CHAPTER
4
Higher Order Linear Equations
4.1
2. We will rst rewrite the equation as y + (sin t/t)y + (3/t)y = cos t/t. Since
the coecient functions p1 (t) = sin t/t, p2 (t) = 3/t and g(t) = cos t/t are continuous
for all t = 0, the solution is sure to exis

CHAPTER
3
Second Order Linear Equations
3.1
3. Let y = ert , so that y = r ert and y = r2 ert . Direct substitution into the
dierential equation yields (6r2 r 1)ert = 0 . Since ert = 0, the characteristic
equation is 6r2 r 1 = 0 . The roots of the equatio

Biochemistry 1 Recommended problems (Ch 8)
2015/10/20
1. Lipids are the biomolecules of choice for storage of metabolic energy because they:
a.
are soluble in water.
b.
yield a large amount of energy upon oxidation.
c.
are highly oxidized.
d.
are easily h

Biochemistry 1 Recommended problems (Ch 7)
2015/10/18
1. The enantiomer of D-mannose would be:
a.
D-galactose.
b.
L-glucose.
c.
D-glucose.
d.
L-mannose.
e.
L-arabinose.
2. Glucose most commonly forms which of the following structures?
a.
a pyranose using

Tom IN. Apostol
CALCULUS
VOLUME II
Mlul ti Variable Calculus and Linear
Algebra, with Applications to
DifFeren tial Equations and Probability
SECOND EDITION
John Wiley & Sons
New York London Sydney Toronto
CONSULTING
EDITOR
George Springer, Indiana Univer

ELEMENTARY
DIFFERENTIAL EQUATIONS WITH
BOUNDARY VALUE PROBLEMS
William F. Trench
Andrew G. Cowles Distinguished Professor Emeritus
Department of Mathematics
Trinity University
San Antonio, Texas, USA
wtrench@trinity.edu
This book has been judged to meet t

Chapter 1
Systems of Linear Equations and Matrices
Section 1.1
Exercise Set 1.1
1. (a), (c), and (f) are linear equations in x1 , x2 , and x3 .
(b) is not linear because of the term x1 x3 .
(d) is not linear because of the term x 2 .
3
(e) is not linear b