### Title Numerical Analysis (Code 09010603)

S.No | Unit | Contents | Learning Objective | Teaching Guidelines | Methodology | Time
(Hrs) |

1 | One | 1. Finite difference operators and their relations
2. Finiding the missing terms and effect of error in a difference tabular values 3. Interpolation with equal intervals 4. Interpolation with unequal intervals 5. Lagrange’s interpolation formulae, Hermite formula |
Students will be able to
To study the difference operators, and Interpolation with equal and unequal intervals |
Lecture should be so effective so that the students can grasp the topic easily | Lecture
Seminar Discussion Assignments Seminar Class Tests |
10 |

2 | Two | · Central Differences: Gauss forward and Gauss’s backward interpolation formulae
· Sterling, Bessel Formula · Probability distribution of random variables, Binomial, Poisson’s and Normal distribution · Numerical differentiation: Derivative of a function using interpolation formulae as studied in section-I &II · Eigen value Problems: Power method, Jacobi’s method · Given’s method, House Holder’s method · QR method, Lanczos method |
Students will be able to
Understand Central difference interpolation, Differentiation of functions with numerical values and Eigen value and Eigen vectors |
Lecture should be so effective so that the students can grasp the topic easily | Lecture
Seminar Discussion Assignments Seminar Class Tests Evaluation of Assignements |
20 |

3 | Three | · Numerical integration: Newton’s Cote’s Quadrature formula
· Trapezoidal, Simpon’s one-third and three-eigth rule · Chebyehev formula, Gauss Quadratic formula · Numerical solution of ODEs: Single-step methods-Picard’s method, Taylor’s series method · Euler’s method, Runge-Kutta method · Modified Euler’s method · Milne-Simpson’s method |
Students will be able to
Understand Numerical integration and Numerical solutions of ODEs with different methods |
Lecture should be so effective so that the students can grasp the topic easily | Lecture
Seminar Discussion Assignments Seminar Class Tests Evaluation of Assignements |
15 |