What is the primary use of Laplace transforms in differential equations?

• To convert algebraic equations into differential equations

• To solve initial value problems, especially non-homogeneous ones

• To simplify complex numbers

• To find the roots of polynomial equations

Which of the following is a common notation for the Laplace transform of a function of time?

• f(s) to F(t)

• f(s) to F(s)

• f(t) to F(s)

• f(t) to F(t)

What does the inverse Laplace transform do?

• Transforms a function of s back into a function of t

• Transforms a function of t into a function of s

• Solves algebraic equations

• Calculates the derivative of a function

What is the integral definition of the Laplace transform?

• An indefinite integral from zero to infinity

• A definite integral from zero to infinity of f(t) times e^(-st) dt

• An indefinite integral of f(t) times e^(st) dt

• A definite integral from negative infinity to infinity of f(t) dt

Which technique is NOT typically used in computing inverse Laplace transforms?

• Integration by parts

• Partial fractions

• Completing the square

• Using a table of inverse transforms