c 2008 by Chris Wendl
Paper or electronic copies for noncommercial use may be made freely
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Lecture Notes on Bundles and Connections
Chris Wendl
September 26, 2008
Preface
These notes w

IEEE 754 FLOATING POINT
REPRESENTATION
Alark Joshi
Slides courtesy of Computer Organization and Design, 4th edition
FLOATING POINT
Representation for non-integral numbers
Like scientific notation
2.34 1056
+0.002 104
+987.02 109
In binary
Including very s

Understanding the IEEE 754 oating point number
system
S. K. Ghoshal
Supercomputer Education and Research Centre
Indian Institute of Science,
Bangalore 560 012 India.
March 27, 1997
Chapter 1
IEEE 754 STANDARD
REPRESENTATION
1.1 Representation of Floating

26
CHAPTER 1. SCIENTIFIC COMPUTING
amples. The IEEE oating-point standard can be found in [131]. A useful tutorial on
oating-point arithmetic and the IEEE standard is [97]. Although it is no substitute for
careful problem formulation and solution, extende

Exponential Notation
The following are equivalent
representations of 1,234
FLOATING POINT
NUMBERS
123,400.0
12,340.0
x 10-1
1,234.0
x 100
123.4
Englander Ch. 5
x 10-2
x 101
12.34
1.234
x 102
x 103
The representations differ
in that the decimal place
the

Floating point
Floating point
In computing, floating point describes a system for representing real numbers which supports a wide range of
values. Numbers are in general represented approximately to a fixed number of significant digits and scaled using an

Floating-point arithmetic
Floating-point computations are vital to many applications. However, its
pretty hard to implement a floating-point system.
Today well look at the IEEE 754 floating-point arithmetic standard.
Floating-point numbers have their own

Appunti sulla rappresentazione dellinformazione
Roberto Beraldi
DISPENSA PER IL CORSO DI
FONDAMENTI DI INFORMATICA
CORSI DI LAUREA IN INGEGNERIA
CHIMICA, DEI MATERIALI,NUCLEARE (vecchi ordinamenti)
Anno Accademico 2001-2002
Versione 1.0
APPUNTI SULLA RAPP

Floating-Point Numbers
Floating-point number system characterized by
four integers:
p
[L, U ]
base or radix
precision
exponent range
Number x represented as
dp1
d
d
x = d0 + 1 + 2 + + p1 E ,
2
where
0 di 1, i = 0, . . . , p 1, and L E U
d0d1 dp1 called ma

18
CHAPTER
BUNDLES
2.
Example 2.1 (The tangent bundle). If M is a smooth n-dimensional
manifold, its tangent bundle
TM=
Tx M
x M
Chapter 2
Bundles
Contents
2.1 Vector bundles
.
17
2.2 Smoothness
.
26
2.3 Operations on vector bundles
. . . . . . . . . .
28

164
APPENDIX
ALGEBRA
A.
MULTILINEAR
A.1 Vector spaces and linear maps
We assume the reader is somewhat familiar with linear algebra, so at least
most of this section should be reviewits main purpose is to establish
notation that is used in the rest of the

96
4.1
Direct sums, tensor products and bun-dles
of linear maps
Suppose E : E ! M and F : F ! M are two vector bundles of rank m and `
respectively, and assume they are either both real (F = R) or both
complex (F = C). In this section we address the follo

70
CHAPTER 3. CONNECTIONS
bundle interesting. We prefer to think of sections as \vector valued"
maps on M , which can be added and multiplied by scalars, and we'd
like to think of the directional derivative ds(x)X as something which
respects this linear s

196
APPENDIX B. LIE GROUPS AND LIE ALGEBRAS
this notion is already familiar to the reader. From a geometric
perspective, it becomes more interesting if we assume that G is also a
topological space or a manifold.
De nition B.1. A topological group G is a g

116
CHAPTER 5. CURVATURE ON BUNDLES
Chapter 5
v
0
p0
Curvature on Bundles
Contents
2
Figure 5.1: Parallel transport along a closed path on S .
Flat sections and connections . . . . . . . . . . 115
Integrability and the Frobenius theorem . . . 117
Curvatur

Examples and First Homework in APM 505 Fall 2012
Contents
Class exercise on oating point arithmetic
Single precision
Exercises
Make sure the data are cleared, clear the screen and close gures
clc
close all
clear all
% set figure size again and reduce l