SpeedLabs Faculty of Mathematics Interview Questions and Answers

I rate myself highly in learning new apps.

• I am a quick learner and can adapt to new interfaces easily.

• I am comfortable exploring new features and functionalities.

• I am able to troubleshoot and solve problems on my own.

• For example, I recently learned how to use a new budgeting app and was able to customize it to my needs within a few hours.

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.

• Afte...read more

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 integratio...read more

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.

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

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...read more