حل مسایل محاسبات عددی

جهت حل سوال اول به لینک زیر بروید و صحت پاسخهای خود را بررسی نمایید.

(تابع را cosx-  قرار دهید و حدس اولیه خود را مشخص نمایید.)

http://wood.mendelu.cz/math/maw-html/?lang=en&form=banach

جهت حل سوال دوم

http://keisan.casio.com/has10/SpecExec.cgi

جهت حل سوال سوم:

http://nastyaccident.com/calculators/calculus/trapezoidalRule

http://nastyaccident.com/calculators/calculus/viewCalculators

نمونه سوالات تستی محاسبات عددی

Q1. The goal of forward elimination steps in the Naïve Gauss elimination method is to reduce the coefficient matrix to a (an) _____________  matrix.

 

diagonal

identity

lower triangular

upper triangular

---

Q2. Division by zero during forward elimination steps in Naïve Gaussian elimination of the set of equations [A][X]=[C] implies the coefficient matrix [A] is

invertible

nonsingular

not determinable to be singular or nonsingular

singular

---

Q3. Using a computer with four significant digits with chopping, Naïve Gauss elimination solution to

is

x₁ = 26.66; x₂ = 1.051

x₁ = 8.769; x₂ = 1.051

x₁ = 8.800; x₂ = 1.000

x₁ = 8.771; x₂ = 1.052

---

Q4. Using a computer with four significant digits with chopping, Gauss elimination with partial pivoting solution to

is

  x₁ = 26.66; x₂ = 1.051

  x₁ = 8.769; x₂ = 1.051

  x₁ = 8.800; x₂ = 1.000

  x₁ = 8.771; x₂ = 1.052

---

Q5. At the end of forward elimination steps of Naïve Gauss Elimination method on the following equations

 

 

 

the resulting equations in the matrix form are given by

 

 

 

The determinant of the original coefficient matrix is

0.00

---

Q6. The following data is given for the velocity of the rocket as a function of time.  To find the velocity at t=21 s, you are asked to use a quadratic polynomial, v(t)=at²+bt+c to approximate the velocity profile.

t	(s)	0	14	15	20	30	35
v(t)	m/s	0	227.04	362.78	517.35	602.97	901.67

The correct set of equations that will find a, b and c are

نمونه سوالات تستی محاسبات عددی

Q1. The bisection method of finding roots of nonlinear equations falls under the category of a (an) ______  method.

openbracketinggraphical

random

---

Q2. If for a real continuous function f(x), you have f(a)f(b)<0, then in the interval [a,b] for f(x)=0, there is (are) one rootan undeterminable number of rootsno rootat least one root

---

Q3. Assuming an initial bracket of [1,5] , the second (at the end of 2 iterations) iterative value of the root of  is0.01.52.03.0

---

To find the root of f(x)=0, a scientist uses the bisection method.  At the beginning of an iteration, the lower and upper guesses of the root are x_l and x_u, respectively.  At the end of this iteration, the absolute relative approximate error in the estimated value of the root would be

 

  

---

For an equation like , a root exists at x=0.  The bisection method cannot be adopted to solve this equation in spite of the root existing at  x=0  because the function 
is a polynomialhas repeated roots at x=0is always non-negativehas a slope of zero at x=0

---

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 range 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?01.22.44.8

دانلود نرم افزار محاسبات ماتریسی

نرم افزاری سبک و آسان برای انواع محاسبات ماتریسی اعم از دترمینان، وارون ، مقادیر ویژه، بردار های ویژه و ..

برای دانلود کلیک کنید.