## Quiz: Excel Differential Equations

**1.** How does the length of the time step (difference in time between successive steps) influence the accuracy of Euler's method?

**A.**Increasing the time step (larger steps) makes the solution more accurate

- Incorrect. Increasing the time steps makes the solution less accurate

**B.**Increasing the time step (larger steps) makes the solution less accurateβ

- Correct.

**C.**Increasing the time step (larger steps) does not change the solution

- Incorrect. Numerical solutions are affected by the time-step length.

**2.** A differential equation has at least one term that contains the derivative of a variable (such as temperature, concentration, or velocity) with respect to another variable (such as time or distance). One example is: dx/dt = v where x is position, t is time, and v is velocity.

**A.**True

- Correct.

**B.**False

- Incorrect.

**3.** What does it mean to discretize a differential equation? (Select two correct answers)

**A.**It is the process of selecting specific points to seek a solution to an otherwise continuous problem.

- Correct. Discrete time points are a sampling of values along a continuous range.

**B.**It gives an analytic (exact) solution to the differential equation once solved.β

- Incorrect. Numerical (discrete) solutions have calculation error that analytic solutions do not have.

**C.**Time steps are chosen to calculate a solution.

- Correct. Numerical solutions require discretization where the solution is obtained at specific time points.