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The University of Sydney
School of Mathematics
& Statistics
Intro to PDEs
MATH2065
MID TERM QUIZ
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MATH2065
Introduction to Partial Differential
Equations
Ordinary Differential Equations Summary
Homogeneous Linear ODEs
The general second-oder linear homogeneous ordinary differential equation is
y 00 + a(x) y 0 + b(x) y = 0 .
Its general solution takes
MATH2065
Introduction to Partial Differential
Equations
Semester 2 Practice Questions (Week 9)
1. Given the function defined on [, ] by
0,
f (x) =
x,
< x < 0
0<x<
with period 2, f (x + 2) = f (x).
(a) Sketch f (x) for 3 < x < 3
(b) Calculate the Fourier
MATH2065
Introduction to Partial Differential
Equations
Semester 2 Practice Questions (Week 11)
1. Find the Fourier Transforms of:
(a)
f (x) =
2x
e
x<0
e3x
x>0
(b)
f (x) =
1 |x|
2. Show that
1<x<1
0 elsewhere
1 k
Fcfw_f (x) = f
,
where > 0 and f(k) =