18.05 Spring 2005 Lecture Notes 18.05 Lecture 1 February 2, 2005
Required Textbook - DeGroot & Schervish, "Probability and Statistics," Third Edition Recommended Introduction to Probability Text - Feller, Vol. 1
1.2-1.4. Probability, Set Operations. What

S. Widnall, J. Peraire 16.07 Dynamics Fall 2009 Version 2.0
Lecture L4 - Curvilinear Motion. Cartesian Coordinates
We will start by studying the motion of a particle. We think of a particle as a body which has mass, but has negligible dimensions. Treating

S. Widnall, J. Peraire 16.07 Dynamics Fall 2009 Version 2.0
Lecture L7 - Relative Motion using Translating Axes
In the previous lectures we have described particle motion as it would be seen by an observer standing still at a fixed origin. This type of mo

S. Widnall, J. Peraire 16.07 Dynamics Fall 2009 Version 2.0
Lecture L8 - Relative Motion using Rotating Axes
In the previous lecture, we related the motion experienced by two observers in relative translational motion with respect to each other. In this l

J. Peraire, S. Widnall 16.07 Dynamics Fall 2009 Version 2.0
Lecture L9 - Linear Impulse and Momentum. Collisions
In this lecture, we will consider the equations that result from integrating Newton's second law, F = ma, in time. This will lead to the princ

S. Widnall, J. Peraire 16.07 Dynamics Fall 2008 Version 2.0
Lecture L10 - Angular Impulse and Momentum for a Particle
In addition to the equations of linear impulse and momentum considered in the previous lecture, there is a parallel set of equations that

J. Peraire, S. Widnall 16.07 Dynamics Fall 2008 Version 2.0
Lecture L11 - Conservation Laws for Systems of Particles
In this lecture, we will revisit the application of Newton's second law to a system of particles and derive some useful relationships expr

S. Widnall, J. Peraire 16.07 Dynamics Fall 2008 Version 2.0
Lecture L12 - Work and Energy
So far we have used Newton's second law F = ma to establish the instantaneous relation between the sum of the forces acting on a particle and the acceleration of tha

S. Widnall, J. Peraire 16.07 Dynamics Fall 2008 Version 2.0
Lecture L13 - Conservative Internal Forces and Potential Energy
The forces internal to a system are of two types. Conservative forces, such as gravity; and dissipative forces such as friction. In

J. Peraire, S. Widnall 16.07 Dynamics Fall 2008 Version 2.0
Lecture L14 - Variable Mass Systems: The Rocket Equation
In this lecture, we consider the problem in which the mass of the body changes during the motion, that is, m is a function of t, i.e. m(t)

J. Peraire, S. Widnall 16.07 Dynamics Fall 2008 Version 1.2
Lecture L15 - Central Force Motion: Kepler's Laws
When the only force acting on a particle is always directed towards a fixed point, the motion is called central force motion. This type of motion

S. Widnall, J. Peraire 16.07 Dynamics Fall 2009 Version 2.0
Lecture L6 - Intrinsic Coordinates
In lecture L4, we introduced the position, velocity and acceleration vectors and referred them to a fixed cartesian coordinate system . Then we showed how they

S. Widnall, J. Peraire 16.07 Dynamics Fall 2008 Version 2.0
Lecture L5 - Other Coordinate Systems
In this lecture, we will look at some other common systems of coordinates. We will present polar coordinates in two dimensions and cylindrical and spherical

UNIVERSIDADE ESTADUAL PAULISTA "JLIO DE MESQUITA FILHO" Campus de Presidente Prudente
ESTATSTICA BSICA
Relatrio das atividades desenvolvidas no perodo da Bolsa de Apoio Acadmico e Extenso I (PAE) de 26/04/2007 28/02/2008.
Bolsista: Fabiano Jos dos Santos

18.05 Lecture 2 February 4, 2005
1.5 Properties of Probability. 1. P(A) [0, 1] 2. P(S) = 1 3. P(Ai ) = P (Ai ) if disjoint Ai Aj = , i = j The probability of a union of disjoint events is the sum of their probabilities. 4. P(), P(S) = P(S ) = P(S) + P() =

18.05 Lecture 3 February 7, 2005
n! Pn,k = (n-k)! - choose k out of n, order counts, without replacement. nk - choose k out of n, order counts, with replacement. n! Cn,k = k!(n-k)! - choose k out of n, order doesn't count, without replacement.
1.9 Multino

18.05 Lecture 4 February 11, 2005
Union of Events P(A1 . An ) = P(Ai ) - P(Ai Aj ) +
i<j i<j<k
P(Ai Aj Ak ) + .
i
It is often easier to calculate P(intersections) than P(unions) Matching Problem: You have n letters and n envelopes, randomly stuff the lett

18.05 Lecture 5 February 14, 2005
2.2 Independence of events. P(A|B) = P(AB) ; P(B) Definition - A and B are independent if P(A|B) = P(A) P(A|B) = P(AB) = P(A) ; P(AB) = P(A)P(B) P(B)
Experiments can be physically independent (roll 1 die, then roll anothe

18.05 Lecture 6 February 16, 2005
Solutions to Problem Set #1 1-1 pg. 12 #9 Bn = i=n Ai , Cn = i=n Ai a) Bn Bn+1 . Bn = An ( i=n+1 Ai ) = An Bn+1 s Bn+1 s Bn+1 An = Bn Cn Cn+1 . Cn = An Cn+1 s Cn = An Cn+1 s Cn+1 b) s n=1 Bn s Bn for all n s i=1 Ai for al

18.05 Lecture 7 February 18, 2005
Bayes' Formula.
Partition B1 , ., Bk k i=1 Bi = S, Bi Bj = for i = j P(A) = k P(ABi ) = k P(A|Bi )P(Bi ) - total probability. i=1 i=1 Example: In box 1, there are 60 short bolts and 40 long bolts. In box 2, there are 10 s

18.05 Lecture 8 February 22, 2005
3.1 - Random Variables and Distributions Transforms the outcome of an experiment into a number. Definitions: Probability Space: (S, A, P) S - sample space, A - events, P - probability Random variable is a function on S wi

S. Widnall 16.07 Dynamics Fall 2009 Version 2.0
Lecture L1 - Introduction
Introduction
In this course we will study Classical Mechanics and its application to aerospace systems. Particle motion in Classical Mechanics is governed by Newton's laws and is so

S. Widnall 16.07 Dynamics Fall 2009 Version 1.0
Lecture L2 - Degrees of Freedom and Constraints, Rectilinear Motion
Degrees of Freedom
Degrees of freedom refers to the number of independent spatial coordinates that must be specified to determine the posit

S. Widnall 16.07 Dynamics Fall 2009 Lecture notes based on J. Peraire Version 2.0
Lecture L3 - Vectors, Matrices and Coordinate Transformations
By using vectors and defining appropriate operations between them, physical laws can often be written in a simp

J. Peraire, S. Widnall 16.07 Dynamics Fall 2009 Version 3.0
Lecture L28 - 3D Rigid Body Dynamics: Equations of Motion; Euler's Equations
3D Rigid Body Dynamics: Euler's Equations
We now turn to the task of deriving the general equations of motion for a th

J. Peraire, S. Widnall 16.07 Dynamics Fall 2009 Version 2.0
Lecture L29 - 3D Rigid Body Dynamics
3D Rigid Body Dynamics: Euler Angles
The difficulty of describing the positions of the body-fixed axis of a rotating body is approached through the use of Eul

J. Peraire, S. Widnall 16.07 Dynamics Fall 2008 Version 2.0
Lecture L30 - 3D Rigid Body Dynamics: Tops and Gyroscopes
3D Rigid Body Dynamics: Euler Equations in Euler Angles
In lecture 29, we introduced the Euler angles as a framework for formulating and

Inertial Instruments and Inertial Navigation
Gimbals Gimbals are essentially hinges that allow freedom of rotation about one axis. Gimbals often have superb bearings and motors to help achieve virtually frictionless behavior. Sensors in the bearings provi

Table of Contents
Microsoft Dynamics 80639 Training
Retail in eCommerce Stores: Installation
and Configuration for Microsoft
Dynamics AX 2012 R3
1
Microsoft Retail in eCommerce Stores: Installation and Configuration for
Microsoft Dynamics AX 2012 R3
Modul

Retail Store Connect Technical Reference
Microsoft Dynamics AX for Retail
January 2011
Microsoft Dynamics is a line of integrated, adaptable business management solutions that enables you
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MODULE 1: INTRODUCTION TO RETAIL POINT OF
SALE (POS) AND OVERVIEW
Module Overview
Microsoft Dynamics AX 2012 R3 for Retail supports multiple retail channels. Retail
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In Retai

Microsoft Dynamics for Retail
Solution Overview
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Contents
EXECUTIVE SUMMARY . 2
THE DYNAMIC RETAILER . 3
FROM VISION TO REALITY . 4
MICROSOFT DYN