Applied Mathematics for Electrical Engineering (3130908)

Interpolation

BE | Semester 3 Unit : Interpolation

Q2 (a) Winter-2019 If $f (x) = \frac{1}{x}$ , prepare the table for finite differences and hence find $[a, b]$ and $[a, b, c]$ .

Unit : Interpolation

Q2 (b) Winter-2019 State Newton’s forward formula and use it to find the approximate value of f(1.6),

$x$ $1$ $1.4$ $1.8$ $2.2$

$f (x)$ $3.49$ $4.82$ $5.96$ $6.50$

Unit : Interpolation

Q2 (c ( i )) Winter-2019 Using quadratic Lagrange interpolation, compute $\ln 9.2$ from $\ln 9.0 = 2.1972, \ln 9.5 = 2.2513, \ln 11 = 2.3979$ .

Unit : Interpolation

Q2 (c ( ii )) Winter-2019 State Newton’s backward formula and use it to find the approximate value of f(7.5), if

$x$ $3$ $4$ $5$ $6$ $7$ $8$

$f (x)$ $28$ $65$ $126$ $317$ $344$ $513$

Unit : Interpolation

Q2 (c ( i )) Winter-2019 Using the relation between the operators, prove that, $(1 + ∆) (1 - \nabla) = 1$ .

Unit : Interpolation