This course will enable the students to -
Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Course Code |
Course Title |
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24CMAT 513 |
Numerical Analysis(Theory)
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CO100: Apply various interpolation methods and finite difference concepts to solve interpolation problems for equal intervals. CO101: Outline the concept of central difference, and numerical differentiation and be able to solve interpolation problems for unequal intervals. CO102: Explain the concept of numerical integration and be able to solve related problems. CO103: Apply numerical methods to find the solution of algebraic equations using different methods under different conditions CO104: Solve the system of linear equations and ordinary differential equations by numerical methods. CO105: Contribute effectively in course-specific interaction.
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Approach in teaching: Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Assigned tasks |
Quiz, Individual and group projects, Open Book Test, Semester End Examination
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Differences, Relation between differences and derivatives, Difference of polynomials, Factorial notation, Newton’s forward and backward interpolation formula (with proof).
Newton’s and Lagrange’s divided differences formulae. Central differences: Gauss’s, Sterling’s and Bessel’s interpolation formulae, Numerical differentiation.
Newton-Cotes quadrature formula, Trapezoidal formula, Simpson’s 1/3rd and 3/8th formulae, Gaussian integration.
Inverse Interpolation , Bisection method, Regula-falsi method, Method of iteration and Newton Raphson’s Method, Newton’s iterative formula for obtaining square and inverse square root.
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.
e- RESOURCES
JOURNALS
Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/numerical-analysis-12
[2] https://nptel.ac.in/courses/111106101
[3] https://perhuaman.files.wordpress.com/2014/07/metodos-numericos.pdf
[4] http://www.ru.ac.bd/stat/wp-content/uploads/sites/25/2019/03/107_03_Scarborough_Numerical-Mathematical-Analysis.pdf
[5] http://www.math.science.cmu.ac.th/docs/qNA2556/ref_na/Katkinson.pdf
[6] https://www.siam.org/publications/journals/siam-journal-on-numerical-analysis-sinum
[7] https://www.springer.com/journal/12258
[8] https://onlinelibrary.wiley.com/journal/10970207
[9] https://maths.iisuniv.ac.in/academic-year/2024-2025