Issued: Thursday, January 24, 2019
Due: Tuesday, February 5, 2019
Problem Set #2
First Order Differential Equations
The function y(t) obeys the differential equation
yt 2u 1 t
for both negative and positive times.
Given the initial condition y(0) = 0 you are required to find an expression for y(t) for t > 0.
Recall that the function u-1(t) is a unit step function, defined by
u-1(t) = 0 ; t < 0
u-1(t) = 1 ; t > 0 or t = 0.
Write down the differential equation for t > 0.
Solve the differential equation in i).
Provide a rough sketch of the solution.
Continuity in three dimensional Cartesian coordinates
In three dimensional Cartesian coordinates the continuity equation is of the form
C x, y, z, t
x, y, z, t
x, y, z, t x x, y, z, t i y x, y, z, t ˆj z x, y, z, t k
x, y, z, t y x, y, z, t z x, y, z, t
x, y, z, t x
Outline a derivation of this equation.
Exercise 3.18 From Weiss
Problems 3.1 and 3.2 From Weiss
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