نمونه سوال محاسبات

Simpson 3/8 Rule For Integration

 

http://mathforcollege.com/nm/mcquizzes/07int/quiz_07int_simpson3by8.pdf

نمونه سوال محاسبات

Linear Regression Problems with Solutions

http://www.analyzemath.com/statistics/linear_regression.html

http://mdm4u1.wetpaint.com/page/Linear+Regression+(good+example)

http://easycalculation.com/statistics/learn-regression.php

Integral Calculus Calculators

Trapezoidal / Trapezium Rule Approximate Numerical Integration

http://easycalculation.com/integration/trapezoidal-rule.php

http://math.la.asu.edu/~surgent/chapter5/New5_4_XBES_June4.pdf.

Simpson's 1/3 Rule Numerical Integration

http://easycalculation.com/integration/simpson-rule.php

http://homepages.math.uic.edu/~hanson/mcs471/pp4.html

Romberg's Method Numerical Integration

http://easycalculation.com/integration/romberg-method.php

نمونه سوال محاسبات

روش تکرار:

http://web.brimsham.com/_includes/attachments/P579/Numerical%20Methods%20Questions.pdf

NEWTON-RAPHSON METHOD

Q2. The Newton-Raphson method formula for finding the square root of a real number R from the equation

is,

 

  

 

 

 

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Q3. The next iterative value of the root of  using Newton-Raphson method, if the initial guess is 3, is 

 1.500

 2.066

 2.167

 3.000

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Q4. The root of the equation f(x)=0  is found by using the Newton-Raphson method.  The initial estimate of the root is x₀=3, andf(3)=5.  The angle the line tangent to the function f(x) makes at x=3 with the x-axis is 57⁰.  The next estimate of the root, x₁ most nearly is 

 -3.247

 -0.2470

 3.247

 6.247

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Q5. The root of is found by using the Newton-Raphson method.  The successive iterative values of the root are given in the table below

Iteration Number	Value of Root
0	2.0000
1	1.6667
2	1.5911
3	1.5874
4	1.5874

The iteration number at which I would first trust at least two significant digits in the answer is

 1

 2

 3

 4

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Q6. The ideal gas law is given by 

      

where where p is the pressure, v is the specific volume, R is the universal gas constant, and T is the absolute temperature.  This equation is only accurate for a limited range of pressure and temperature.  Vander Waals came up with an equation that was accurate for larger ranges of pressure and temperature given by

       

 

where a and b are empirical constants dependent on a particular gas.  Given the value of R=0.08, a=3.592, b=0.04267, p=10 andT=300 (assume all units are consistent), one is going to find the specific volume, v, for the above values.  Without finding the solution from the Vander Waals equation, what would be a good initial guess for v?

 0

 1.2

 2.4

 4.8

FALSE POSITION METHOD

http://mathforcollege.com/nm/mcquizzes/03nle/quiz_03nle_falseposition.pdf

SECANT METHOD

The secant method formula for finding the square root of a real number R from the equation is

 

 

 

 

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Q3..The next iterative value of the root of  using secant method, if the initial guesses are 3 and 4, is

 2.2857

 2.5000

 5.5000

 5.7143

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Q4. The root of the equation f(x)=0  is found by using secant method.  Given one of the initial estimates is x₀=3 and f(3)=5, and the angle the secant makes with the function f(x) is 57⁰, the next estimate of the root, x₁, is

 -3.2470

 -0.24704

 3.2470

 6.2470

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Q5. For finding the root of sin(x)=0, the following choice of initial guesses would not be appropriate.

  Π/4 and Π/2

  Π/4 and 3Π/4

  -Π/2 and Π/2

  Π/3 and Π/2

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Q6. When drugs are given orally to a patient, the drug concentration c in the blood stream is given by a formula where K is dependent on parameters such as the dose administered while a is dependent on the absorption  and elimination rates of the drug.  If  K=2 and a=0.25, where t is in seconds and c is in mg/ml, the time at which the maximum concentration is reached is given by the solution of the equation,