Quiz: Excel Differential Equations
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(:title Quiz: Excel Differential Equations:)
(:keywords quiz, test, Python, variable, ODE, differential, Euler, expression, introduction, course:)
(:description Learning assessment on Excel solution for differential equations with explicit Euler's method.:)
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'''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
-->(:toggle hide q1a button show="Select":)
(:div id=q1a:)
-->%red%Incorrect.%% Increasing the time steps makes the solution less accurate
(:divend:)
->'''B.''' Increasing the time step (larger steps) makes the solution less accurate
-->(:toggle hide q1b button show="Select":)
(:div id=q1b:)
-->%blue%Correct.%%
(:divend:)
->'''C.''' Increasing the time step (larger steps) does not change the solution
-->(:toggle hide q1c button show="Select":)
(:div id=q1c:)
-->%red%Incorrect.%% Numerical solutions are affected by the time-step length.
(:divend:)
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'''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
-->(:toggle hide q2a button show="Select":)
(:div id=q2a:)
-->%blue%Correct.%%
(:divend:)
->'''B.''' False
-->(:toggle hide q2b button show="Select":)
(:div id=q2b:)
-->%red%Incorrect.%%
(:divend:)
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'''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.
-->(:toggle hide q3a button show="Select":)
(:div id=q3a:)
-->%blue%Correct.%% Discrete time points are a sampling of values along a continuous range.
(:divend:)
->'''B.''' It gives an analytic (exact) solution to the differential equation once solved.
-->(:toggle hide q3b button show="Select":)
(:div id=q3b:)
-->%red%Incorrect.%% Numerical (discrete) solutions have calculation error that analytic solutions do not have.
(:divend:)
->'''C.''' Time steps are chosen to calculate a solution.
-->(:toggle hide q3c button show="Select":)
(:div id=q3c:)
-->%blue%Correct.%% Numerical solutions require discretization where the solution is obtained at specific time points.
(:divend:)
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(:keywords quiz, test, Python, variable, ODE, differential, Euler, expression, introduction, course:)
(:description Learning assessment on Excel solution for differential equations with explicit Euler's method.:)
----
'''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
-->(:toggle hide q1a button show="Select":)
(:div id=q1a:)
-->%red%Incorrect.%% Increasing the time steps makes the solution less accurate
(:divend:)
->'''B.''' Increasing the time step (larger steps) makes the solution less accurate
-->(:toggle hide q1b button show="Select":)
(:div id=q1b:)
-->%blue%Correct.%%
(:divend:)
->'''C.''' Increasing the time step (larger steps) does not change the solution
-->(:toggle hide q1c button show="Select":)
(:div id=q1c:)
-->%red%Incorrect.%% Numerical solutions are affected by the time-step length.
(:divend:)
----
'''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
-->(:toggle hide q2a button show="Select":)
(:div id=q2a:)
-->%blue%Correct.%%
(:divend:)
->'''B.''' False
-->(:toggle hide q2b button show="Select":)
(:div id=q2b:)
-->%red%Incorrect.%%
(:divend:)
----
'''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.
-->(:toggle hide q3a button show="Select":)
(:div id=q3a:)
-->%blue%Correct.%% Discrete time points are a sampling of values along a continuous range.
(:divend:)
->'''B.''' It gives an analytic (exact) solution to the differential equation once solved.
-->(:toggle hide q3b button show="Select":)
(:div id=q3b:)
-->%red%Incorrect.%% Numerical (discrete) solutions have calculation error that analytic solutions do not have.
(:divend:)
->'''C.''' Time steps are chosen to calculate a solution.
-->(:toggle hide q3c button show="Select":)
(:div id=q3c:)
-->%blue%Correct.%% Numerical solutions require discretization where the solution is obtained at specific time points.
(:divend:)
----
