Numerical Analysis
This course will enable the students to -
- Understand different numerical methods to obtain approximate solutions to mathematical problems.
- learn numerical methods to solve interpolation based problems, ordinary differential equations, various numerical root finding problems.
Course Outcomes (COs):
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Course Code |
Course Title |
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CMAT513 |
Numerical Analysis(Theory)
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The students will be able to – CO75: Apply various interpolation methods and finite difference concepts to solve interpolation problems for equal intervals. CO76: Describe the concept of central difference, Numerical differentiation and be able to solve interpolation problems for unequal intervals. CO77: Understand the concept of Numerical Integration and be able to solve related problems. CO78: Apply numerical methods to find our solution of algebraic equations using different methods under different conditions CO79: Solve the system of linear equations and ordinary differential equations by numerical methods. CO80: 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
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(Note: Non-Programmable scientific calculator up to 100 MS is permitted)
Differences, Relation between differences and derivatives, Difference of polynomials, Factorial notation, Newton’s forward and backward interpolation formula (with proof).
Divided differences: Newton’s and Lagrange’s divided differences formulae. Central differences: Gauss’s, Sterling’s and Bessel’s interpolation formulae, Numerical differentiation.
Numerical integration: Newton-Cotes quadrature formula, Trapezoidal formula, Simpson’s 1/3rd and 3/8th formulae, Gaussian integration.
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.
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.
- 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.
- 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.
