Subject Matter Expert (Mathematics)

Subject Matter Expert (Mathematics) Interview Questions and Answers

Updated 1 Mar 2021

Q1. How to find integral of complex function?

Ans.

The integral of a complex function can be found using techniques such as contour integration and Cauchy's integral formula.

Contour integration is a powerful technique for evaluating complex integrals.
Cauchy's integral formula relates the value of a complex integral to the values of a function on a closed contour.
Residue theorem is often used to evaluate complex integrals around simple closed contours.
Complex integration requires knowledge of complex analysis and the propertie...read more

Ans.

The domain of a function is the set of all possible input values, while the range is the set of all possible output values.

The domain of the function f(x) = √x is all non-negative real numbers, since the square root of a negative number is undefined.
The range of the function f(x) = √x is all non-negative real numbers, since the square root of a non-negative number is always non-negative.
The domain can be represented as [0, +∞) and the range as [0, +∞).

Ans.

Bernoulli differential equation is a type of first-order ordinary differential equation that can be solved using a substitution method.

Bernoulli differential equation is of the form dy/dx + P(x)y = Q(x)y^n, where n is a constant.
To solve Bernoulli differential equation, a substitution is made to transform it into a linear differential equation.
The substitution u = y^(1-n) is commonly used to transform the equation.
After substitution, the resulting linear differential equation...read more

Ans.

A series converges when the sum of its terms approaches a finite value as the number of terms increases.

A series converges if the sequence of partial sums approaches a finite limit.
Convergence can be determined by analyzing the behavior of the terms in the series.
If the terms of the series decrease in magnitude and approach zero, the series may converge.
Convergence can also be determined using convergence tests such as the ratio test or the comparison test.
Examples of converg...read more

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Ans.

A one-one function is a function in which each element in the domain maps to a unique element in the codomain.

Also known as an injective function.
No two elements in the domain map to the same element in the codomain.
Each element in the codomain has at most one pre-image in the domain.
Example: f(x) = x^2 is not a one-one function, but f(x) = x is a one-one function.