EXAM
Exam 2 Takehome Exam Math 2350-02&04, Spring 2008 April 23, 2008 Corrected Version April 28, 2008
This is a Takehome Exam. You may discuss the problems with others, but write up your own solutions. If not otherwise instructed, you can use a calculat
MATH 2350: CALCULUS III
Spring 2011, Sections 002 & 004
Supplementary Note - Equation of a Plane through Three Given Points
The goal of this note is to give an idea on the equation of planes. In particular, how to obtain the equation of a plane given thre
MATH 2350: CALCULUS III
Spring 2011, Sections 002 & 004
Supplementary Note # 2 Distance Formul
The goal of this note is to give a summary of all the distance formulas in chapter 9.
Prerequisites:
Given a point P with coordinates (x, y, z ) we can associa
MATH 2350: CALCULUS III
Spring 2011, Sections 002 & 004
Supplementary Note # 3 Vector Functions In One Parameter
The goal of this note is to give a summary the concepts in chapter 10.1 and 10.2.
Vector functions of parameter t are of the form F (t) = f1
MATH 2350: CALCULUS III
Spring 2011, Sections 002 & 004
Supplementary Note # 4 Two Problems
Two similar looking problems which are actually quite dierent.
For example: Two bees y on a path modeled using one parameter t with t 0, by the two vector valued f
MATH 2350: CALCULUS III
Spring 2011, Sections 002 & 004
Supplementary Note # 5 Equations of Motion
A summary of 10.3 and a little bit more
Projectiles: An Example
Suppose that a baseball is thrown from the roof of a building on a at ground. Suppose that w
MATH 2350: CALCULUS III
Spring 2011, Sections 002 & 004
Supplementary Note # 6 Theory of Curves
A summary of 10.4 and a little bit more
Arc length of a curve between two points on a curve
b
2
1 + [f (x)] dx
For a scalar function; y = f (x) in R2 :
s=
a
Chapter 17
COMPRESSIBLE FLOW
or the most part, we have limited our consideration so far to flows for which density variations and thus compressibility effects are negligible. In this chapter we lift this limitation and consider flows that involve signific
40 pts.
Problem 1. Suppose that we want to hit a target 5000 feet away with a cannon that has a muzzle speed of 700 feet per second. Find the two angles at which we can fire the cannon to hit the target. What is the time of flight for the larger of the tw
Chapter 12
THERMODYNAMIC PROPERTY RELATIONS
n the preceding chapters we made extensive use of the property tables. We tend to take the property tables for granted, but thermodynamic laws and principles are of little use to engineers without them. In this
Chapter 13
GAS MIXTURES
p to this point, we have limited our consideration to thermodynamic systems that involve a single pure substance such as water. Many important thermodynamic applications, however, involve mixtures of several pure substances rather
Chapter 14
GASVAPOR MIXTURES AND AIR-CONDITIONING
A
t temperatures below the critical temperature, the gas phase of a substance is frequently referred to as a vapor. The term vapor implies a gaseous state that is close to the saturation region of the subs
Chapter 15
CHEMICAL REACTIONS
n the preceding chapters we limited our consideration to nonreacting systems-systems whose chemical composition remains unchanged during a process. This was the case even with mixing processes during which a homogeneous mixtu
Chapter 16
CHEMICAL AND PHASE EQUILIBRIUM
n Chapter 15 we analyzed combustion processes under the assumption that combustion is complete when there is sufficient time and oxygen. Often this is not the case, however. A chemical reaction may reach a state o