'Numerical Methods' is a course offered in the fifth semester of B. Tech. in Mechanical Engineering program at School of Engineering, Amrita Vishwa Vidyapeetham.
Unit 1
Review of Errors: Accuracy and Precision, round-off error and truncation error. (Sec. 2.2-2.4)
Roots of Transcendental and Polynomial Equations: Bisection method, Iteration methods based on first degree equation, Rate of convergence, System of nonlinear equations. (Sec. 4.2, 4.3, 5.1-5.3, 5.5)
Review of Matrix Algebra: Systems of Equations, Eigenvalues and Eigen vectors.
Solution of System of Linear Algebraic Equations: Gauss Elimination and Gauss Jordan Methods. Iteration Methods. Eigenvalues and Eigenvectors: Jacobi Method for symmetric matrices and Power Method for arbitrary matrices. (Sec. 8.2, 8.7, 10.2, 22.2)
Unit 2
Interpolation and Approximation: Lagrange and Newton interpolation for unequal intervals, Finite difference operators, Interpolating polynomials using finite differences. (Sec. 13.1 – 13.4, 13.6)
Unit 3
Review of Ordinary Differential Equations:
Solutions of Ordinary Differential Equations: Initial value problems - Single step methods - Taylor Series Method, Second , Third and Fourth order Runge Kutta Methods. (Sec.20.1 – 20.3, 21.2)
Lab-Implementation of these methods: MATLAB or EXCEL or Free and Open Source Software (FOSS) tools like R-programming and Scilab.
- Steven Chapra and Raymond Canale, Numerical Methods for Engineers, McGraw Hill, 2007.
- M. K. Jain, S. R. K. Iyengar and R. K. Jain, Numerical methods for Scientific and Engineering Computation, New Age International Publishers, Fifth edition, 2007.
- C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis, 7th edition, Addison Wesley, 2009.
- Rizwan Butt, Introduction to Numerical Analysis Using MATLAB, Jones and Bartlett Publisher, 2010.
- Abdelwahab Kharab, Ronald B., An Introduction to Numerical Methods: A MATLAB Approach, Third Edition, CRC Press, 2012.
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