CP508: Numerical Methods Teaching Scheme Credits L
T
P
C
2
0
2
4
Marks Distribution Theory Marks Practical Marks ESE
CE
ESE
CE
70
30
30
20
Total Marks 150
Course Content: Sr. No.
1.
Topics Numerical Analysis and Computers:
Teaching Hrs. 02
Concepts and definitions; Representation of numbers in computers; types of errors; Basic sources of errors; Significant figures; accuracy and precision. 2.
Approximate Solutions of Nonlinear Equations and System of Linear Equations:
06
Bisection method; Method of false position; Newton - Raphson method; Secant; Successive approximation method; Polynomial division; Baristow method. 3
Numerical Solution of Partial Differential Equations:
06
Direct methods: Gauss elimination, Gauss Jordan and Crout’s LUfactorization methods; Indirect methods: Gauss Seidel and Jacobi’s methods. 4
Interpolation, Curve Fitting:
06
Finite differences of various orders; difference table; Newton’s formulae for interpolation; Lagrange’s Interpolation formula; Least square curve fitting. 5
Numerical Solution of Ordinary Differential Equation:
Single step methods – Taylor series, Error estimate for Euler’s method; Runge - Kutta method of 2nd order; Predictor corrector methods – Adams – Moulton method, Milne’s method.
05
6
05
Numerical Differentiation and Integration:
Numerical Differentiation; trapezoid rule; Simpson’s rules; Newton – cotes quadrature formula; Gaussian integration; Moving average; Mean Square Error (MSE). Total Hrs.
30
Reference Books: 1. S. S. Sastry, “Introductory Methods of Numerical Analysis”, Prentice Hall of India. 2. S. C. Chapra and R. P. Canale, “Numerical Methods for Engineers”, McGrow Hill International Edition. 3. Rajaraman V., ss“Computer Oriented Numerical Methods”, Prentice Hall of India. 4. M. K. Jain, S.R.K. Iyengar, R. K. Jain, “Numerical Methods for Scientific and Engineering Computation”, New Age International publishers. 5. Veerarajan & Ramchnadran, “Numerical Methods with programs in C and C++”, Tata McGraw Hill. 6. Dr. B. S. Grewal, “Numerical Methods in Engineering and Science”, Khanna Publication.
