Trapezoidal Rule and Midpoint Rule Error Bounds
1. Trapezoidal Rule
Theorem 1.1 (Error Bound for Trapezoidal Rule). Assume f (x) is continuous on
[a, b]. Let KT = max of f (x) on [a, b] and n be the
Integration by parts proof
Theorem: Let F and G be dierentiable on [a, b] and assume that F and G are continuous on
[a, b]. Then
F (x)G (x) dx = F (x)G(x)
F (x)G(x) dx
(Important: G(x) can be any ant
Full Name:
MATH 122: Sample Final Exam
Section:
Thursday, December 10, 2009
Show all work and justify your answers. Your solutions should read nicely and be legible. They
should not be composed of reg
Section:
Full Name:
I Thursday, December 10, 2009
MATH 122: Sample Final Exam
Show all work and justify your answers. Your solutions should read nicely and be legible. They
should not be composed
Math 21122
Integration, Dierential Equations and
Approximations
Syllabus, Fall 2012
Time and Place: WEH 7500
MWF 8:309:20, 9:3010:20
Instructor: Dr. Greggo M. Johnson
Oce: Wean Hall 8122
Phone: 412
Carnegie Mellon University
33106 Fall12
Physics Department
Roy A. Briere
Work and Gravity
There are so many signs that it is easy to get confused when studying gravitational potentials.
I know I made
MATH 122: Extra Credit Solutions
2
2
1. f (x) = ex so f (x) = 2xex . Using this information and the equation f g = f g + g f we get
2
2
2
2
2
2xex g = 2xex g + ex g g ex (2x 1) = 2xex g
2x
g
g =
2x 1
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20162018 Transfer Guide for Austin Community College Students
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PHYS2102 (Aktas) Practice Test 2 Hill, Ryan  [email protected]
Probl
6/25/17
The Coulomb Balance
Equipment Needed
Calipers, Digital
Coulomb Balance, Sgt.W.
Jack, Table
Laser, HeNe
Lead, Banana Jack (3)
Level, Bullseye
or 6 in torpedo
Power Supply, Pasco SF9585A
Power
THE UNIVERSITY OF TEXAS AT AUSTIN
ME 333T Engineering Communication
Fall 2010 COURSE DESCRIPTION AND SYLLABUS
INSTRUCTORS:
Professor Moore
[email protected]
Office: ETC 5.140
Office Hours: M 4
Algebra II
Assessment
Eligible Texas Essential
Knowledge and Skills
Texas Education Agency
Student Assessment Division
January 2014
STAAR Algebra II Assessment
Mathematical Process Standards
These stu
Cindy Raisor Fall 2004 Texas A&M University
Template for Technical Memo
To:
From:
Date:
Subject:
Name and title of recipient (Physics TA)
Your name and title (relationship to recipient)
Date submitte
33106 Fall 2012
R.A. Briere
Summary Of Some Thermodynamic Equations
Abstract
This note summarizes the equations for Q, W , and U frequently used in thermodynamics. You may nd the table on the last pa
Carnegie Mellon University
33106 Fall11
Physics Department
Roy A. Briere
PostExam IV Review Items (for Final)
The Final Exam is inclusive; it will cover all of the material in the course:
Scalars,
Carnegie Mellon University
Physics for Engineering Students I
Fall 2012
R.A. Briere
Center of Mass and Elastic Collisions
1
Center of Mass
We can dene the centerofmass coordinate and velocity for a
Carnegie Mellon University
Physics for Engineering Students I
Fall 2012
R.A. Briere
Chapter 2 Examples
These problems are old favorites of mine from the 10th edition. The rst one is now 264 in the
13
Carnegie Mellon University
33106 Fall11
Physics Department
Roy A. Briere
Exam I Review Items
Chapter 1: Units, Scalars, Vectors, .
Physical quantities have a type: scalar and vector are enough for us
o
C ourse2 4101F undamentals f M echanicalEngineering
#2 (75 minutes)
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Monday,N ovember19,2012
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Assigned P roblems t o b e h anded i n f or a g
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#1)
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Carnegie Mellon University
33106 Fall11 UPDATED
Physics Department
Roy A. Briere
Exam III Review Items
We have nished so far:
Kinematics: descriptions of motion with x, v, a, t, g, T, R, etc.
i,
Dyna