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UNIVERSITY OF PETROLEUM & ENERGY STUDIES, DEHRADUN

Department of Mathematics

Course: B. Tech. IV Semester Branch: FSE, MS-NT, ICE, EE

Subject: Applied Numerical Methods Subject Code: MATH 301

Tutorial-1

1. Prove the following relations where the operators have their usual meanings:

(i) cosh 2u where u hD (ii) 2

21 12 4

(iii) 2 2 2 3 3 4 47 ........

12h D h D h D (iv)

22

2 21 12

2. The following table gives the pressure of a steam at a given temperature. Using Newtons

formula, compute the pressure for a temperature of 1420C

Temperature, 0C 140 150 160 170 180

Pressure, kgf/cm2

3.685 4.854 6.302 8.076 10.225

3. The following table give the marks secured by 492 students in Mathematics;

Marks No. of Students

210 43 54 74 32 79

Find out;

(i) Number of students who secured more than 48 but less than 50 marks.

(ii) Number of students who secured less than 48 but not less than 45.

4. The table gives the distances in nautical miles of the visible horizon for the given heights in feet

above the earth's surface :

Height (x) 100 150 200 250 300 350 400

Distance (y)

10.63 13.03 15.04 16.81 18.42 19.90 21.27

Find the value of y when x = 375 ft.

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5. The following are the mean temperatures (F) on three days, 30 days apart round the periods

of summer and winter. Estimate the approximate dates and values of maximum temperature in

summer and minimum temperature in winter.

Day

Summer Winter

Date Temperature Date Temperature

0

30

60

15 June

15 July

14 August

58.8

63.4

62.5

16 December

15 January

14 February

40.7

38.1

39.3

6. The function ( )y f x is given at the points (7, 3), (8, 1), (9, 1) and (10, 9). Find the value of

y for 9.5x using Lagranges interpolation formula.

7. Apply Stirlings formula to find the value of (1.22)f from the following table which gives the

value of2

2

0

1( )

2

xx

f x e dx

at intervals of 0.5x from 0x to 2x .

x 0 0.5 1.0 1.5 2.0

( )f x 0 0.191 0.341 0.433 0.477

8. Using Gausss backward formula, estimate the number of persons earning wages between $ 60

and $ 70 from the following data:

Wages ($): Below 40 4060 6080 80100 100120

Number of people: 250 120 100 70 50

(in thousands)

9. Given the record of height from the earths surface for a rocket at intervals of time in a laboratory

of ISRO. Assuming that the height of atmosphere is 80 km, find the time when the rocket

leaves the atmosphere, by using Bessels formula.

Height (km) 65 75 85 95

Time (sec) 30 34 36 37

10. Estimate the production for 1964 and 1966 from the following data:

Year: 1961 1962 1963 1964 1965 1966 1967

Production: 200 220 260 350 430