107
107

Nov 14, 2013
11/13

Nov 14, 2013
by
Santosh Vempala

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Theorem 1. If G is bipartite, then P=M.

Topics: Maths, Graph Theory, Optimization and Control, Basics, Connectivity and Matchings, Optimization,...

Source: http://www.flooved.com/reader/1319

245
245

Nov 14, 2013
11/13

Nov 14, 2013
by
Victor Flynn

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These notes are modi�ed from previous versions (due to Neil Dummigan,Alan Lauder and Roger Heath-Brown) and have been recently revised by me. They draw mainly upon �A Classical Introduction to Modern Number Theory�, by Ireland and Rosen, and �Algebraic Number Theory�, by Stewart and Tall. While I take full responsibility for their current contents, considerable thanks are clearly due to Neil, Alan and Roger.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1060

157
157

Nov 14, 2013
11/13

Nov 14, 2013
by
Vladan Vuletic

texts

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Today � Finish proof: inverse Fourier transform � Exact de�nition of expectation values, uncertainties � Proof (see notes): _x_k � 1, _x_p � h�, ___t � 1, _E_t � �h 2 2 2 2 � Compton scattering Photoelectric e_ect

Topics: Physics, Particle Physics and Fields, Quantum Physics, Specific Reactions and Phenomenology, Photon...

Source: http://www.flooved.com/reader/3099

84
84

Nov 14, 2013
11/13

Nov 14, 2013
by
Richard M. Dudley

texts

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eye 84

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Topics: Maths, Statistics and Probability, Statistics, Mathematics

Source: http://www.flooved.com/reader/2163

152
152

Nov 14, 2013
11/13

Nov 14, 2013
by
Arthur Mattuck;Haynes Miller;Jeremy Orloff;John Lewis

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eye 152

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This is meant as a follow-up on the review of vectors and matrices in the previous session.

Topics: Maths, Linear Algebra and Geometry, Vectors and Matrices, Linear Algebra, Linear Independence,...

Source: http://www.flooved.com/reader/1458

315
315

Nov 14, 2013
11/13

Nov 14, 2013
by
Fredrik Jonsson

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This course is intended as an introduction to the wide �eld of phenomena encountered in nonlinear optics. The course covers:� The theoretical foundation of nonlinear interaction between light and matter.� Perturbation analysis of nonlinear interaction between light and matter.� The Bloch equation and its interpretation.� Basics of soliton theory and the inverse scattering transform. It should be emphasized that the course does not cover state-of-the-art material constants of nonlinear...

Topics: Physics, Acoustics, Optics and Waves, Optics�, Nonlinear Optics, Wave Optics, Polarization,...

Source: http://www.flooved.com/reader/2971

231
231

Nov 14, 2013
11/13

Nov 14, 2013
by
Alan Edelman

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This handout provides the essential elements needed to understand �nite random matrix theory. A cursory observation should reveal that the tools for in�nite random matrix theory are quite di_erent from the tools for �nite random matrix theory. Nonetheless, there are signi�cantly more published applications that use �nite random matrix theory as opposed to in�nite random matrix theory. Our belief is that many of the results that have been historically derived using �nite random...

Topics: Maths, Linear Algebra and Geometry, Vectors and Matrices, Matrices, Mathematics

Source: http://www.flooved.com/reader/975

71
71

Nov 14, 2013
11/13

Nov 14, 2013
by
Jerry Griffiths

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eye 71

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In the previous chapters we have considered the collision between two electromagnetic waves, permitting them also to be coupled to gravitational waves. In this chapter a situation is considered in which a plane gravitational wave approaches and collides with a plane electromagnetic wave. In this situation, the �eld equations are identical to those of previous chapters but the initial conditions are di_erent.

Topic: Maths

Source: http://www.flooved.com/reader/2793

153
153

Nov 14, 2013
11/13

Nov 14, 2013
by
Richard Stanley

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eye 153

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Topics: Maths, Logic, Numbers and Set Theory, Algebra, Posets and Zorn�s Lemma, Groups, Hasse Diagrams...

Source: http://www.flooved.com/reader/1045

184
184

Nov 14, 2013
11/13

Nov 14, 2013
by
Vladan Vuletic

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eye 184

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Can we �derive� Newton�s F = ma from the SE?

Topics: Physics, Quantum Physics, Quantum Mechanics, Quantum Systems with Finite Hilbert Space,...

Source: http://www.flooved.com/reader/3084

133
133

Nov 14, 2013
11/13

Nov 14, 2013
by
Hung Cheng

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In this lecture and the next two lectures, we�ll briefly review partial differential equations (PDEs). As PDEs are much more difficult to solve than ODEs, we shall start with the simplest of PDEs, those of the first order.

Topics: Maths, Analysis and Calculus, Differential Equations (ODEs & PDEs), Mathematics

Source: http://www.flooved.com/reader/1336

105
105

Nov 14, 2013
11/13

Nov 14, 2013
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff

texts

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eye 105

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Topics: Maths, Differential Equations (ODEs & PDEs), Ordinary Differential Equations (ODEs),...

Source: http://www.flooved.com/reader/1450

215
215

Nov 14, 2013
11/13

Nov 14, 2013
by
Abhinav Kumar

texts

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eye 215

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comment 0

Topics: Maths, Algebra, Number Theory, Mathematics

Source: http://www.flooved.com/reader/1130

109
109

Nov 14, 2013
11/13

Nov 14, 2013
by
Daniel Kleitman;Peter Shor

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eye 109

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Seeking the Best Expected Rank: This problem can also be handled by the same general approach. If there are N possible choices all together, we can compute a threshold for each stage, where we accept the first candidate which is less than or equal to the threshold. Call this threshold T(s), where s is the number of candidates still unseen.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1886

131
131

Nov 14, 2013
11/13

Nov 14, 2013
by
Zoltan Spakovszky

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In this section, we examine the issue of how we obtain the heat needed for work production. For the most part, this is from converting chemical energy into heat, so the discussion will be on reacting mixtures of gas which are involved in chemical combustion processes. The topic addressed is �thermochemistry�, which is the combining of thermodynamics with chemistry to predict such items as how much heat is released from a chemical reaction. This is the �Q� or �q� that we have used in...

Topic: Maths

Source: http://www.flooved.com/reader/3204

436
436

Nov 14, 2013
11/13

Nov 14, 2013
by
Richard Fitzpatrick

texts

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eye 436

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Topics: Physics, Electromagnetism and Electromagnetic Radiation, Classical Electromagnetism, Physics

Source: http://www.flooved.com/reader/2723

119
119

Nov 14, 2013
11/13

Nov 14, 2013
by
Jacob Lurie

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Let V be a �nite dimensional vector space over F2, and let TV denote Lannes�s T-functor. In previous lectures we have established two very important properties of TV : � The functor TV is exact. � For every 2-pro�nite space X, there is a canonical isomorphism... Our goal in this lecture is to deduce a conceptual consequence of these facts, which makes no mention of modules over the Steenrod algebra.

Topics: Maths, Algebra, Topology and Metric Spaces, Mathematics

Source: http://www.flooved.com/reader/2213

289
289

Nov 14, 2013
11/13

Nov 14, 2013
by
Jin Au Kong

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eye 289

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Topics: Physics, Electromagnetism and Electromagnetic Radiation, Mathematical Methods in Physics, Calculus...

Source: http://www.flooved.com/reader/2569

68
68

Nov 14, 2013
11/13

Nov 14, 2013
by
Jerry Griffiths

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In this chapter we will consider only vacuum solutions. This will enable us to continue to concentrate on the collision of gravitational waves. Various techniques will be discussed here, and the main solutions that have been obtained using them will be described in the next chapter. Many techniques are also known by which solutions of the Einstein�Maxwell equations, and other non-vacuum solutions, can be generated from known vacuum solutions. These will be discussed later in Chap-ter 15.

Topic: Maths

Source: http://www.flooved.com/reader/2786

144
144

Nov 14, 2013
11/13

Nov 14, 2013
by
Matthew Hancock

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We now introduce the Fourier Transform and show how it is related to the solution of the Heat Problem on an in�nite domain.

Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Partial Differential Equations (PDEs),...

Source: http://www.flooved.com/reader/1670

95
95

Nov 14, 2013
11/13

Nov 14, 2013
by
Chiang C. Mei

texts

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eye 95

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Topics: Physics, Classical Mechanics, Fluid Mechanics, General Theory in Fluid Dynamics, Fluid Dynamics,...

Source: http://www.flooved.com/reader/2611

107
107

Nov 14, 2013
11/13

Nov 14, 2013
by
Alan Guth;Barton Zwiebach

texts

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eye 107

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Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...

Source: http://www.flooved.com/reader/3161

151
151

Nov 14, 2013
11/13

Nov 14, 2013
by
Alan Guth;Barton Zwiebach

texts

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eye 151

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Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes,...

Source: http://www.flooved.com/reader/3155

137
137

Nov 14, 2013
11/13

Nov 14, 2013
by
Abhinav Kumar

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Generating Functions- for a sequence a0. . .we can de�neA(x) =ann�0a xn

Topics: Maths, Algebra, Number Theory, Mathematics

Source: http://www.flooved.com/reader/1125

151
151

Nov 14, 2013
11/13

Nov 14, 2013
by
Vladan Vuletic

texts

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eye 151

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Photoelectric e_ect Observed 1888; explanation, Einstein 1905. A negatively charged metal plate loses charge slowly if illuminated with light, while a positive charge remains. Light of su_ciently short wavelength releases electrons, the electron current is proportional to the intensity of the light. Light below a certain cut o_ frequency _0 does not release any electrons, no matter how high the intensity. Energy of released electrons can be measured by determining voltage V that prevents them...

Topic: Maths

Source: http://www.flooved.com/reader/3100

163
163

Nov 14, 2013
11/13

Nov 14, 2013
by
Erik Demaine

texts

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eye 163

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Topics: Maths, Statistics and Probability, Probability, Mathematics

Source: http://www.flooved.com/reader/1568

143
143

Nov 14, 2013
11/13

Nov 14, 2013
by
Predrag Cvitanovi?;R. Mainieri

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eye 143

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So far we have concentrated on describing the trajectory of a single initial point. Our next task is to de�ne and determine the size of a neighborhood of x(t). We shall do this by assuming that the �ow is locally smooth and by describing the local geometry of the neighborhood by studying the �ow linearized around x(t). Nearby points aligned along the stable (contracting) directions remainin the neighborhood of the trajectory x(t) = ft(x0); the ones to keep an eye on are the points which...

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2743

149
149

Nov 14, 2013
11/13

Nov 14, 2013
by
Markus Zahn

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eye 149

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Topics: Physics, Electromagnetism and Electromagnetic Radiation, Classical Electromagnetism�, Physics

Source: http://www.flooved.com/reader/2858

156
156

Nov 14, 2013
11/13

Nov 14, 2013
by
Eduardo Fradkin

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eye 156

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The Dirac equation is a relativistic wave equation which describes the quantum dynamics of spinors. We will see in this section that a consistent description of this theory cannot be done outside the framework of (local) relativistic Quantum Field Theory.

Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...

Source: http://www.flooved.com/reader/2878

111
111

Nov 14, 2013
11/13

Nov 14, 2013
by
Daniel H. Rothman

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eye 111

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Summary Finally, we summarize the characteristics of dissipative systems: � Energy not conserved. � Irreversible. � Contraction of areas (volumes) in phase space.

Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics

Source: http://www.flooved.com/reader/1830

130
130

Nov 14, 2013
11/13

Nov 14, 2013
by
Alan Guth;Barton Zwiebach

texts

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eye 130

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Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Strings and Branes, D...

Source: http://www.flooved.com/reader/3171

308
308

Nov 14, 2013
11/13

Nov 14, 2013
by
Eduardo Fradkin

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eye 308

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We will now turn to the problem of the quantization of the simplest gauge theory, the free electromagnetic �eld. This is an abelian gauge theory. In Physics 583 we will discuss at length the quantization of non-abelian gauge �elds. Unlike abelian theories, such as the free electromagnetic �eld, even in the absence of matter �elds, non-abelian gauge theories are not free �elds and have highly non-trivial dynamics. In Physics 582 we will discuss canonical quantization and path-integral...

Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...

Source: http://www.flooved.com/reader/2880

89
89

Nov 14, 2013
11/13

Nov 14, 2013
by
Y. Lekili

texts

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eye 89

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Topics: Maths, Linear Algebra and Geometry, Geometry, Mathematics

Source: http://www.flooved.com/reader/1957

99
99

Nov 14, 2013
11/13

Nov 14, 2013
by
Jeff Viaclovsky

texts

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Approximations. Let ... Then h _ C� (in�nitely di_erentiable with continuous derivatives).

Topics: Maths, Analysis and Calculus, Analysis, Integration, Mathematics

Source: http://www.flooved.com/reader/1792

123
123

Nov 14, 2013
11/13

Nov 14, 2013
by
Rodolfo R. Rosales

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In two dimensions a Hopf bifurcation occurs as a Spiral Point switches from stable to unstable (or vice versa) and a periodic solution appears. There are, however, more details to the story than this: The fact that a critical point switches from stable to unstable spiral (or vice versa) alone does not guarantee that a periodic solution will arise, though one almost always does. Here we will explore these questions in some detail, using the method of multiple scales to find precise conditions...

Topics: Maths, Differential Equations (ODEs & PDEs), Partial Differential Equations (PDEs), Mathematics

Source: http://www.flooved.com/reader/1176

586
586

Nov 14, 2013
11/13

Nov 14, 2013
by
Thomas Ward;Alan Camina

texts

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eye 586

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Topics: Maths, Analysis and Calculus, Complex Analysis, Contour Integration and Cauchy�s Theorem,...

Source: http://www.flooved.com/reader/3421

327
327

Nov 14, 2013
11/13

Nov 14, 2013
by
Anirban Kundu;Jyoti Prasad Saha

texts

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eye 327

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Topic: Maths

Source: http://www.flooved.com/reader/3380

108
108

Nov 14, 2013
11/13

Nov 14, 2013
by
Daniel Kleitman;Peter Shor

texts

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eye 108

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A binary tree is a tree in which each vertex has either 2 or 0 descendants. We can assign a code word to each leaf of a binary tree by starting at the top and assigning 0 to one descendant and 1 to the other, adding the bit onto the bits already possessed by the parent. If we do this the words at depth d in the tree will have a code word of length d.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1871

175
175

Nov 14, 2013
11/13

Nov 14, 2013
by
Markus Zahn

texts

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eye 175

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Topics: Physics, Electromagnetism and Electromagnetic Radiation, Classical Electromagnetism�, Physics

Source: http://www.flooved.com/reader/2846

146
146

Nov 14, 2013
11/13

Nov 14, 2013
by
Ben Simons

texts

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eye 146

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Previously, we have seen that, when treated in a mean-�eld or saddle-point approximation,the �eld theory of the weakly interacting Bose gas shows a transition to a Bose-Einsteincondensed phase when _ =0where the order parameter, the complex condensate wave-function _0acquires a non-zero expectation value, |_0| = _ ___Ld/g. The spontaneousbreaking of the continuous symmetry associated with the phase of the order parameter isaccompanied by the appearance of massless collective phase...

Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...

Source: http://www.flooved.com/reader/3060

104
104

Nov 14, 2013
11/13

Nov 14, 2013
by
Michel X. Goemans

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Today we will brie�y survey matroid representation and then discuss some problems in matroid optimization and the corresponding applications. The tools we develop will help us answer the following puzzle: Puzzle: A game is played on a graph G(V, E) and has two players, George and Ari. Ari�s moves consist of ��xing� edges e _ E. George�s moves consist of deleting any un�xed edge. The game ends when every edge has been either �xed or deleted. Ari wins if the graph at the end of...

Topics: Maths, Optimization and Control, Optimization, Mathematics

Source: http://www.flooved.com/reader/1923

172
172

Nov 14, 2013
11/13

Nov 14, 2013
by
David Tong

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Our goal in this section is to use the techniques of statistical mechanics to describe the dynamics of the simplest system: a gas. This means a bunch of particles, �ying around in a box. Although much of the last section was formulated in the language of quantum mechanics, here we will revert back to classical mechanics. Nonetheless, a recurrent theme will be that the quantum world is never far behind: we�ll see several puzzles, both theoretical and experimental, which can only truly be...

Topic: Maths

Source: http://www.flooved.com/reader/3130

98
98

Nov 14, 2013
11/13

Nov 14, 2013
by
Dmitry Panchenko

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Topics: Maths, Statistics and Probability, Probability, Statistics, Hypothesis testing, Uniformly Most...

Source: http://www.flooved.com/reader/1639

302
302

Nov 14, 2013
11/13

Nov 14, 2013
by
Matthew Hancock

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We introduce another powerful method of solving PDEs. First, we need to consider some preliminary de�nitions and ideas.

Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Partial Differential Equations (PDEs),...

Source: http://www.flooved.com/reader/1671

114
114

Nov 14, 2013
11/13

Nov 14, 2013
by
Jeff Viaclovsky

texts

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eye 114

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Topics: Maths, Analysis and Calculus, Differential Equations (ODEs & PDEs), Mathematics

Source: http://www.flooved.com/reader/993

1,205
1.2K

Nov 14, 2013
11/13

Nov 14, 2013
by
Prof. Richard Hammack

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such a function f, a single real number input x determines a unique single output value

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3480

150
150

Nov 14, 2013
11/13

Nov 14, 2013
by
Ben Simons

texts

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eye 150

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Matsubara Summations Basic idea: by introducing auxiliary function g(z) that has simple poles of strength unity at z = i_n, Cauchy�s theorem implies

Topics: Physics, Condensed Matter, Particle Physics and Fields, Statistical Physics and Thermodynamics,...

Source: http://www.flooved.com/reader/3057

126
126

Nov 14, 2013
11/13

Nov 14, 2013
by
R. Victor Jones

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Consider a totally coherent wave propagating in the positive direction....For later reference, we note that the full (non-normalized) Jones vector representation of this field is given by...We can be easily shown that...

Topics: Physics, Acoustics, Optics and Waves, Optics�, Quantum Optics�, Wave Optics, Polarization,...

Source: http://www.flooved.com/reader/2991

106
106

Nov 14, 2013
11/13

Nov 14, 2013
by
Emma Carberry

texts

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eye 106

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Topics: Maths, Linear Algebra and Geometry, Differential Geometry, Mathematics

Source: http://www.flooved.com/reader/1098

191
191

Nov 14, 2013
11/13

Nov 14, 2013
by
Albert R. Meyer

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In particular, when we make an estimate by repeated sampling, we need to know how much con�dence we should have that our estimate is OK. Technically, this reduces to �nding the probability that an estimate deviates a lot from its expected value. This topic of deviation from the mean is the focus of this �nal chapter.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1719

172
172

Nov 14, 2013
11/13

Nov 14, 2013
by
Jonathan Kelner

texts

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Today�s lecture covers three main parts: � Courant-Fischer formula and Rayleigh quotients � The connection of _2 to graph cutting � Cheeger�s Inequality

Topics: Maths, Linear Algebra and Geometry, Graph Theory, Optimization and Control, Vectors and Matrices,...

Source: http://www.flooved.com/reader/2019

164
164

Nov 14, 2013
11/13

Nov 14, 2013
by
Predrag Cvitanovi?;Gregor Tanner;G�bor Vattay

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eye 164

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Semiclassical approximations to quantum mechanics are valid in the regime where the de Broglie wavelength _ _ _/p of a particle with momentump is much shorter than the length scales across which the potential of the system changes signi�cantly. In the short wavelength approximation the particleis a point-like object bouncing o_ potential walls, the same way it does in the classical mechanics. The novelty of quantum mechanics is the interference of the point-like particle with other versions...

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2752

166
166

Nov 14, 2013
11/13

Nov 14, 2013
by
Denis Auroux

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The three theorems we have studied: the divergence theorem and Stokes� theorem in space, and Green�s theorem in the plane (which is really just a special case of Stokes� theo_rem) are widely used in physics and continuum mechanics, in the study of �elds, potentials, heat �ow, wave motion in liquids, gases, and solids, and thermodynamics, to name some of the uses. Often partial di_erential equations which model some physical situation are de_rived using the vector integral calculus...

Topics: Maths, Analysis and Calculus, Calculus, Mathematics

Source: http://www.flooved.com/reader/1821

110
110

Nov 14, 2013
11/13

Nov 14, 2013
by
Katrin Wehrheim

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Until Weierstrass published his shocking paper in 1872, most of the mathematical world (including luminaries like Gauss) believed that a continuous function could only fail to be differentiable at some collection of isolated points. In fact, it turns out that �most� continuous functions are non-differentiable at all points. (To understand what this statement could mean, you should take courses in topology and measure theory.) However, Weierstrass was not, in fact, the �rst to construct...

Topics: Maths, Analysis and Calculus, Mathematics

Source: http://www.flooved.com/reader/1197

2,600
2.6K

Nov 14, 2013
11/13

Nov 14, 2013
by
Prof. Peter J. Cameron

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Topic: Mathematics

Source: http://www.flooved.com/reader/3518

300
300

Nov 14, 2013
11/13

Nov 14, 2013
by
Mr. Travis Byington;Lawrence Evans;Mr. Ryan Magee;Hao Zhang

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...This course take up those loose ends and discusses the discoveries about them by scientists of the 18th and 19th centuries. It turns out that the questions are all related to one another. Like gravity, electric and magnetic interactions also require acting �at a distance� without any apparent intervening medium. In the mid-19th century the description of these phenomena turned away from the mechanical point of view, and centered instead on the idea of �elds. In the last half of that...

Topics: Physics, Electromagnetism and Electromagnetic Radiation, Classical Electromagnetism�,...

Source: http://www.flooved.com/reader/2907

71
71

Nov 14, 2013
11/13

Nov 14, 2013
by
Chiang C. Mei

texts

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eye 71

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Topics: Physics, Classical Mechanics, Fluid Mechanics�, General Theory in Fluid Dynamics, Fluid Dynamics,...

Source: http://www.flooved.com/reader/2598

91
91

Nov 14, 2013
11/13

Nov 14, 2013
by
Scott Aaronson

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Our �rst example of a public-key cryptosystem, in which two people exchanging messages did not have to meet beforehand, was Di_e-Hellman. We then talked about the RSA cryptosystem, which is probably the most widely used today. Here are the basics of how it works:

Topic: Maths

Source: http://www.flooved.com/reader/1309

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Nov 14, 2013
11/13

Nov 14, 2013
by
Jonathan Kelner

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In this lecture we will introduce Multiplicative Weights, a simple technique with many applications. We start with an example.

Topics: Maths, Game Theory, Zero-Sum Games, Mathematics

Source: http://www.flooved.com/reader/2028

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105

Nov 14, 2013
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Nov 14, 2013
by
Dmitry Panchenko

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Topics: Maths, Statistics and Probability, Mathematics

Source: http://www.flooved.com/reader/1630

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Nov 14, 2013
11/13

Nov 14, 2013
by
Richard Melrose

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The wave equation in one space and one time variable

Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics

Source: http://www.flooved.com/reader/1501

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86

Nov 14, 2013
11/13

Nov 14, 2013
by
Chiang C. Mei

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Topics: Physics, Classical Mechanics, Fluid Mechanics, General Theory in Fluid Dynamics, Fluid Dynamics,...

Source: http://www.flooved.com/reader/2623

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174

Nov 14, 2013
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Nov 14, 2013
by
Dmitry Panchenko

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Covariance of X and Y is de�ned as: ... Positive when both high or low in deviation

Topics: Maths, Statistics and Probability, Mathematics

Source: http://www.flooved.com/reader/1625

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392

Nov 14, 2013
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Nov 14, 2013
by
James Nearing

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If the subject of ordinary di_erential equations is large, this is enormous. I am going to examine only one corner of it, and will develop only one tool to handle it: Separation of Variables. Another major tool is the method of characteristics and I�ll not go beyond mentioning the word. When I develop a technique to handle the heat equation or the potential equation, don�t think that it stops there. The same set of tools will work on the Schroedinger equation in quantum mechanics and on the...

Topics: Physics, Condensed Matter, Mathematical Methods in Physics, Structural, Mechanical, and Thermal...

Source: http://www.flooved.com/reader/3023

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109

Nov 14, 2013
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Nov 14, 2013
by
Chiang C. Mei

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Topics: Physics, Classical Mechanics, Fluid Mechanics�, General Theory in Fluid Dynamics, Fluid Dynamics,...

Source: http://www.flooved.com/reader/2616

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144

Nov 14, 2013
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Nov 14, 2013
by
Eduardo Fradkin

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We now turn our attention to interacting quantum �eld theories. All of the results that we will derive in this section apply equally to both relativistic and non-relativistic theories with only minor changes. Here we will use the path integrals approach we developed in previous chapters.

Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...

Source: http://www.flooved.com/reader/2872

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113

Nov 14, 2013
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Nov 14, 2013
by
R. Artuso;Predrag Cvitanovi?;H.H. Rugh

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As we shall see, the trace formulas and spectral determinants work well, sometimes very well. The question is: Why? And it still is. The heuristic manipulations of chapter 18 were naive and reckless, as we are facing in�nite-dimensional vector spaces and singular integral kernels. We now outline the key ingredients of proofs that put the trace and determinant formulas on solid footing. This requires taking a closer look at the evolution operators from a mathematical point of view, since up to...

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2779

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116

Nov 14, 2013
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Nov 14, 2013
by
Arthur Mattuck;Haynes Miller;Jeremy Orloff;John Lewis

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In this note we state Green�s formula and look at some examples. We will prove it in the next note.

Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics

Source: http://www.flooved.com/reader/1397

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Nov 14, 2013
11/13

Nov 14, 2013
by
Prof. Peter J. Cameron

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This course introduces the basic notions of probability theory and develops them to the stage where one can begin to use probabilistic ideas in statistical inference and modelling, and the study of stochastic processes. Probability axioms. Conditional probability and independence. Discrete random variables and their distributions. Continuous distributions. Joint distributions. Independence. Expectations. Mean, variance, covariance, correlation. Limiting distributions

Topic: Mathematics

Source: http://www.flooved.com/reader/3509

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Nov 14, 2013
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Nov 14, 2013
by
Andrew Brooke-Taylor

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We shall associate a �Cartan matrix� to the system _ _ _ and derive some properties of this matrix. An abstract Cartan matrix will be any square matrix with this list of properties. It turns out that an abstract Cartan matrix essentially determines the root system. In this paper we will work toward making this statement precise and proving it. The problem of classi�cation of root systems is reduced then to the classi�cation of the Cartan matrices.

Topics: Maths, Linear Algebra and Geometry, Linear Algebra, Mathematics

Source: http://www.flooved.com/reader/1662

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148

Nov 14, 2013
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Nov 14, 2013
by
Matthew Hancock

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We now consider D�Alembert�s solution for a �nite string.

Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Partial Differential Equations (PDEs),...

Source: http://www.flooved.com/reader/1676

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Nov 14, 2013
11/13

Nov 14, 2013
by
Daniel Kleitman;Peter Shor

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A sequence of zeroes and ones can represent a message, a sequence of data in a computer or in digital communications, but it also can represent all sorts of mathematical or real world objects. Thus a sequence of length n can represent the outcome of n coin tosses, or a binary valued vector of length n, or a polynomial of degree up to n-1 with binary coefficients, or a number. We will now discuss three other interpretations for such a sequence.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1868

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130

Nov 14, 2013
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Nov 14, 2013
by
Chiang C. Mei

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Topics: Physics, Classical Mechanics, Fluid Mechanics, General Theory in Fluid Dynamics, Fluid Dynamics

Source: http://www.flooved.com/reader/2576

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Nov 14, 2013
11/13

Nov 14, 2013
by
Abhinav Kumar

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Topics: Maths, Linear Algebra and Geometry, Algebraic Geometry, Mathematics

Source: http://www.flooved.com/reader/2207

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Nov 14, 2013
11/13

Nov 14, 2013
by
Richard Melrose

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Now say that X is a set, R is a ring of subsets and we have a function � : R _ [0, �). This is the �measure�, what we�re looking for. One of the properties we need for this function is additivity : �(A _ B) = �(A) + �(B), if A, B _ R, A _ B = _ From just this property we can derive a number of properties about �....

Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics

Source: http://www.flooved.com/reader/1498