Perturbative and Non-perturbative Aspects of the Chern-Simons-Witten Theory

The Area of a Triangle

The e of Tingle tkhlid June 1, 015 1 Intodution In this tile we will e disussing the vious methods used fo detemining the e of tingle. Let [X] denote the e of X. Using se nd Height To stt off, the simplest

A Study of Some Integral Problems Using Maple

Mthemtis n Sttistis (): -, 0 DOI: 0.89/ms.0.000 http://www.hpub.og A Stuy of Some Integl Poblems Ug Mple Chii-Huei Yu Deptment of Mngement n Infomtion, Nn Jeon Univesity of Siene n Tehnology, Tinn City,

Class Summary. be functions and f( D) , we define the composition of f with g, denoted g f by

Clss Summy.5 Eponentil Functions.6 Invese Functions nd Logithms A function f is ule tht ssigns to ech element D ectly one element, clled f( ), in. Fo emple : function not function Given functions f, g:

Mathematical Reflections, Issue 5, INEQUALITIES ON RATIOS OF RADII OF TANGENT CIRCLES. Y.N. Aliyev

themtil efletions, Issue 5, 015 INEQULITIES ON TIOS OF DII OF TNGENT ILES YN liev stt Some inequlities involving tios of dii of intenll tngent iles whih inteset the given line in fied points e studied

Radial geodesics in Schwarzschild spacetime

Rdil geodesics in Schwzschild spcetime Spheiclly symmetic solutions to the Einstein eqution tke the fom ds dt d dθ sin θdϕ whee is constnt. We lso hve the connection components, which now tke the fom using

Illustrating the space-time coordinates of the events associated with the apparent and the actual position of a light source

Illustting the spe-time oointes of the events ssoite with the ppent n the tul position of light soue Benh Rothenstein ), Stefn Popesu ) n Geoge J. Spi 3) ) Politehni Univesity of Timiso, Physis Deptment,

Influence of the Magnetic Field in the Solar Interior on the Differential Rotation

Influene of the gneti Fiel in the Sol Inteio on the Diffeentil ottion Lin-Sen Li * Deptment of Physis Nothest Noml Univesity Chnghun Chin * Coesponing utho: Lin-Sen Li Deptment of Physis Nothest Noml Univesity

Math 4318 : Real Analysis II Mid-Term Exam 1 14 February 2013

Mth 4318 : Rel Anlysis II Mid-Tem Exm 1 14 Febuy 2013 Nme: Definitions: Tue/Flse: Poofs: 1. 2. 3. 4. 5. 6. Totl: Definitions nd Sttements of Theoems 1. (2 points) Fo function f(x) defined on (, b) nd fo

THEORY OF EQUATIONS OBJECTIVE PROBLEMS. If the eqution x 6x 0 0 ) - ) 4) -. If the sum of two oots of the eqution k is -48 ) 6 ) 48 4) 4. If the poduct of two oots of 4 ) -4 ) 4) - 4. If one oot of is

Physics 217 Practice Final Exam: Solutions

Physis 17 Ptie Finl Em: Solutions Fll This ws the Physis 17 finl em in Fll 199 Twenty-thee students took the em The vege soe ws 11 out of 15 (731%), nd the stndd devition 9 The high nd low soes wee 145

CHAPTER 7 Applications of Integration

CHAPTER 7 Applitions of Integtion Setion 7. Ae of Region Between Two Cuves.......... Setion 7. Volume: The Disk Method................. Setion 7. Volume: The Shell Method................ Setion 7. A Length

Analysis of Variance for Multiple Factors

Multiple Fto ANOVA Notes Pge wo Fto Anlsis Anlsis of Vine fo Multiple Ftos Conside two ftos (tetments) A nd B with A done t levels nd B done t levels. Within given tetment omintion of A nd B levels, leled

INTEGRATION. 1 Integrals of Complex Valued functions of a REAL variable

INTEGRATION NOTE: These notes re supposed to supplement Chpter 4 of the online textbook. 1 Integrls of Complex Vlued funtions of REAL vrible If I is n intervl in R (for exmple I = [, b] or I = (, b)) nd

MAT 403 NOTES 4. f + f =

MAT 403 NOTES 4 1. Fundmentl Theorem o Clulus We will proo more generl version o the FTC thn the textook. But just like the textook, we strt with the ollowing proposition. Let R[, ] e the set o Riemnn

Lecture 10. Solution of Nonlinear Equations - II

Fied point Poblems Lectue Solution o Nonline Equtions - II Given unction g : R R, vlue such tht gis clled ied point o the unction g, since is unchnged when g is pplied to it. Whees with nonline eqution

Electromagnetism Notes, NYU Spring 2018

Eletromgnetism Notes, NYU Spring 208 April 2, 208 Ation formultion of EM. Free field desription Let us first onsider the free EM field, i.e. in the bsene of ny hrges or urrents. To tret this s mehnil system

Properties and Formulas

Popeties nd Fomuls Cpte 1 Ode of Opetions 1. Pefom ny opetion(s) inside gouping symols. 2. Simplify powes. 3. Multiply nd divide in ode fom left to igt. 4. Add nd sutt in ode fom left to igt. Identity

10.3 The Quadratic Formula

. Te Qudti Fomul We mentioned in te lst setion tt ompleting te sque n e used to solve ny qudti eqution. So we n use it to solve 0. We poeed s follows 0 0 Te lst line of tis we ll te qudti fomul. Te Qudti

This immediately suggests an inverse-square law for a "piece" of current along the line.

Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iot-svt Lw T nvese-sque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line

More Properties of the Riemann Integral

More Properties of the Riemnn Integrl Jmes K. Peterson Deprtment of Biologil Sienes nd Deprtment of Mthemtil Sienes Clemson University Februry 15, 2018 Outline More Riemnn Integrl Properties The Fundmentl

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3

DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl

1 PYTHAGORAS THEOREM 1. Given a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

1 PYTHAGORAS THEOREM 1 1 Pythgors Theorem In this setion we will present geometri proof of the fmous theorem of Pythgors. Given right ngled tringle, the squre of the hypotenuse is equl to the sum of the

General Physics II. number of field lines/area. for whole surface: for continuous surface is a whole surface

Genel Physics II Chpte 3: Guss w We now wnt to quickly discuss one of the moe useful tools fo clculting the electic field, nmely Guss lw. In ode to undestnd Guss s lw, it seems we need to know the concept

Week 8. Topic 2 Properties of Logarithms

Week 8 Topic 2 Popeties of Logithms 1 Week 8 Topic 2 Popeties of Logithms Intoduction Since the esult of ithm is n eponent, we hve mny popeties of ithms tht e elted to the popeties of eponents. They e

The study of dual integral equations with generalized Legendre functions

J. Mth. Anl. Appl. 34 (5) 75 733 www.elsevier.om/lote/jm The study of dul integrl equtions with generlized Legendre funtions B.M. Singh, J. Rokne,R.S.Dhliwl Deprtment of Mthemtis, The University of Clgry,

Mark Scheme (Results) January 2008

Mk Scheme (Results) Jnuy 00 GCE GCE Mthemtics (6679/0) Edecel Limited. Registeed in Englnd nd Wles No. 4496750 Registeed Office: One90 High Holbon, London WCV 7BH Jnuy 00 6679 Mechnics M Mk Scheme Question

Friedmannien equations

..6 Fiedmnnien equtions FLRW metic is : ds c The metic intevl is: dt ( t) d ( ) hee f ( ) is function which detemines globl geometic l popety of D spce. f d sin d One cn put it in the Einstein equtions

STD: XI MATHEMATICS Total Marks: 90. I Choose the correct answer: ( 20 x 1 = 20 ) a) x = 1 b) x =2 c) x = 3 d) x = 0

STD: XI MATHEMATICS Totl Mks: 90 Time: ½ Hs I Choose the coect nswe: ( 0 = 0 ). The solution of is ) = b) = c) = d) = 0. Given tht the vlue of thid ode deteminnt is then the vlue of the deteminnt fomed

Chapter Direct Method of Interpolation More Examples Mechanical Engineering

Chpte 5 iect Method o Intepoltion Moe Exmples Mechnicl Engineeing Exmple Fo the pupose o shinking tunnion into hub, the eduction o dimete o tunnion sht by cooling it though tempetue chnge o is given by

Qualitative Analysis for Solutions of a Class of. Nonlinear Ordinary Differential Equations

Adv. Theo. Appl. Mech., Vol. 7, 2014, no. 1, 1-7 HIKARI Ltd, www.m-hiki.com http://dx.doi.og/10.12988/tm.2014.458 Qulittive Anlysis fo Solutions of Clss of Nonline Odiny Diffeentil Equtions Juxin Li *,

Applications of Definite Integral

Chpter 5 Applitions of Definite Integrl 5.1 Are Between Two Curves In this setion we use integrls to find res of regions tht lie between the grphs of two funtions. Consider the region tht lies between

Scientific Computing & Modelling NV, Vrije Universiteit, Theoretical Chemistry, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands c

Electonic Supplementy Mteil (ESI) fo Physicl Chemisty Chemicl Physics. This jounl is The Royl Society of Chemisty 2014 Suppoting Infomtion fo: Pedicting phosphoescent lifetimes nd zeo-field splitting of

Physics 505 Fall 2005 Midterm Solutions. This midterm is a two hour open book, open notes exam. Do all three problems.

Physics 55 Fll 5 Midtem Solutions This midtem is two hou open ook, open notes exm. Do ll thee polems. [35 pts] 1. A ectngul ox hs sides of lengths, nd c z x c [1] ) Fo the Diichlet polem in the inteio

Applications of Definite Integral

Chpter 5 Applitions of Definite Integrl 5.1 Are Between Two Curves In this setion we use integrls to find res of regions tht lie between the grphs of two funtions. Consider the region tht lies between

Lecture 1 - Introduction and Basic Facts about PDEs

* 18.15 - Introdution to PDEs, Fll 004 Prof. Gigliol Stffilni Leture 1 - Introdution nd Bsi Fts bout PDEs The Content of the Course Definition of Prtil Differentil Eqution (PDE) Liner PDEs VVVVVVVVVVVVVVVVVVVV

A NOTE ON THE POCHHAMMER FREQUENCY EQUATION

A note on the Pohhmme feqeny eqtion SCIENCE AND TECHNOLOGY - Reseh Jonl - Volme 6 - Univesity of Mitis Rédit Mitis. A NOTE ON THE POCHHAMMER FREQUENCY EQUATION by F.R. GOLAM HOSSEN Deptment of Mthemtis

2. Topic: Summation of Series (Mathematical Induction) When n = 1, L.H.S. = S 1 = u 1 = 3 R.H.S. = 1 (1)(1+1)(4+5) = 3

GCE A Level Otober/November 008 Suggested Solutions Mthemtis H (970/0) version. MATHEMATICS (H) Pper Suggested Solutions. Topi: Definite Integrls From the digrm: Are A = y dx = x Are B = x dy = y dy dx

Algebra Based Physics. Gravitational Force. PSI Honors universal gravitation presentation Update Fall 2016.notebookNovember 10, 2016

Newton's Lw of Univesl Gvittion Gvittionl Foce lick on the topic to go to tht section Gvittionl Field lgeb sed Physics Newton's Lw of Univesl Gvittion Sufce Gvity Gvittionl Field in Spce Keple's Thid Lw

Co-ordinated s-convex Function in the First Sense with Some Hadamard-Type Inequalities

Int. J. Contemp. Mth. Sienes, Vol. 3, 008, no. 3, 557-567 Co-ordinted s-convex Funtion in the First Sense with Some Hdmrd-Type Inequlities Mohmmd Alomri nd Mslin Drus Shool o Mthemtil Sienes Fulty o Siene

( ) D x ( s) if r s (3) ( ) (6) ( r) = d dr D x

SIO 22B, Rudnick dpted fom Dvis III. Single vile sttistics The next few lectues e intended s eview of fundmentl sttistics. The gol is to hve us ll speking the sme lnguge s we move to moe dvnced topics.

AP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals

AP Clulus BC Chpter 8: Integrtion Tehniques, L Hopitl s Rule nd Improper Integrls 8. Bsi Integrtion Rules In this setion we will review vrious integrtion strtegies. Strtegies: I. Seprte the integrnd into

Part 4. Integration (with Proofs)

Prt 4. Integrtion (with Proofs) 4.1 Definition Definition A prtition P of [, b] is finite set of points {x 0, x 1,..., x n } with = x 0 < x 1

FI 2201 Electromagnetism

FI 1 Electomgnetism Alexnde A. Isknd, Ph.D. Physics of Mgnetism nd Photonics Resech Goup Electosttics ELECTRIC PTENTIALS 1 Recll tht we e inteested to clculte the electic field of some chge distiution.

Integrals and Polygamma Representations for Binomial Sums

3 47 6 3 Jounl of Intege Sequences, Vol. 3 (, Aticle..8 Integls nd Polygmm Repesenttions fo Binomil Sums Anthony Sofo School of Engineeing nd Science Victoi Univesity PO Box 448 Melboune City, VIC 8 Austli

SPA7010U/SPA7010P: THE GALAXY. Solutions for Coursework 1. Questions distributed on: 25 January 2018.

SPA7U/SPA7P: THE GALAXY Solutions fo Cousewok Questions distibuted on: 25 Jnuy 28. Solution. Assessed question] We e told tht this is fint glxy, so essentilly we hve to ty to clssify it bsed on its spectl

Topics for Review for Final Exam in Calculus 16A

Topics fo Review fo Finl Em in Clculus 16A Instucto: Zvezdelin Stnkov Contents 1. Definitions 1. Theoems nd Poblem Solving Techniques 1 3. Eecises to Review 5 4. Chet Sheet 5 1. Definitions Undestnd the

10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =

Chpte 1 nivesl Gvittion 11 *P1. () The un-th distnce is 1.4 nd the th-moon 8 distnce is.84, so the distnce fom the un to the Moon duing sol eclipse is 11 8 11 1.4.84 = 1.4 The mss of the un, th, nd Moon

RELATIVE KINEMATICS. q 2 R 12. u 1 O 2 S 2 S 1. r 1 O 1. Figure 1

RELAIVE KINEMAICS he equtions of motion fo point P will be nlyzed in two diffeent efeence systems. One efeence system is inetil, fixed to the gound, the second system is moving in the physicl spce nd the

MATH34032: Green s Functions, Integral Equations and the Calculus of Variations 1. 1 [(y ) 2 + yy + y 2 ] dx,

MATH3403: Green s Funtions, Integrl Equtions nd the Clulus of Vritions 1 Exmples 5 Qu.1 Show tht the extreml funtion of the funtionl I[y] = 1 0 [(y ) + yy + y ] dx, where y(0) = 0 nd y(1) = 1, is y(x)

Green s Theorem. (2x e y ) da. (2x e y ) dx dy. x 2 xe y. (1 e y ) dy. y=1. = y e y. y=0. = 2 e

Green s Theorem. Let be the boundry of the unit squre, y, oriented ounterlokwise, nd let F be the vetor field F, y e y +, 2 y. Find F d r. Solution. Let s write P, y e y + nd Q, y 2 y, so tht F P, Q. Let

1 Using Integration to Find Arc Lengths and Surface Areas

Novembe 9, 8 MAT86 Week Justin Ko Using Integtion to Find Ac Lengths nd Sufce Aes. Ac Length Fomul: If f () is continuous on [, b], then the c length of the cuve = f() on the intevl [, b] is given b s

defined on a domain can be expanded into the Taylor series around a point a except a singular point. Also, f( z)

08 Tylo eie nd Mcluin eie A holomophic function f( z) defined on domin cn be expnded into the Tylo eie ound point except ingul point. Alo, f( z) cn be expnded into the Mcluin eie in the open dik with diu

Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) ,

R Pen Towe Rod No Conttos Ae Bistupu Jmshedpu 8 Tel (67)89 www.penlsses.om IIT JEE themtis Ppe II PART III ATHEATICS SECTION I (Totl ks : ) (Single Coet Answe Type) This setion ontins 8 multiple hoie questions.

Review of Mathematical Concepts

ENEE 322: Signls nd Systems view of Mthemticl Concepts This hndout contins ief eview of mthemticl concepts which e vitlly impotnt to ENEE 322: Signls nd Systems. Since this mteil is coveed in vious couses

9.4 The response of equilibrium to temperature (continued)

9.4 The esponse of equilibium to tempetue (continued) In the lst lectue, we studied how the chemicl equilibium esponds to the vition of pessue nd tempetue. At the end, we deived the vn t off eqution: d

arxiv: v1 [hep-th] 6 Jul 2016

INR-TH-2016-021 Instbility of Sttic Semi-Closed Wolds in Genelized Glileon Theoies Xiv:1607.01721v1 [hep-th] 6 Jul 2016 O. A. Evseev, O. I. Melichev Fculty of Physics, M V Lomonosov Moscow Stte Univesity,

Chapter 1. Model Theory

Chte odel heo.. Intoduction Phsicl siultion of hdulic henoenon, such s the flow ove sillw, in the lboto is clled hsicl odel o onl odel. Potote is the hdulic henoen in the ntue like the sillw ove d. odels

9.1 The multiplicative group of a finite field. Theorem 9.1. The multiplicative group F of a finite field is cyclic.

Chapte 9 Pimitive Roots 9.1 The multiplicative goup of a finite fld Theoem 9.1. The multiplicative goup F of a finite fld is cyclic. Remak: In paticula, if p is a pime then (Z/p) is cyclic. In fact, this

Matrices SCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics (c) 1. Definition of a Matrix

tries Definition of tri mtri is regulr rry of numers enlosed inside rkets SCHOOL OF ENGINEERING & UIL ENVIRONEN Emple he following re ll mtries: ), ) 9, themtis ), d) tries Definition of tri Size of tri

10 Statistical Distributions Solutions

Communictions Engineeing MSc - Peliminy Reding 1 Sttisticl Distiutions Solutions 1) Pove tht the vince of unifom distiution with minimum vlue nd mximum vlue ( is ) 1. The vince is the men of the sques

Chapter 7. Kleene s Theorem. 7.1 Kleene s Theorem. The following theorem is the most important and fundamental result in the theory of FA s:

Chpte 7 Kleene s Theoem 7.1 Kleene s Theoem The following theoem is the most impotnt nd fundmentl esult in the theoy of FA s: Theoem 6 Any lnguge tht cn e defined y eithe egul expession, o finite utomt,

Chapter 6 Notes, Larson/Hostetler 3e

Contents 6. Antiderivtives nd the Rules of Integrtion.......................... 6. Are nd the Definite Integrl.................................. 6.. Are............................................ 6. Reimnn

where the box contains a finite number of gates from the given collection. Examples of gates that are commonly used are the following: a b

CS 294-2 9/11/04 Quntum Ciruit Model, Solovy-Kitev Theorem, BQP Fll 2004 Leture 4 1 Quntum Ciruit Model 1.1 Clssil Ciruits - Universl Gte Sets A lssil iruit implements multi-output oolen funtion f : {0,1}

Physics 604 Problem Set 1 Due Sept 16, 2010

Physics 64 Polem et 1 Due ept 16 1 1) ) Inside good conducto the electic field is eo (electons in the conducto ecuse they e fee to move move in wy to cncel ny electic field impessed on the conducto inside

1.2. Linear Variable Coefficient Equations. y + b "! = a y + b " Remark: The case b = 0 and a non-constant can be solved with the same idea as above.

1 12 Liner Vrible Coefficient Equtions Section Objective(s): Review: Constnt Coefficient Equtions Solving Vrible Coefficient Equtions The Integrting Fctor Method The Bernoulli Eqution 121 Review: Constnt

Note 16. Stokes theorem Differential Geometry, 2005

Note 16. Stokes theorem ifferentil Geometry, 2005 Stokes theorem is the centrl result in the theory of integrtion on mnifolds. It gives the reltion between exterior differentition (see Note 14) nd integrtion

Section 4.4. Green s Theorem

The Clulus of Funtions of Severl Vriles Setion 4.4 Green s Theorem Green s theorem is n exmple from fmily of theorems whih onnet line integrls (nd their higher-dimensionl nlogues) with the definite integrls

Equations from the Millennium Theory of Inertia and Gravity. Copyright 2004 Joseph A. Rybczyk

Equtions fo the illenniu heoy of Ineti nd vity Copyight 004 Joseph A. Rybzyk ollowing is oplete list of ll of the equtions used o deived in the illenniu heoy of Ineti nd vity. o ese of efeene the equtions

EECE 260 Electrical Circuits Prof. Mark Fowler

EECE 60 Electicl Cicuits Pof. Mk Fowle Complex Numbe Review /6 Complex Numbes Complex numbes ise s oots of polynomils. Definition of imginy # nd some esulting popeties: ( ( )( ) )( ) Recll tht the solution

Course Updates. Reminders: 1) Assignment #8 available. 2) Chapter 28 this week.

Couse Updtes http://www.phys.hwii.edu/~vne/phys7-sp1/physics7.html Remindes: 1) Assignment #8 vilble ) Chpte 8 this week Lectue 3 iot-svt s Lw (Continued) θ d θ P R R θ R d θ d Mgnetic Fields fom long

MATH 409 Advanced Calculus I Lecture 22: Improper Riemann integrals.

MATH 409 Advned Clulus I Leture 22: Improper Riemnn integrls. Improper Riemnn integrl If funtion f : [,b] R is integrble on [,b], then the funtion F(x) = x f(t)dt is well defined nd ontinuous on [,b].

16z z q. q( B) Max{2 z z z z B} r z r z r z r z B. John Riley 19 October Econ 401A: Microeconomic Theory. Homework 2 Answers

John Riley 9 Otober 6 Eon 4A: Miroeonomi Theory Homework Answers Constnt returns to sle prodution funtion () If (,, q) S then 6 q () 4 We need to show tht (,, q) S 6( ) ( ) ( q) q [ q ] 4 4 4 4 4 4 Appeling

r r E x w, y w, z w, (1) Where c is the speed of light in vacuum.

ISSN: 77-754 ISO 900:008 Cetified Intentionl Jonl of Engineeing nd Innovtive Tehnology (IJEIT) olme, Isse 0, Apil 04 The Replement of the Potentils s Conseene of the Limittions Set by the Lw of the Self

(A) 6.32 (B) 9.49 (C) (D) (E) 18.97

Univesity of Bhin Physics 10 Finl Exm Key Fll 004 Deptment of Physics 13/1/005 8:30 10:30 e =1.610 19 C, m e =9.1110 31 Kg, m p =1.6710 7 Kg k=910 9 Nm /C, ε 0 =8.8410 1 C /Nm, µ 0 =4π10 7 T.m/A Pt : 10

Optimization. x = 22 corresponds to local maximum by second derivative test

Optimiztion Lectue 17 discussed the exteme vlues of functions. This lectue will pply the lesson fom Lectue 17 to wod poblems. In this section, it is impotnt to emembe we e in Clculus I nd e deling one-vible

7.5-Determinants in Two Variables

7.-eteminnts in Two Vibles efinition of eteminnt The deteminnt of sque mti is el numbe ssocited with the mti. Eve sque mti hs deteminnt. The deteminnt of mti is the single ent of the mti. The deteminnt

Solutions to Midterm Physics 201

Solutions to Midtem Physics. We cn conside this sitution s supeposition of unifomly chged sphee of chge density ρ nd dius R, nd second unifomly chged sphee of chge density ρ nd dius R t the position of

] dx (3) = [15x] 2 0

Leture 6. Double Integrls nd Volume on etngle Welome to Cl IV!!!! These notes re designed to be redble nd desribe the w I will eplin the mteril in lss. Hopefull the re thorough, but it s good ide to hve

COMPUTER AIDED ANALYSIS OF KINEMATICS AND KINETOSTATICS OF SIX-BAR LINKAGE MECHANISM THROUGH THE CONTOUR METHOD

SINTIFI PROINGS XIV INTRNTIONL ONGRSS "MHINS. THNOLОGIS. MTRILS." 17 - SUMMR SSSION W ISSN 55-X PRINT ISSN 55-1 OMPUTR I NLYSIS OF KINMTIS N KINTOSTTIS OF SIX-R LINKG MHNISM THROUGH TH ONTOUR MTHO Pof.so..

Solutions to Assignment 1

MTHE 237 Fll 2015 Solutions to Assignment 1 Problem 1 Find the order of the differentil eqution: t d3 y dt 3 +t2 y = os(t. Is the differentil eqution liner? Is the eqution homogeneous? b Repet the bove

SOLUTIONS ( ) ( )! ( ) ( ) ( ) ( )! ( ) ( ) ( ) ( ) n r. r ( Pascal s equation ). n 1. Stepanov Dalpiaz

STAT UIU Pctice Poblems # SOLUTIONS Stepov Dlpiz The followig e umbe of pctice poblems tht my be helpful fo completig the homewo, d will liely be vey useful fo studyig fo ems...-.-.- Pove (show) tht. (

Supplementary Information. Origin of Chains of Au-PbS Nano-Dumbbells in. Space

Supplementy Infomtion Oigin of Chins of Au-PbS Nno-Dumbbells in Spe Chndn Mondl, Ali Hossin Khn, Bidis Ds, Somobt Ahy* & Sujit Sengupt*, Cente fo Advned Mteils, Indin Assoition fo the Cultivtion of Siene,

Calculus Cheat Sheet. Integrals Definitions. where F( x ) is an anti-derivative of f ( x ). Fundamental Theorem of Calculus. dx = f x dx g x dx

Clulus Chet Sheet Integrls Definitions Definite Integrl: Suppose f ( ) is ontinuous Anti-Derivtive : An nti-derivtive of f ( ) on [, ]. Divide [, ] into n suintervls of is funtion, F( ), suh tht F = f.

Jim Lambers MAT 280 Spring Semester Lecture 26 and 27 Notes

Jim Lmbers MAT 280 pring emester 2009-10 Lecture 26 nd 27 Notes These notes correspond to ection 8.6 in Mrsden nd Tromb. ifferentil Forms To dte, we hve lerned the following theorems concerning the evlution

Chapter Seven Notes N P U1C7

Chpte Seven Notes N P UC7 Nme Peiod Setion 7.: Angles nd Thei Mesue In fling, hitetue, nd multitude of othe fields, ngles e used. An ngle is two diffeent s tht hve the sme initil (o stting) point. The

SAMPLE LABORATORY SESSION FOR JAVA MODULE B. Calculations for Sample Cross-Section 2

SAMPLE LABORATORY SESSION FOR JAVA MODULE B Calulations fo Sample Coss-Setion. Use Input. Setion Popeties The popeties of Sample Coss-Setion ae shown in Figue and ae summaized below. Figue : Popeties of

Proving the Pythagorean Theorem

Proving the Pythgoren Theorem W. Bline Dowler June 30, 2010 Astrt Most people re fmilir with the formul 2 + 2 = 2. However, in most ses, this ws presented in lssroom s n solute with no ttempt t proof or

Data Structures. Element Uniqueness Problem. Hash Tables. Example. Hash Tables. Dana Shapira. 19 x 1. ) h(x 4. ) h(x 2. ) h(x 3. h(x 1. x 4. x 2.

Element Uniqueness Poblem Dt Stuctues Let x,..., xn < m Detemine whethe thee exist i j such tht x i =x j Sot Algoithm Bucket Sot Dn Shpi Hsh Tbles fo (i=;i

Mathematics 19A; Fall 2001; V. Ginzburg Practice Final Solutions

Mthemtics 9A; Fll 200; V Ginzburg Prctice Finl Solutions For ech of the ten questions below, stte whether the ssertion is true or flse ) Let fx) be continuous t x Then x fx) f) Answer: T b) Let f be differentible

Module 4: Moral Hazard - Linear Contracts

Module 4: Mol Hzd - Line Contts Infomtion Eonomis (E 55) Geoge Geogidis A pinipl employs n gent. Timing:. The pinipl o es line ontt of the fom w (q) = + q. is the sly, is the bonus te.. The gent hooses

f (x)dx = f(b) f(a). a b f (x)dx is the limit of sums

Green s Theorem If f is funtion of one vrible x with derivtive f x) or df dx to the Fundmentl Theorem of lulus, nd [, b] is given intervl then, ording This is not trivil result, onsidering tht b b f x)dx

On Natural Partial Orders of IC-Abundant Semigroups

Intentionl Jounl of Mthemtics nd Computtionl Science Vol. No. 05 pp. 5-9 http://www.publicsciencefmewok.og/jounl/ijmcs On Ntul Ptil Odes of IC-Abundnt Semigoups Chunhu Li Bogen Xu School of Science Est

From E.G. Haug Escape Velocity To the Golden Ratio at the Black Hole. Branko Zivlak, Novi Sad, May 2018

Fom E.G. Haug Esape eloity To the Golden Ratio at the Blak Hole Banko Zivlak, bzivlak@gmail.om Novi Sad, May 018 Abstat Esape veloity fom the E.G. Haug has been heked. It is ompaed with obital veloity

The Riemann and the Generalised Riemann Integral

The Riemnn nd the Generlised Riemnn Integrl Clvin 17 July 14 Contents 1 The Riemnn Integrl 1.1 Riemnn Integrl............................................ 1. Properties o Riemnn Integrble Funtions.............................

arxiv:hep-th/ v2 11 Nov 2004

Gibbons-Maeda-de Sitte Black Holes Chang Jun Gao 1 Shuang Nan Zhang 1,2,3,4 1 Depatment of Physics and Cente fo Astophysics, Tsinghua Univesity, Beijing 100084, Chinamailaddess) 2 Physics Depatment, Univesity

We know that if f is a continuous nonnegative function on the interval [a, b], then b

1 Ares Between Curves c 22 Donld Kreider nd Dwight Lhr We know tht if f is continuous nonnegtive function on the intervl [, b], then f(x) dx is the re under the grph of f nd bove the intervl. We re going

u t = k 2 u x 2 (1) a n sin nπx sin 2 L e k(nπ/l) t f(x) = sin nπx f(x) sin nπx dx (6) 2 L f(x 0 ) sin nπx 0 2 L sin nπx 0 nπx

Chpter 9: Green s functions for time-independent problems Introductory emples One-dimensionl het eqution Consider the one-dimensionl het eqution with boundry conditions nd initil condition We lredy know

Section 3.6. Definite Integrals

The Clulus of Funtions of Severl Vribles Setion.6 efinite Integrls We will first define the definite integrl for funtion f : R R nd lter indite how the definition my be extended to funtions of three or

Answers to test yourself questions

Answes to test youself questions opic Descibing fields Gm Gm Gm Gm he net field t is: g ( d / ) ( 4d / ) d d Gm Gm Gm Gm Gm Gm b he net potentil t is: V d / 4d / d 4d d d V e 4 7 9 49 J kg 7 7 Gm d b E

School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 4 Due on Sep. 1, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt