712
712

2020
2020

2020
by
A. S. Eddington

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By his theory of relativity Albert Einstein has provoked a revolution of thought in physical science. The achievement consists essentially in this:�Einstein has succeeded in separating far more completely than hitherto the share of the observer and the share of external nature in the things we see happen. The perception of an object by an observer depends on his own situation and circumstances; for example, distance will make it appear smaller and dimmer. We make allowance for this almost...

Topics: Physics, Astronomy and Astrophysics�, Fundamental Astronomy and Astrophysics, Instrumentation,...

Source: http://www.flooved.com/reader/3122

374
374

Oct 1, 2013
10/13

Oct 1, 2013
by
Ted Sundstrom

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This book may be different than other mathematics textbooks you have used since one of the main goals of this book is to help you to develop the ability to construct and write mathematical proofs. So this book is not just about mathematical content but is also about the process of doing mathematics. Along the way, you will also learn some important mathematical topics that will help you in your future study of mathematics.

Topic: Mathematics

Source: http://www.flooved.com/reader/3545

159
159

Aug 20, 2013
08/13

Aug 20, 2013
by
Prof. Robert A. Beezer

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Topic: Mathematics

Source: http://www.flooved.com/reader/3473

3,138
3.1K

Aug 19, 2013
08/13

Aug 19, 2013
by
Matt Boelkins

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Topics: Calculus, Mathematics

Source: http://www.flooved.com/reader/3547

671
671

Aug 16, 2013
08/13

Aug 16, 2013
by
Prof. Carl Stitz;Prof. Jeff Zeager

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Section 0.1 (Basic Set Theory and Interval Notation) contains a brief summary of the set theory terminology used throughout the text including sets of real numbers and interval notation. Section 0.2 (Real Number Arithmetic) lists the properties of real number arithmetic.1 Section 0.3 (Linear Equations and Inequalities) focuses on solving linear equations and linear inequalities from a strictly algebraic perspective. The geometry of graphing lines in the plane is deferred until Section 2.1...

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3498

2,742
2.7K

Aug 16, 2013
08/13

Aug 16, 2013
by
Dr Thomas W. Judson

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The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory

Topics: Group Theory, Permutations, Cosets, Mathematics

Source: http://www.flooved.com/reader/3494

4,136
4.1K

Aug 11, 2013
08/13

Aug 11, 2013
by
Prof. David Guichard

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The emphasis in this course is on problems�doing calculations and story problems. To master problem solving one needs a tremendous amount of practice doing problems.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3506

3,354
3.4K

Jul 4, 2013
07/13

Jul 4, 2013
by
Prof. Carl Stitz;Prof. Jeff Zeager

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Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3486

1,243
1.2K

Jul 4, 2013
07/13

Jul 4, 2013
by
Prof. Carl Stitz;Prof. Jeff Zeager

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comment 0

Topics: Algebra, Mathematics

Source: http://www.flooved.com/reader/3475

2,229
2.2K

Jul 4, 2013
07/13

Jul 4, 2013
by
Prof. Carl Stitz;Prof. Jeff Zeager

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Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3503

4,859
4.9K

Jun 3, 2013
06/13

Jun 3, 2013
by
Prof. Michael Corral

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This book covers elementary trigonometry. It is suitable for a one-semester course at the college level, though it could also be used in high schools

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3504

1,641
1.6K

May 29, 2013
05/13

May 29, 2013
by
Ji_� Lebl

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This book is a one semester course in basic analysis

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3479

3,817
3.8K

May 21, 2013
05/13

May 21, 2013
by
Prof. Michael Corral

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This book covers calculus in two and three variables. It is suitable for a one-semester course, normally known as �Vector Calculus�, �Multivariable Calculus�, or simply �Calculus III�. The prerequisites are the standard courses in single-variable calculus (a.k.a. Calculus I and II).

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3505

117
117

Apr 21, 2013
04/13

Apr 21, 2013
by
Predrag Cvitanovi?;L.V. Vela-Arevalo

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Here we brie�y review parts of classical dynamics that we will need lateron; symplectic invariance, canonical transformations, and stability of Hamiltonian �ows. If your eventual destination are applications such as chaos in quantumand/or semiconductor systems, read this chapter. If you work in neuroscience or �uid dynamics, skip this chapter, continue reading with the billiard dynamics of chapter 8 which requires no incantations of symplectic pairs or loxodromic quartets.

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2739

89
89

Apr 21, 2013
04/13

Apr 21, 2013
by
R. Artuso;Predrag Cvitanovi?

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This chapter is concerned with the mode locking problems for circle maps:besides its physical relevance it nicely illustrates the use of cycle expansions away from the dynamical setting, in the realm of renormalization theory at the transition to chaos.

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2742

164
164

Apr 21, 2013
04/13

Apr 21, 2013
by
Predrag Cvitanovi?;Gregor Tanner;G�bor Vattay

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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

143
143

Apr 21, 2013
04/13

Apr 21, 2013
by
Predrag Cvitanovi?;R. Mainieri

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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

93
93

Apr 21, 2013
04/13

Apr 21, 2013
by
Gregor Tanner

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So far much has been said about 1-dimensional maps, game of pinball and other curious but rather idealized dynamical systems. If you have become impatient and started wondering what good are the methods learned so far in solving real physical problems, we have good news for you. We will showin this chapter that the concepts of symbolic dynamics, unstable periodic orbits,and cycle expansions are essential tools to understand and calculate classical and quantum mechanical properties of nothing...

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2740

114
114

Apr 21, 2013
04/13

Apr 21, 2013
by
Predrag Cvitanovi?;E.A. Spiegel

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This chapter (which reader can safely skip on the �rst reading) is about noise, how it a_ects classical dynamics, and the ways it mimics quantum dynamics.

Topic: Maths

Source: http://www.flooved.com/reader/2745

98
98

Apr 21, 2013
04/13

Apr 21, 2013
by
Predrag Cvitanovi?;Gregor Tanner;G�bor Vattay

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We derive here the Gutzwiller trace formula and the semiclassical zeta function, the central results of the semiclassical quantization of classically chaotic systems. In chapter 35 we will rederive these formulas for the case of scattering in open systems. Quintessential wave mechanics e_ects such as creeping, di_raction and tunneling will be taken up in chapter 38.

Topics: Physics, Quantum Physics, Quantum Mechanics, Semiclassical Theories and Applications, Physics

Source: http://www.flooved.com/reader/2753

112
112

Apr 21, 2013
04/13

Apr 21, 2013
by
R. Mainieri;Predrag Cvitanovi�c;E.A. Spiegel

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We define a dynamical system (M, f) and classify its solutions as equilibria, periodic, and aperiodic. An �aperiodic� solution is either �wandering� or belongs to a non�wandering set, which in turn can be decomposed into chain-recurrent sets. Various cases are illustrated with concrete examples, such as the Rossler and Lorenz systems.

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2738

101
101

Apr 21, 2013
04/13

Apr 21, 2013
by
N. Whelan

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As noted in chapter 37, the classical mechanics of the helium atom is unde�ned at the instant of a triple collision. This is a common phenomenon - there is often some singularity or discontinuity in the classical mechanics of physical systems.This discontinuity can even be helpful in classifying the dynamics. The points in phase space which have a past or future at the discontinuity form manifolds which divide the phase space and provide the symbolic dynamics. The general rule is that quantum...

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2734

107
107

Apr 21, 2013
04/13

Apr 21, 2013
by
R. Artuso;Predrag Cvitanovi?;L. Rondoni;E.A. Spiegel

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We shall now show that the global evolution of the density of representative points is conveniently formulated in terms of linear action of evolution operators. We shall also show that the important, long-time �natural� invariant densities are unspeakably unfriendly and essentially uncomputable everywhere singular func-tions with support on fractal sets. Hence, in chapter 17 we rethink what is it that the theory needs to predict (�expectation values� of �observables�), relate these...

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2757

145
145

Apr 21, 2013
04/13

Apr 21, 2013
by
R. Artuso;Predrag Cvitanovi?;P. Dahlqvist;Gregor Tanner

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In the theory of chaotic dynamics developed so far we assumed that the evolution operators have discrete spectra... given by the zeros of... .The assumption was based on the tacit premise that the dynamics is everywhere exponentially unstable. Real life is nothing like that - state spaces are generically in�nitely interwoven patterns of stable and unstable behaviors. The stable (in the case of Hamiltonian �ows, integrable) orbits do not communicate with the ergodic components of the phase...

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2741

176
176

Apr 21, 2013
04/13

Apr 21, 2013
by
Predrag Cvitanovi?;N. Whelan;A. Wirzba

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So far the trace formulas have been derived assuming that the system underconsideration is bound. As we shall now see, we are in luck - the semiclassics of bound systems is all we need to understand the semiclassics for open, scattering systems as well. We start by a brief review of the quantum theory of elastic scattering of a point particle from a (repulsive) potential, and then develop the connection to the standard Gutzwiller theory for bound systems. We do this in two steps - �rst, a...

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2749

114
114

Apr 21, 2013
04/13

Apr 21, 2013
by
Predrag Cvitanovi?;Gregor Tanner;G�bor Vattay

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You have read the �rst volume of this book. So far, so good � anyone can play a game of classical pinball, and a skilled neuroscientist can poke rat brains. We learned that information about chaotic dynamics can be obtained by calculating spectra of linear operators such as the evolution operator of sect. 17.2 or the associated partial di_erential equations such as the Liouville equation (16.36). The spectra of these operators can be expressed in terms of periodic orbits of the...

Topics: Physics, Quantum Physics, Quantum Mechanics, Physics

Source: http://www.flooved.com/reader/2747

113
113

Apr 21, 2013
04/13

Apr 21, 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

1,617
1.6K

Mar 1, 2013
03/13

Mar 1, 2013
by
Prof. Al Doerr;Prof. Kenneth Levasseur

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In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topics in...

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3507

253
253

Feb 20, 2013
02/13

Feb 20, 2013
by
Luis Alvarez-Gaume;Miguel A. Vazquez-Mozo

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In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String Theory.

Topic: Maths

Source: http://www.flooved.com/reader/2942

296
296

Jan 17, 2013
01/13

Jan 17, 2013
by
Michael Monoyios

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These notes contain the core material. Some material is marked with an asterix and is not examinable. Some probability theory underlying conditional expectation and martingales is contained in the supplementary notes Background Probability, available on the course website. These are for those who wish to brush up on some probabilistic material, and are (I hope) helpful in developing intuition for notions like �ltrations and adaptedness of stochastic proicesses, using the binomial stock price...

Topics: Maths, Stochastic Analysis, Stochastic Processes, Financial Mathematics, Random Walks, Ito's...

Source: http://www.flooved.com/reader/1058

399
399

Jan 2, 2013
01/13

Jan 2, 2013
by
Janet Dyson

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This course builds on the ideas from Analysis I and also uses many of the results from that course. I have put some of the most important results from Analysis I in these notes but I will not write them on the board in the lecture.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1057

310
310

2013
2013

2013
by
Richard Earl

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In this �rst course in abstract algebra we concentrate on groups. Two other important algebraic structures are rings and �elds � you will likely have met the �eld axioms in LinearAlgebra I and Analysis I.

Topics: Maths, Algebra, Groups, Geometry and Groups, Groups, Group Actions, Permutations, Group Actions,...

Source: http://www.flooved.com/reader/1069

1,205
1.2K

2013
2013

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

293
293

2013
2013

2013
by
Prof. Philip Dawid

texts

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Topic: Maths

Source: http://www.flooved.com/reader/3470

1,810
1.8K

2013
2013

2013
by
Peter Ouwehand

texts

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Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3361

214
214

Dec 4, 2012
12/12

Dec 4, 2012
by
Christina Goldschmidt

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These notes are intended to complement the contents of the lectures. They contain more material than the lectures and, in particular, a few more examples. You are nonetheless strongly encouraged to attend all of the lectures. An original version of the �rst part of these notes was written by Alison Etheridge and I have also made extensive use of notes by Neil Laws and Jonathan Marchini.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1092

628
628

Dec 1, 2012
12/12

Dec 1, 2012
by
G.'t Hooft;S. Vandoren

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Prologue General relativity is a beautiful scheme for describing the gravitational �eld and the equations it obeys. Nowadays this theory is often used as a prototype for other, more intricate constructions to describe forces between elementary particles or other branches of fundamental physics. This is why in an introduction to general relativity it is of importance to separate as clearly as possible the various ingredients that together give shape to this paradigm. After explaining the...

Topic: Maths

Source: http://www.flooved.com/reader/2932

303
303

Nov 22, 2012
11/12

Nov 22, 2012
by
Z. Qian

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Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1094

1,596
1.6K

Nov 20, 2012
11/12

Nov 20, 2012
by
Prof. John Erdman

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The current set of notes is an activity-oriented companion to the study of real analysis. It is intended as a pedagogical companion for the beginner, an introduction to some of the main ideas in real analysis, a compendium of problems I think are useful in learning the subject, and an annotated reading/reference list

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3485

98
98

Nov 8, 2012
11/12

Nov 8, 2012
by
Zdzislaw (Gustav) Meglicki

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In this module we are also going to take another look at quantum mechanics, asking if quantum mechanics can be simulated by jump Markov processes. There was a vigorous discussion about this in the literature.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1660

1,367
1.4K

Oct 11, 2012
10/12

Oct 11, 2012
by
Peter M. Neumann

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These notes are intended as a rough guide to the eight-lecture course Introduction to Pure Mathematics which is a part of the Oxford 1st-year undergraduate course for the Preliminary Examination in Mathematics. Please do not expect a polished account. They are my personal lecture notes, not a carefully checked textbook. Nevertheless, I hope they may be of some help.

Topic: Maths

Source: http://www.flooved.com/reader/1056

177
177

Aug 30, 2012
08/12

Aug 30, 2012
by
Zdzislaw (Gustav) Meglicki

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We introduce homogeneous Markov processes and show how the apparatus developed so far simplifies for this class. This module does not discuss more specific Markov processes--continuous, jump, birth-death, etc.

Topics: Maths, Stochastic Analysis, Stochastic Processes, Markov Processes, Mathematics

Source: http://www.flooved.com/reader/1591

3,330
3.3K

Jul 3, 2012
07/12

Jul 3, 2012
by
Barbara Illowsky;Susan Dean

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The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two� and four�year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3483

496
496

Jun 18, 2012
06/12

Jun 18, 2012
by
Susan Dean;Barbara Illowsky

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Abstract: This module provides examples of Hypothesis Testing of a Single Mean and a Single Proportion as a part of the Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Topics: Maths, Statistics and Probability, Statistics, Hypothesis Testing, Mathematics

Source: http://www.flooved.com/reader/1565

714
714

Jun 16, 2012
06/12

Jun 16, 2012
by
Prof. Martin V. Day

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simultaneously.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3478

2,706
2.7K

May 1, 2012
05/12

May 1, 2012
by
William F. Trench

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The book is designed to �ll the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics.

Topics: Real Numbers, Analysis, Mathematics

Source: http://www.flooved.com/reader/3549

2,327
2.3K

Feb 29, 2012
02/12

Feb 29, 2012
by
Prof. Jim Hefferon

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on functions involving a single independent variable and a single dependent variable. For

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3490

443
443

Jan 6, 2012
01/12

Jan 6, 2012
by
Prof. P.D. Magnus

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forall x is an open access introductory textbook in formal logic. It covers translation, proofs, and formal semantics for sentential and predicate logic.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3495

1,332
1.3K

2012
2012

2012
by
Prof. Joseph Fields

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f(x). However, many of the functions of importance both within mathematics itself as

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3477

1,710
1.7K

2012
2012

2012
by
Peter Ouwehand

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These notes are for a short course in set theory at the undergraduate level at Stellenbosch University. No pretense at orignality is claimed. Though ampli�ed by material from a number of additional sources, the debt to the �rst few chapters of the book Set Theory, by Thomas Jech, Springer 2003, should be easily discernible.

Topics: Maths, Logic, Numbers and Set Theory, Set Theory, Mathematics

Source: http://www.flooved.com/reader/3368

570
570

2012
2012

2012
by
Peter Ouwehand

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Topic: Maths

Source: http://www.flooved.com/reader/3386

22,374
22K

2012
2012

2012
by
David Lippman;Jeff Eldridge;Mike Kenyon;Lawrence Morales;Melonie Rasmussen

texts

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Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/3501

1,731
1.7K

2012
2012

2012
by
Reinhard Diestel

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This is the electronic �professional edition� of the Springer book "Graph Theory", from their series Graduate Texts in Mathematics, vol. 173.... this book o_ers an introduction to the theory of graphs as part of (pure) mathematics; it contains neither explicit algorithms nor �real world� applications. My hope is that the potential for depth gained by this restriction in scope will serve students of computer science as much as their peers in mathematics...

Topics: Maths, Graph Theory, Basics, Connectivity and Matchings, Extremal Graph Theory, Eigenvalue Methods,...

Source: http://www.flooved.com/reader/3447

477
477

Nov 11, 2011
11/11

Nov 11, 2011
by
Frederique Oggier

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These notes were written to suit the contents of the course �Algebraic methods� given at NTU from August to October 2009, 2010 and 2011. Exercises have been collected during these past years from di_erent sources.

Topic: Maths

Source: http://www.flooved.com/reader/3353

3,463
3.5K

Sep 2, 2011
09/11

Sep 2, 2011
by
David H. Collingwood;K. David Prince;Matthew M. Conroy

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This book is full of worked out examples. We use the the notation �Soluttion.� to indicate where the reasoning for a problem begins; the symbol is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you �nd a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the �nal examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with...

Topic: Mathematics

Source: http://www.flooved.com/reader/3446

488
488

Jul 14, 2011
07/11

Jul 14, 2011
by
Rupinder Sekhon

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In this chapter, you will learn to: 1. Solve financial problems that involve simple interest. 2. Solve problems involving compound interest. 3. Find the future value of an annuity, and the amount of payments to a sinking fund. 4. Find the present value of an annuity, and an installment payment on a loan.

Topics: Maths, Stochastic Analysis, Financial Mathematics, Mathematics

Source: http://www.flooved.com/reader/1779

296
296

Jul 12, 2011
07/11

Jul 12, 2011
by
Rory Adams;Mark Horner;Heather Williams

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Logarithms are commonly refered to as logs, are the "opposite" of exponentials, just as subtraction is the opposite of addition and division is the opposite of multiplication. Logs "undo" exponentials. Technically speaking, logs are the inverses of exponentials. The logarithm of a number x in the base a is defined as the number n such that a^n = x.

Topics: Maths, Mathematics

Source: http://www.flooved.com/reader/1683

1,279
1.3K

Jul 1, 2011
07/11

Jul 1, 2011
by
Sergei Treil

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Topics: Linear Algebra, Vectors, Eigenvalues and Eigenvectors, Determinant and Trace, Dual of a...

Source: http://www.flooved.com/reader/3458

182
182

Apr 25, 2011
04/11

Apr 25, 2011
by
Andrew Snowden

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In this paper, we �rst develop and prove a special case of the Hurewicz theorem. We then give a few results from the theory of the higher homotopy groups. Finally, we state the full form of the Hurewicz theorem (without proof). We discuss some applications throughout the paper.

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

Source: http://www.flooved.com/reader/1114

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105

Apr 15, 2011
04/11

Apr 15, 2011
by
Steven G. Johnson

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These notes give a brief introduction to the mo_tivations, concepts, and properties of distributions, which generalize the notion of functions f(x) to al_low derivatives of discontinuities, �delta� functions, and other nice things. This generalization is in_creasingly important the more you work with linear PDEs, as we do in 18.303.

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

Source: http://www.flooved.com/reader/1680

182
182

Mar 11, 2011
03/11

Mar 11, 2011
by
Joel Kamnitzer

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Topic: Maths

Source: http://www.flooved.com/reader/3400

308
308

2011
2011

2011
by
J. D. Huba

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Topic: Maths

Source: http://www.flooved.com/reader/2984

116
116

2011
2011

2011
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff

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We now look at the pure resonant case for a second-order LTI DE. We will use the language of spring-mass systems in order to interpret the results in physical terms, but in fact the mathematics is the same for any second-order LTI DE for which the coef�cient of the �rst derivative is equal to zero.

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

Source: http://www.flooved.com/reader/1456

101
101

2011
2011

2011
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff

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We will call A cos(_t _ _) amplitude-phase form and a cos(_t) + b sin(_t) rectangular or Cartesian form. You should be familiar with amplitude-phase form; we usually prefer it because both amplitude and phase have geometric and physical meaning for us.

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

Source: http://www.flooved.com/reader/1452

95
95

2011
2011

2011
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff

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To solve linear differential equations with constant coef�cients, we need to be able to �nd the real and complex roots of polynomial equations. Though a lot of this is done today with calculators and computers, one still has to know how to do an important special case by hand: �nding the roots of z^n = _, where _ is a complex number, i.e., �nding the n-th roots of _. Polar representation will be a big help in this.

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

Source: http://www.flooved.com/reader/1387

192
192

2011
2011

2011
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff

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De�nitions: To describe the complex numbers, we use a formal symbol i representing �_1 ; then a complex number is an expression of the form: a + ib a, b real numbers.

Topics: Maths, Logic, Numbers and Set Theory, Analysis and Calculus, History and Philosophy of Mathematics,...

Source: http://www.flooved.com/reader/1246

92
92

2011
2011

2011
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff

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De�nitions: A sinusoidal function (or sinusoidal oscillation or sinusoidal signal) is one that can be wrtten in the form f (t) = A cos(_t _ _).

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

Source: http://www.flooved.com/reader/1429

113
113

2011
2011

2011
by
John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff

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Another Proof of the Superposition Principle: The superposition principle is so important a concept that it is worth reviewing yet again. Here we will use the integrating factors formula for the solution to �rst order linear ODE�s to give another simple proof of this principle.

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

Source: http://www.flooved.com/reader/1441

102
102

2011
2011

2011
by
Arthur Mattuck;Haynes Miller;Jeremy Orloff;John Lewis

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The Complex Plane: Complex numbers are represented geometrically by points in the plane: the number a + ib is represented by the point (a, b) in Cartesian coordinates. When the points of the plane are thought of as representing complex numbers in this way, the plane is called the complex plane.

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

Source: http://www.flooved.com/reader/1383

156
156

Dec 28, 2010
12/10

Dec 28, 2010
by
Peter Dourmashkin

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So far we have introduced the concepts of kinematics to describe motion in one dimension; however we live in a multidimensional universe. In order to explore and describe motion in this universe, we begin by looking at examples of two-dimensional motion, of which there are many; planets orbiting a star in elliptical orbits or a projectile moving under the action of uniform gravitation are two common examples. We will now extend our definitions of position, velocity, and acceleration for an...

Topic: Maths

Source: http://www.flooved.com/reader/3308

186
186

Dec 28, 2010
12/10

Dec 28, 2010
by
Peter Dourmashkin

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When the acceleration is a non-constant function, we would like to know how the x-component of the velocity changes for a time interval !t = [0, t]. Since the acceleration is non-constant we cannot simply multiply the acceleration by the time interval. We shall calculate the change in the x-component of the velocity for a small time interval !ti " [ti , ti +1] and sum over these results. We then take the limit as the time intervals become very small and the summation becomes an integral of...

Topics: Physics, Classical Mechanics, Physics

Source: http://www.flooved.com/reader/3297

282
282

Dec 28, 2010
12/10

Dec 28, 2010
by
Peter Dourmashkin

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Topics: Physics, Classical Mechanics, Classical Mechanics of Discrete Systems, Fundamental Concepts,...

Source: http://www.flooved.com/reader/3306

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157

Dec 28, 2010
12/10

Dec 28, 2010
by
Peter Dourmashkin

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So far we have analyzed the motion of point-like bodies under the action of forces using Newton�s Laws of Motion. We shall now introduce the Principle of Conservation of Energy to study the changes in energy of a system between an initial state and final state. In particular we shall introduce the concept of potential energy to describe the effect of conservative internal forces acting on the constituent components of a system.

Topic: Maths

Source: http://www.flooved.com/reader/3293

279
279

Dec 28, 2010
12/10

Dec 28, 2010
by
Peter Dourmashkin

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Topics: Maths, Physics, Dynamics and Relativity, Classical Mechanics, Dynamics and Relativity, Classical...

Source: http://www.flooved.com/reader/3304

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320

Dec 28, 2010
12/10

Dec 28, 2010
by
Peter Dourmashkin

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favoritefavoritefavoritefavoritefavorite ( 1 reviews )

Topics: Physics, Classical Mechanics, Physics

Source: http://www.flooved.com/reader/3310