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Lecture 10
Analysis
a ys s o
of Qu
Quiz #
#1
Sample Problems for Miderm Exam
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
Slide 1
ECE 7030 Summer 2007 Quiz #1
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Problem #1, Set Theory
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Problem #2, Relations and Mappings
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Problem #2, continued
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Problem #3, Math Logic
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Problem #3, continued
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Problem #4, Algebraic Structures
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Problem #4, continued
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Problem #5, Linear Mappings and Matrices
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Problem #5, continued
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Additional Examples:
Last Semester Midterm Exam
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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ECE-7030 Fall 2006 MidTerm Exam
Open books, open notes
1. (Set theory, 6pt) Given that (A ∪ B) ⊂ (C ∩ D), is it correct that (A ∩ B) ⊂ (C ∪ D) ? Draw an
illustration.
2. ((Relations and mappings,
pp g , 6pt)
p ) Consider a binary
y relation B ⊂ C 2 such that
((u, v) ∈ B) ⇔ (u ∈ C) ∧ (v ∈C) ∧ (v = cos(u)). Is binary relation v = b(u) a mapping? If yes, define
the domain, codomain, range. Find if it is an injection and whether it is a surjection. For given v ∈C
find the algorithm to recover u ∈C such that (u, v) ∈ B.
3 (Math Logic,
3.
Logic 6pt) Find the truth value of the formula
((A ∨ B) → (C ∧ D )) → ((A ∧ B ) → (C ∨ D ))
4. (Algebraic structures, 6pt) In the set of real functions of real variable f(x) defined over the interval
x ∈ [0, 1], consider a subset such that d4f/dx4 = f(x) and f(0) = 0. Does this subset form a linear
subspace? If yes, find its dimension and basis.
5. (Linear Mappings and Matrices, 6pt) Find the LU-decomposition of the matrix
⎛ 3 2 −1⎞
⎜
ˆA = ⎜ 6 1 0 ⎟
⎜− 9 0 2 ⎟
⎝
⎠
Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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Ivan Avrutsky, ECE7030, Math Methods in Engineering, Lecture 10, Summer 2007
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