dy/dx - = 1 - y,y(0) = 0 is an example of

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Exponential Function

In mathematics, an exponential function is a function of the form. where b is a positive real number, and in which the argument x occurs as an exponent. For real numbers c and d, a function of the form is also an exponential function, as it can be rewritten as.

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Logarithmic Function

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.
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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Polynomial Function

In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate, x, is x² − 4x + 7
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@zareen said in MTH603 Quiz 1 Solution and Discussion:

While using the Composite Trapezoidal form for integrating y = f(x) in [0,10] which is subdivided in equally spaced interval of width ‘h =2’, then which of the following is the area of associated trapezoidal strip over subinterval:[2,4] ? MTH603

In mathematics, and more specifically in numerical analysis, the trapezoidal rule is a technique … The trapezoidal rule works by approximating the region under the graph of the … {\displaystyle {d^{2}g_{k} \ over dt.

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

(y2 + y4)/2

IR Row Orbital Symmetry function Bonding a1 s(M) s( M) Sigma s(L) (s1 +s2+s3+s4)/2 p(L) (x1+y1+z1−x2− y2+z2−x3+y3 −z3 +x4− y4−z4)/ √ 12 e 1 d(M) dx2 (M)

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

For a function ‘f(x) = x’, with a step size of ‘h=0.01’, which of the following gives the 1st derivative at x =1 by using two point formula? MTH603

approximate the function f (x) = cos x by the series. 2. 4. 2 … An equation f(x)=0 is said to be the algebraic equation in x if it is purely a … between these two points and therefore, a root lies between these two points.

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Y’=(x)=1+Some truncation Error

EXAMPLE 1 Bound for Local Truncation Error Find a bound for the local … the local truncation error for any of the five steps given in Table 6.1.1 by replacing c by …
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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Please share your Quiz

Choose your region. Enter your name. Answer 10 Questions about yourself. Your quiz link will be created. Share your quiz link with your friends. Your friends will …

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@zareen said in MTH603 Quiz 3 Solution and Discussion:

δ = E 1/2 - E 1/2

δ δ. + terms involving high powers of δx1, δx2 are infinitesimal their squares and higher powers … [eh - 1] ∆ex = (eh – 1)( e(x+h) - ex ) = (eh – 1)2 ex. ∴∆2 eax …
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@zareen said in MTH603 Quiz 1 Solution and Discussion:

In Simpson’s 1/3 rule, the global error is of ……………… MTH603

Mth603 Just Final term MCQS (latest quiz included and FAQs and Glossary is also included in this file) Plz. … This preview shows page 1 - 3 out of 46 pages. … True False In Simpson’s 3/8 rule, the global error is of O(h2) O(h3) O(h4) None of …

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Extrapolation

Reff

In mathematics, extrapolation is a type of estimation, beyond the original observation range, the value of a variable on the basis of its relationship with another …

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Interpolation

Reff
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing new data points within the range of a discrete set of known data points.

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Divided difference

Reff

Divided differences is a recursive division process. The method can be used to calculate the coefficients in the interpolation polynomial in the Newton form.

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Which of the following systems of linear equations has a strictly diagonally dominant coefficient matrix?
−x1+12x2+5x3=8
9x1+5x2−3x3=12
2x1−4x2+7x3=−15

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Eigenvalues of a _________ matrix are all real.

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@zareen said in MTH603 Quiz 1 Solution and Discussion:

Eigenvalues of a _________ matrix are all real.

If each entry of an n×n matrix A is a real number, then the eigenvalues of A are all real numbers. False. In general, a real matrix can have a complex number eigenvalue. In fact, the part (b) gives an example of such a matrix.