ECE 202H
Spring 2011
Page
1
of
2
ECE 202H:
Homework #3
Due:
3 February 2011 at 1:30 PM
(5 Points)
Questions that are marked with a circled asterisk
⊛
are to be submitted at the beginning of class on the specified due
date.
All other problems are provided for practice and are representative of problems that may be included on exams.
Solutions to all problems will be posted after the due date.
SHOW ALL WORK!
Foundational Mathematics
1.
⊛
The Chain Rule for a function of two variables states that if
𝑥
=
𝑥
(
𝑡
)
and
𝑦
=
𝑦
(
𝑡
)
where
𝑥
and
𝑦
are
differentiable at
𝑡
and also
𝑤
=
𝑓
(
𝑥
,
𝑦
)
is differentiable at
(
𝑥
(
𝑡
),
𝑦
(
𝑡
))
, then
𝑤
=
𝑓
(
𝑥
(
𝑡
),
𝑦
(
𝑡
))
is differentiable at
𝑡
and its derivative is given by
𝜕𝑤
𝜕𝑡
=
𝜕𝑤
𝜕𝑥
𝜕𝑥
𝜕𝑡
+
𝜕𝑤
𝜕𝑦
𝜕𝑦
𝜕𝑡
Suppose that
𝑧
(
𝑡
)
is differentiable at
𝑡
and
𝑤
=
𝑓
((
𝑥
(
𝑡
),
𝑦
(
𝑡
),
𝑧
(
𝑡
))
is differentiable at
(
𝑥
(
𝑡
),
𝑦
(
𝑡
),
𝑧
(
𝑡
))
.
State the
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 Spring '11
 TALAVAGE
 Calculus, Derivative, Fundamental Theorem Of Calculus, LTI system theory, Impulse response

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