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First-day Handout
Fall 2015
M 427J Differential Equations with Linear Algebra
Instructor:
Office Hours:
Text:
Class Time:
Discussion Time:
Dr. Bill Wolesensky, RLM 13.160, wolesensky@math.utexas.edu
MWF 11:00 12:00 or by appointment
Differential Equations
First-day Handout
Fall 2015
M 427J Differential Equations with Linear Algebra
Instructor:
Office Hours:
Text:
Class Time:
Discussion Time:
Dr. Bill Wolesensky, RLM 13.160, wolesensky@math.utexas.edu
MWF 11:00 12:00 or by appointment
Differential Equations
M427J Sample Exam 1
NO NOTES. NO CALCULATORS. I WONT TAKE QUESTIONS ABOUT THESE PROBLEMS.
1. Find the general solution of (y x3 ) dx + (x + y 3 ) dy = 0.
2. Find the general solution of y +
2t
cot t
y=
.
2
1+t
1 + t2
3. Find the general solution of y + 16
Solutions to evens, Section 2.5
2. You need to consider two cases for . The rst case is when
y(t) = c1 e
where
A=
When
=
2
2t
+ c2 te
2t
6=
2: This gives
+ (At + B) e
1
; and B =
+4 +4
( + 2)(
2
t
2
:
+ 4 + 4)
2; your guess should now be
yp = t2 (At + B)e
Solutions to evens, Section 2.2.1
2.
y(t) = e
3
4t
4.
y(t) = e
1
8t
"
"
c1 cos
c1 cos
p
23
t
4
p
15
t
8
!
!
+ c2 sin
+ c2 sin
p
23
t
4
!#
p
!#
p
!#
15
t
8
6.
y(t) = e
8.
y(t) = e
1
4t
"
c1 cos
p
t
sin(2t)
23
t
4
1
!
+ c2 sin
23
t
4
Solutions to evens, Section 1.9
2.
My
= Nt
=) My Nt = 0
Z
=)
My Nt dy = k(t)
Z
=) M
Nt dy = k(t)
4.
h(t; y) = y + tety + t + C
6.
h(t; y) =
1 2 t
y e
2
ye2t = C
:
8.
t2 cos y + t3 y
12.
h(t; y) =
16.
h(t; y) =
1 2
y =
2
2
1 2 1 2ty
t + e =C
2
2
d
y 2 cos
Chapter 32The Reception and Transmission of Extracellular Information
MULTIPLE CHOICE
1. Hormones and other signal molecules bind with _ affinities to their receptors and are produced at
concentrations _ their KD values.
a. low; far above
b. moderate; far
Chapter 30Protein Synthesis
MULTIPLE CHOICE
1. The adapter molecule that interacts specifically with both nucleic acids and amino acids is:
a. rRNA.
b. tRNA.
c. mRNA.
d. ssRNA.
e. all are true.
ANS: B
PTS: 1
2. Amino-acyl-tRNA synthetases catalyze the rea
Chapter 31Completing the Protein Life Cycle: Folding, Processing, and Degradation
MULTIPLE CHOICE
1. The information for folding each protein into its unique three-dimensional architecture resides within
its _.
a. primary structure
b. amino acid content
c
Chapter 29Transcription and the Regulation of Gene Expression
MULTIPLE CHOICE
1. Both prokaryotes and differentiated eukaryotic cells express _ of their genes at any given time in
the process called _.
a. a small number; transcription
b. a small number; t
Chapter 26The Synthesis and Degradation of Nucleotides
MULTIPLE CHOICE
1. All of the following statements about nucleotides are true EXCEPT:
a. They are produced by nearly all organisms.
b. The rate of proliferation of a cell can determine the amount of D
Chapter 25Nitrogen Acquisition and Amino Acid Metabolism
MULTIPLE CHOICE
1. What is nitrogen fixation?
a. The reduction of NO3 to NH4+.
b. The formation of NH4+ from N2 gas.
c. The oxidation of NH4+ to N2.
d. The oxidation of NH4+ to NO3.
e. The formation
Version 238/ADCDC Quiz 1 Lyon (52635) This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. There is only one try for each question - no retries for answers on this quiz.