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Flooved is an online education platform founded in 2011, that seeks to provide free education to a global audience by providing lecture notes, handouts, and study guides online, beginning with undergraduate mathematics and physics content.



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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
Flooved
Oct 1, 2013 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
Flooved
Aug 20, 2013 Prof. Robert A. Beezer
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Topic: Mathematics
Source: http://www.flooved.com/reader/3473
Flooved
Aug 19, 2013 Matt Boelkins
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Topics: Calculus, Mathematics
Source: http://www.flooved.com/reader/3547
Flooved
Aug 16, 2013 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
Flooved
Aug 16, 2013 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
Flooved
Aug 11, 2013 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
Flooved
Jul 4, 2013 Prof. Carl Stitz;Prof. Jeff Zeager
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eye 3,354

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Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/3486
Flooved
Jul 4, 2013 Prof. Carl Stitz;Prof. Jeff Zeager
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eye 1,243

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Topics: Algebra, Mathematics
Source: http://www.flooved.com/reader/3475
Flooved
Jul 4, 2013 Prof. Carl Stitz;Prof. Jeff Zeager
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Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/3503
Flooved
Jun 3, 2013 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
Flooved
May 29, 2013 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
Flooved
May 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Apr 21, 2013 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
Flooved
Mar 1, 2013 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
Flooved
Feb 20, 2013 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
Flooved
Jan 17, 2013 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
Flooved
Jan 2, 2013 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
Flooved
2013 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
Flooved
2013 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
Flooved
2013 Prof. Philip Dawid
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Topic: Maths
Source: http://www.flooved.com/reader/3470
Flooved
2013 Peter Ouwehand
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Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/3361
Flooved
Dec 4, 2012 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
Flooved
Dec 1, 2012 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
Flooved
Nov 22, 2012 Z. Qian
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Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/1094
Flooved
Nov 20, 2012 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
Flooved
Nov 8, 2012 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
Flooved
Oct 11, 2012 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
Flooved
Aug 30, 2012 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
Flooved
Jul 3, 2012 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
Flooved
Jun 18, 2012 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
Flooved
Jun 16, 2012 Prof. Martin V. Day
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simultaneously.
Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/3478
Flooved
May 1, 2012 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
Flooved
Feb 29, 2012 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
Flooved
Jan 6, 2012 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
Flooved
2012 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
Flooved
2012 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
Flooved
2012 Peter Ouwehand
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Topic: Maths
Source: http://www.flooved.com/reader/3386
Flooved
2012 David Lippman;Jeff Eldridge;Mike Kenyon;Lawrence Morales;Melonie Rasmussen
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Topics: Maths, Mathematics
Source: http://www.flooved.com/reader/3501
Flooved
2012 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
Flooved
Nov 11, 2011 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
Flooved
Sep 2, 2011 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
Flooved
Jul 14, 2011 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
Flooved
Jul 12, 2011 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
Flooved
Jul 1, 2011 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
Flooved
Apr 25, 2011 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
Flooved
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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
Flooved
Mar 11, 2011 Joel Kamnitzer
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Topic: Maths
Source: http://www.flooved.com/reader/3400
Flooved
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eye 308

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Topic: Maths
Source: http://www.flooved.com/reader/2984
Flooved
2011 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
Flooved
2011 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
Flooved
2011 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
Flooved
2011 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
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2011 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
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2011 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
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2011 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
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Dec 28, 2010 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
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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
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Dec 28, 2010 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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Dec 28, 2010 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
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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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Dec 28, 2010 Peter Dourmashkin
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Topics: Physics, Classical Mechanics, Physics
Source: http://www.flooved.com/reader/3310