MATH 285 FALL 2015
HOMEWORK 9DUE ON NOVEMBER 23-25
p
(1) (a) Find the area of the portion of the sphere x2 +y 2 +z 2 = 1 that is cut out by the cone z x2 + y 2 .
(b) Use a surface integral to find the
Our Changing Atmosphere
Lecture 04 (Thu 15 Sep)
Temperature of the Earth (part 2)
Atmospheric Composition
Atoms and Molecules
1
Where were we? Physics concepts
Energy is conserved (neither made nor d
Our Changing Atmosphere
Lecture 05 (Tue 20 Sep)
Molecule Wrap-up:
Ionic, Covalent and Hydrogen bonding
Exchanging energy with molecules
Describing Light/Radiation
1
Register to Vote
US national electi
Practice test for midterm 1
This should take you about 80 minutes to complete.
1. For each of the five questions below, state whether the assertion is true of false. If it is true, justify it, and
if
Review problems for midterm 2
1. Let D be the region bounded by the x-axis and the function y = 1 x2 . Express the volume of the solid
lying between the xy-plane and the graph of (x, y) = x3 sin y as
Practice test for midterm 2 -
Solutions
This should take you about 80 minutes to complete.
1. For each of the questions below, state whether the assertion is true of false. If it is true, justify it,
Practice test for midterm 2
This should take you about 80 minutes to complete.
1. For each of the five questions below, state whether the assertion is true of false. If it is true, justify it, and
if
Math 285 Practice Problems
Fall 2013
Math 285
Practice Problems, Page 1 of 3
1. For each question below, state whether the statement is true or false. If it is true, justify it, and if it is
false, gi
Review problems for midterm 1
1. (a) Find the equation of the tangent plane to the surface
x2 exy + z 2 = 1
at (1, 0, 1).
(b) Find the equation of the line perpendicular to the surface in (a) at the p
1. (10 points) Let P be the plane a: + y + 2 =1 and Q be the plane so 2y + z = 1.
(a) (5 pts) F ind a parametric equation of the line of intersection of P and Q.
(b) (5 pts) Find the equation of the p
Math 285 Practice Problems
Fall 2013
Solutions
Math 285
Solutions
Practice Final, Page 1 of 9
1. For each question below, state whether the statement is true or false. If it is true, justify it, and i
Our Changing Atmosphere
Lecture 03 (Tue 13 Sep)
Heat and Temperature
Conservation of Energy
Temperature of the Earth (part 1)
Reading and Homework
First reading was due a few hours ago
Next reading
AOSS/CHEM/ENVIRON/ENSCEN 105
Our Changing Atmosphere
Fall 2016
Introduction and Overview
AOSS 105
Relevance
Everyone cares about the weather
AOSS 105
Goals of this intro session
Explain the class pur
Our Changing Atmosphere
Lecture 06 (Thu 22 Sep)
Blackbody Emission
Absorption and Emission Lines in the
EM Spectrum
Modtran
1
Voter Registration
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registration forms
Links to
MATH 285 FALL 2015
HOMEWORK 4DUE ON OCTOBER 9
(1) Suppose that f : Rn R and g : Rn R are two functions defined in Rn . If
lim f (x) = 0,
xx0
|g(x)| M,
for some positive constant M . Prove that
lim f (
MATH 285 FALL 2015
HOMEWORK 6DUE ON OCTOBER 30
(1) Consider a curve c(s) that has unit speed, i.e. kc0 (s)k = 1. The curvature at a point c(s) on this
curve is defined by k = kc00 (s)k.
(a) Find the l
MATH 285 FALL 2015
HOMEWORK 10DUE ON DECEMBER 9
In this homework, any functions appearing in your argument are assumed to be continuous in their domain.
(1) Compute the following line integral for (a)
MATH 285 FALL 2015
HOMEWORK 7DUE ON NOVEMBER 6
(1) Let D := cfw_(x, y)|1 x2 + y 2 2, y 0. Evaluate
RR
D
xydxdy.
(2) Evaluate the following iterated integrals:
4
Z
2
Z
1
Z
x2
/4
Z
(sec5 x)dxdy.
e dxdy,
MATH 285 FALL 2015
HOMEWORK 2DUE ON SEPTEMBER 25
(1) Prove the following properties for cross product:
a b = 0 if and only if a
and b
are parallel or a
or b
is zero.
a b = b a.
(a) b = (a b) = a (b).
MATH 285 FALL 2015
HOMEWORK 3DUE ON OCTOBER 2
(1) Let
x
.
x2 + y 2
Find the level set cfw_(x, y)|f (x, y) = c. Sketch the level sets when c > 0, c = 0 and c < 0.
f (x, y) =
(2) Let
(
f (x, y) =
xy 3
x
MATH 285 FALL 2015
HOMEWORK 1DUE ON SEPTEMBER 18
(1) Prove that the line segment joining the midpoints of two sides of a triangle is parallel to and has
half the length of the third side.
(2) Let ` be
MATH 285 FALL 2015
HOMEWORK 8DUE ON NOVEMBER 13
(1) (a) Write the equations for the surfaces z 2 = 31 (x2 +y 2 ) and x2 +y 2 +z 2 = 9z in spherical coordinates.
(b) Find the volume of the solid above
MATH 285 FALL 2015
HOMEWORK 5DUE ON OCTOBER 21
(1) Let f : R R be a function with continuous derivatives of any order. Use an induction argument
to prove the following formula for any positive integer
Our Changing Atmosphere
Lecture 08 (Thu 29 Sep)
Ideal Gas Law:
density, temperature, & pressure
Layers of the Atmosphere
Radiative Forcing
1
Announcements
Readings from the textbook from here on out
F