PDE: Heat & Wave Quiz

Froggy Jumps

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Test basics of PDEs.

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mocha

Malaysia

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Froggy Jumps PDE: Heat & Wave QuizOnline version Test basics of PDEs. by mocha 1 What does α in the heat equation signify physically? a Electrical conductivity b Thermal diffusivity c Wave speed 2 Which equation models wave propagation in a string (1D)? a ∂²u/∂t² = c² ∂²u/∂x² b ∂u/∂t = α ∂²u/∂x² c ∂u/∂t = c ∂u/∂x 3 In separation of variables for the heat equation, u(x,t) = X(x)T(t), what ODE does T(t) satisfy? a dT/dt = λ T b d²T/dt² = -λ T c dT/dt = -λ α T 4 What boundary condition is common for rod problems in PDEs? a u_x(0,t) = u_x(L,t) = 0 b u(0,t) = u(L,t) = 0 c ∂u/∂t(0,t) = 0 5 Which term appears in the heat equation but not in the pure wave equation? a Spatial derivative ∂u/∂x b Second time derivative ∂²u/∂t² c First time derivative ∂u/∂t 6 What is the physical interpretation of the wave equation? a describes vibrations and signals b describes diffusion of heat over time c describes chemical reactions 7 Which method is commonly used to solve both PDEs on bounded domains? a Separation of variables b Laplace transform only c Finite differences only

Froggy Jumps

PDE: Heat & Wave QuizOnline version

Test basics of PDEs.

by mocha

What does α in the heat equation signify physically?

Electrical conductivity

Thermal diffusivity

Wave speed

Which equation models wave propagation in a string (1D)?

∂²u/∂t² = c² ∂²u/∂x²

∂u/∂t = α ∂²u/∂x²

∂u/∂t = c ∂u/∂x

In separation of variables for the heat equation, u(x,t) = X(x)T(t), what ODE does T(t) satisfy?

dT/dt = λ T

d²T/dt² = -λ T

dT/dt = -λ α T

What boundary condition is common for rod problems in PDEs?

u_x(0,t) = u_x(L,t) = 0

u(0,t) = u(L,t) = 0

∂u/∂t(0,t) = 0

Which term appears in the heat equation but not in the pure wave equation?

Spatial derivative ∂u/∂x

Second time derivative ∂²u/∂t²

First time derivative ∂u/∂t

What is the physical interpretation of the wave equation?

describes vibrations and signals

describes diffusion of heat over time

describes chemical reactions

Which method is commonly used to solve both PDEs on bounded domains?

Separation of variables

Laplace transform only

Finite differences only

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PDE: Heat & Wave Quiz

Froggy Jumps

About this activity

Created by

Download the paper version to play

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PDE: Heat & Wave QuizOnline version

by mocha

What does α in the heat equation signify physically?

Which equation models wave propagation in a string (1D)?

In separation of variables for the heat equation, u(x,t) = X(x)T(t), what ODE does T(t) satisfy?

What boundary condition is common for rod problems in PDEs?

Which term appears in the heat equation but not in the pure wave equation?

What is the physical interpretation of the wave equation?

Which method is commonly used to solve both PDEs on bounded domains?

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