MT-334 NUMERICAL METHODS FOR ENGINEERS
CREDIT HOURS
Theory = 3
Practical = 0
COURSE LEARNING OUTCOMES (CLOs)
| S. No. | CLOs | PLO | Taxonomy |
| 1 | To be displayed. | TBD |
TBD |
| 2 | To be displayed. | TBD | TBD |
| 3 | To be displayed. | TBD | TBD |
| 4 | To be displayed. | TBD | TBD |
| 5 | To be displayed. | TBD | TBD |
COURSE CONTENT
- Error Analysis: Error analysis, Types of error, Sources of error, Norms of vectors and matrices, single and double precision, absolute error, round off error, absolute relative error, absolute relative percentage error
- Interpolation and Curve Fitting: Newton forward, backward, and central difference interpolation; Lagrange’s interpolation; error in interpolation; curve fitting; applications in engineering
- Numerical Differentiation and Integration: Derivation of numerical differentiation of first order and second order derivatives using two points, three points, and five points formulae along with its application in engineering, Numerical integration: Trapezoidal rule, Simpson’s rules, Composite Trapezoidal Simpson Rules and Romberg integration, applications in engineering
- Numerical Solutions of a System of Linear Equations: Solution of system of linear algebraic equations, Gauss elimination method, LU factorization, Solution of system of linear equations by Jacobi, Gauss Seidel and SOR methods, Tridiagonal solver, applications in engineering
- Numerical Solutions for Nonlinear Equations: Bisection method, Regula Falsi method, Newton-Raphson method, Secant method, Convergence analysis of these methods, applications in engineering
- Numerical Methods for Initial Value Problems (IVPs) and Boundary Value Problems (BVPs): Euler’s method and its variations, Taylor’s higher order methods, Runge-Kutta methods of order 2, 3, and 4, Stiff ODEs, Error analysis, consistency, stability and convergence, numerical solution of system of ODEs, Numerical solution of BVPs by Finite Difference Method, Applications in engineering
- Numerical Methods for Computing Eigenvalues: Eigenvalues and Eigenvectors of matrix, power method, inverse power method, Shifted inverse power method, applications in engineering
- Numerical Optimization: Unconstrained Optimization, Golden search ratio, Lagrange Multipliers, Method of steepest ascent and descent, applications in engineering disciplines
RECOMMENDED BOOKS
Text Book(s)
- Steven Chapra, Raymond Canale, ‘Numerical Methods for Engineers’, 8th ed., McGraw Hill, 2020.
Reference Book(s)
- Qingkai Kong, Timmy Siauw, Alexandre Bayen, ‘Python Programming and Numerical Methods: A Guide for Engineers and Scientists’, 1st ed., Academic Press, 2020.
*For details of Taxonomy Levels CLICK HERE
