Subject Matter Expert (Mathematics) Interview Questions and Answers

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

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, +∞).

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

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