

 

CMAT 411

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Numerical Analysis

(Theory)

 

 

 

 

 

 

 

The students will be able to –

CO56: Apply various interpolation methods and finite difference concepts to solve interpolation problems for equal intervals.

CO57: Describe the concept of central difference, Numerical differentiation and be able to solve interpolation problems for unequal intervals.

CO58: Understand the concept of Numerical Integration and be able to solve related problems.

CO59: Apply numerical methods to find our solution of
algebraic equations using different methods under different conditions

CO60: Solve the system of linear equations and ordinary differential equations by numerical methods.

CO61: Provide suitable and effective methods called Numerical Methods, for obtaining approximate representative numerical results of the problems.

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Giving tasks

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 (Note: Non-Programmable scientific calculator up to 100 MS is permitted)

 

Unit I: 
I
9.00
Differences, Relation between differences and derivatives, Difference of polynomials, Factorial notation, Newton’s forward and backward interpolation formula (with proof).
 
Unit II: 
II
9.00
Divided differences: Newton’s and Lagrange’s divided differences formulae. Central differences: Gauss’s, Sterling’s and Bessel’s interpolation formulae, Numerical differentiation.  
 
Unit III: 
III
9.00
Numerical integration: Newton-Cotes quadrature formula, Trapezoidal formula, Simpson’s 1/3rd and 3/8th formulae, Gaussian integration.
 
Unit IV: 
IV
9.00
Inverse Interpolation, Numerical solution of algebraic and transcendental equations: Bisection method, Regula-falsi method, Method of iteration and Newton Raphson’s Method, Newton’s iterative formula for obtaining square and inverse square root.
 
Unit V: 
V
9.00
Solution of a system of linear equations: Direct method (Gauss elimination method, LU-decomposition method), Iterative methods (Jacobi and Gauss Seidal method, SOR method), Theorems based on iterative methods, Solutions of first order ordinary differential equations: Picard’s method, Euler’s method, Runge-Kutta method.
 
Essential Readings: 
  • J.L. Bansal and J.P.N. Ojha, Numerical Analysis, Jaipur publishing house, 2015.
  • M.C. Goyal, D.C. Sharma and Kavita Jain, Numerical Analysis, RBD, 2015.
  • M.K. Jain and Iyengar, Numerical Methods Problems and Solutions, New Age International Ltd., 2007.
  • James B. Scarborough, Numerical Mathematical Analysis, Oxford and IBH publishing 1966.
  • J.P. Chauhan, Numerical Analysis, Krishna Prakashan Meerut, 2014.
References: 
  • Curtis F. Gerald and Patrick O. Wheatley, Applied Numerical Analysis, Pearson, 2003.
  • Gourdin and Boumahrat, Applied Numerical Methods, Prentice Hall of India,2004.
  • Melvin J. Maron and Robert J. Lopez, Numerical Analysis a Practical Approach, Machmillon Publishing Company, New York, 3rd Edition,1991.
  • H.C. Saxena, Finite differences& Numerical analysis, S.Chand, and Co. New Delhi, 2010.
  • B.S. Goel and S.K. Mittal, Numerical Analysis, Pragati Prakashan, Meerut, 2007.
  • Walter Gautschi, Numerical Analysis, Birkhauser Springer US, 2012.
Academic Year: 
2022-2023
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