### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# INTERM MATH PHYSICS PHYS 4112

LSU

GPA 3.66

### View Full Document

## 41

## 0

## Popular in Course

## Popular in Physics 2

This 21 page Class Notes was uploaded by Alverta Blick III on Tuesday October 13, 2015. The Class Notes belongs to PHYS 4112 at Louisiana State University taught by J. Dowling in Fall. Since its upload, it has received 41 views. For similar materials see /class/222999/phys-4112-louisiana-state-university in Physics 2 at Louisiana State University.

## Popular in Physics 2

## Reviews for INTERM MATH PHYSICS

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/13/15

11 6405614451 INTEGML Eli3 1 5Llc1lVG 4 G usslj am Read Ez 97 S 3 we chvsp do 9ltz a lt a 396 q gramsst The ocunof m 046 2 e 4 I 140 lt3 x is symme fc 39 2500 4 CK HMC H COCK 3 D L Amm x 0Q 0 gtltZ xZ FDA 15 oQxquot 3a OLX AFCQ 0 06 we Can ma1 6 1 145 CL prbpcr 0amp2 5TH Babb n 537 nor114 3 92A OD G CD J cx Fr I 000 4 He cc S GCX2a27lt 1 z A 3900 15519 3 Gacx 0 We C5 ca r wJ e VHLC cuisi e oe n in Wed m 7024 7 z 1 W2 i 031 4 7 y AX 012 Cui 0L7 9gb 7c E 01quot We can 1850519 7 0 96 4 Gcw 559691 vau ol 43 46 S camb d norme Wm Q f lquot v 7C 1 1 awme g cm 0 I39N IP01 ThWY we AQE tnTE 55775 J7 m The 301 4 55 5 52 44104 1 617 ewee by we FCxltx03 igt SCPGO ch X o ace PCE4 K4 3 c SCM UCQE 7 g 5quot o0 17C7Lgt 7C0 n S ib 50 we 344 de x mc Fuac 39O39L Q55ocCa 0744 4 6 5c 4Aegg M Equot lt 41 2 r7 56 q Er FLK 5amp3 e we 71 Emr V X X 17 x Fin equotlt 041 Q Ara E Q q Z 41 t39 Stu9540 0137 R4 ff 691 JICK a 521 PW 0 16 z 204quot Swot 36 quotf er IL 7 g 51 S H753 3 Si 0 4kquot A ire9K i 3 CPUBLNZJLL 39M o Azo h x C lyzZ 71 5 3 IUT e cm 39 o KJ39E q1 quot l 715 V I 4 i S G Ctbh q Z L Er C E O h fz 30 9 9 WW PamI Folems immediq 7L6 Ad IQEM q ch gt L 9 81 It 5 3591 lt V 9 05 9 JFCeZ Fibs ce 494 93 EfceWr i w FE 1 FCH X E e autoc f5 0490 5M awn 1ccx gt 1 ll Ha f L 14m V 69c comm g M g N742 y Ea a F cV I t Z 7918 I 7 x v 7 1 K x A xviJr AL eggpqv WC AM quot fl 9 9339 Maec m Wot42 A 91 Z i ZCfCK2VLI V 724 J v 13001 EE ahvio P j z 39 397 391 7 66 60 a r 2 2 rquotquotWs K x 7 2 6Acx t r 3 7 2 M 2 21 quotStaten Q meWgz Tr X Get Fltgt 1 Z 1 V Alec z i 1Jr lt37 3 t FM 84 c a o e G C 49 t1 WG10 m S e 4 t 0 00 4 1 dkquot 15o0 571 3 8 444 t4 gt39D Q L 39 r We can Oake W C 81an i 35 FOFL M4 0 xxxarty C r39 z 3 ac quot17 at lt4 cl C S lic r rr 37 3quot r g 2quot gt J t cl l 7 quot 5 Ls 7471ng 5 Cries oL MC CC 960 130 752 39 as w at Sott a cut 1 0 z m 21 2 ca 33 quotty 39 MM e h 039 O no h39 N V x n 2quot 2 2 i S 9 quot 13 t V 139 n o 39139 an r tanH quott 2 E 4 1 0 2hlh Q 0quot 11 indl 4 Zia H bk 1 2244 Z C 739 up N7 7C I y a Mao aw i mme x i 39T 3 21 m r r 7 a I 393 k 391 g M K d 1 3 S Z CW 1 012 ELK07c cq g cm 76 saxLy 10005ng Sol VIVE N 7 e39cezz s Tee aging C7 mam HQCP VCJ 045 46 437 3 39f eMJ Aa9 are Orvarr o a G rc gk C01 1 Hence 3Q 9 01 lt41 753 x7 to L 4491 er carer y keep 0441 339 7 M5 03 EINGTIE39IN suMM TIOru ConVENTsz CEZC Mow Theore cq Playsiab CERmsf39CJ r M quv Le u LU UL 0 V 3 iv VZ JV 1 3 a UV 392 VVIULV1fU3V3 3 2 w 4quot 339 UUO39Y L s Sun oonz 125195475319 INDCch d EXam ICLS 5 Cb a 1 E a J an E n 1sz TQJ3 I A a 3 VU c U c Z CW4 ax Camp a 4 gulf 1 Qi bll ai sa 61 I I 9 1 4 3 VuU 5 Z 1239 3 V 2U39C a 0 a k Qa QaaK 7395de 2an T0050 1 UIVI Uguvl U3 VI LAN U 1V1 Ugvz Coming oI is jeaerqlfeqmn of CM Proclod39 Remll L7quot 02 U3 15 lt7 L39va V3 is 9 a x lt gt TE UV 2 UV WV341 L Ou TEXQ P opacT J J U39V39 2 V E U VA A INA15ft opUQT on po r Fri00007 6 A CQNTRAHT ON lt51 T r1 u v gt TL C WV 39 U V 3 39 L l L A BEFd E CON Tadlt72on 3 Tbji E T is co seas14 rcmt Wow A FTEL CON TRAcTIOIV i 3 TM 2 U arr 15 A 39e r o ghtr TEA SGK L1 L5 4 3014412 2quot IN GEN544L IF lqbguzz s 0 L L n HPAW or 11me 0 CON 7 44 cToV Con Tqbc n dumg quot A Frag a N E Tab kn we LJ 2 wag4 W 4 TEWSGR 0F RWY1 hisch AFTEQ com Macrmm I T413713 z 1 art JIM T451 LJ Lj39 Q44 aV L Lx SINCE and 3 ape JAMaw VQI 3UQ5 Cue can IEEDEFNE I I Say 3 T443713 and 51k 3 T44wtd FRI quotTHEv we cm waTE I 8394quot Qquot gt44 54 Who1 6 BC w zllTE l By WW I f 0F VivIzmpos f 0Wch I 4 PRO05a XFRM PM A SEC 0ND RHAfr T510502 6259 ONE CONTQ axmw 0939 Q ifr F2 F obucfv s fr me pgaa Wag OW QIMW 0 i 0F 4 Pi 00502 722M we Planar CON1054 4 97 R4NK Te Iarcrc q Q r T 43ch 0L p13 7 1 719424 15 THE 977 4le TEN 501 TKANJ MKMAO39ZCN RULE LET us CONTIQACT39 1367 5 5950 BY TA39HIIVG 325 and 50quot CONTRA7 TAyn J 0K 6935 art 0J1 Ttale t ll chr I T paI3 04 C93 QYL QR 145414 L J wow 4 PIN 4 Hod PROTS 15 0130 a w 745 Fwwmu Dar P oDoc Q 09 COLUMNS MD 2 ov Th Roranmy M4772 A 039th 0 Cr 1 0quot a A vu 13 O L a L 9 swce we Ra mvo cmww OF A Fol2M 4N oRTmNoazmAL S E 739 A A A It 9L1 L4 q ch 013 f q 1 q 3 at CR 6213 2 124 Q12 163 43 6131 cu as 6 31 0133 H A A A all Chi 0113 4r a 14 z can an q TIL and Q 5 43 132 an n35 JM TE H mm 907 was pa QT 1 Y4 c No 77 on LET TQJ 135 A ZNI7 12mm TEA50K V r 3 gt 7 Tu Trix Ti 39 E T432 z T 3 Ta 3 463 39 CALM BE coaxingv 45 4 3x3 M rev n H 3 LET v LV VS V31 393 Evtcilct B E 4 4 s7 RAPNK 724v 5m L UEcTQOZ7 THEN 71 Vki Va T45 1 15 320 164va TENch A CONTKA c7761 of A gall 22sbVH 775Nqu 6t uss A 9 st z4Vft TEAASQK C UE CTOK I 39 Li W 39 V T quot2 r 3 IN Ivy90K NothT Oy as w TE A a U E T t V quotA 4 WE V T THE Do P opua39 0F 4 Uecm ouer 4 Zr0 Envyf 7 55001 15 chra 77755 JDQE S IV T con907a U 5 t v7 w h 4 CE ML YHHE77L4C vs 4 wmsymhe7caq um MIA4 ragyadej 37 an D 24 NH TEN 5 6R C V 4104 3 E sewerage REfKESaNT EP 3v 4 A 3A 3 M 4772 x Tu Tn T393 T21 T21 T23 Tat T3 T3 l l W 4 L 4 W l A 3x3 vazlx AND 2m xmm mVSQL s s S syn257ch 1FF Tago TJ5X 6 Tu 71 Tr Li 5 TS le 711 143 z 39439 z 6 T g 1quot3 T33 3 A 1965 M47704 24m Raw1 773w 502 A l 5 AWl s ynnemlc lF 2 ED 73439 6 3 Ta TB 0 4 3 39e Trz an Ta we 0 e T13 TL 0 V 1 Q C INCE X quotX gt X 31 T g4 TM 6 aco ANY 2ND KANA quotTE950 C le 4LW9XS 135 oRII i39EY 48 a 775 60quot 0F 4 Sri maagT fc 4D 41715me 3792 TEN 50R 1 1 T4 a 6 Tm La 395 Wm LN 1 T 1 Tquot 4 41 H39 4 9 T wobboizoo IHR Fobnxogk hon do Ra wth Emlh Il Napalm uqkkmcxxfhiw n L n T gt H 1 HAD 5 H gta II HM ba fm 11 m nIFHD 4 nix 1 lllllll kkilt ou m m cm IPQDAONQ L00 dowlmxh 2m mt NbOLIUm gt A gth n D 2 ll WOmZNL vgv hxtxm Y n 2 3 1gt TuJOQOO VEOM kk u gt 0 QWJSRQ A yp olv 0le E M47 400 Sam E awK v 15039 W507 MD 219 Tans 75 ream 1 Rm 2 1 Ra t L 1415 1quot Sp 739ng 619 1 1 RJO39GLVQ TENJo S 7 Gilif 5 p T7545 H F ALL QUE L 620077wa JZW39E 5 n V Non25220 vgworzs v THE 4 lt gt 4 Wampum U T V 5 A AOIYZEZO v15 cmfi 4N1 TI15 woos N w Dr s 307 4397 60 FWth u 1 v 7mm 12 5 350M 344 MSOZ f J j 4 1 a V 050 U T V 4quot Uolt T413 3 s 9 J L 50 By DEFINTGN of Mom 76739 7 e 101ch HENC E 7 ms 371 coarsemam 50 Cd MJST P oUE 77er xf 7x79st FriM15 LA E A 775445on 4550107 U4 Til GLUEv 4 4 4550 U Miro V 14 WOFEQ 457 fZ aVf TEA564 f l 5 VA 04 UJ mamz urea Lx Mk V 39 3 ayk V P12010131 sctvzxn v 4 3 2 CH3 3 pRo E xF f L 4 I I I lNuEZJE HEMc l 39 n Q Engithn CARVQ Qgt ou h l a uamp xx 96 me SEQ lhv wb o M qu OQNKK 5 V w LI k muQWxx WNW Q RN m KfsQQ hM MW I MVbu 0 x 040E G 0 i u Hint x7 0 Ix lt2 gt r r 1239 1 Q d 1 i 0 l A 30 Jd I gt31 mt xw kaS 9 5ng w gz 3 The un nonnalized Gaussian is given by gx Exp xquot2 9x e39x2 It looks like thiS P1 t9x x 3 3 The area under the curve is area Integrategx x Infinity Infinity 7T ote this is equal to Euler Gammal2 Gamma l 2 Vzr We can define a normalized Gaussian with area one as Gx gx SqrtPi Gx 72 It looks like thiS 2 11 911 nb P1 tGxx 3 3 73 72 71 1 2 3 The area under the curve is IntegrateGx x Infinity Infinity 1 We can estimate the width as the distance between the inflection points which we find by setting the second derivative to zero SolveDDGx x x 0 x l l H I H J 2 2 The standard normal distribution is defined to have both area and width of one phix Exp xquot2 2 Sqrt2Pi Philx Integratephix x Infinity Infinity 1 SolveDDphix x x 0 x pH 1 x gtl The erf function is erfx Integrate2 Gt t 0 x This is a built in function in Mathematica ca11ed Erfx note that Erfx s antisymmetric or odd with special values Erf oo 1 Erf00 Erfcn1 II he plot is 11 911 nb 3 PlotErfx x 3 3 10 This is just the area under the curve of G from x to x PlotGx x 1 1 PlotRangea o 1 The complementary error function is Erfc with Erfc cn 2 Erfc01 Erfcm0 i 4 11 911 nb PlotErfcx x 3 3 The imaginary error function is Erfi with Erfi oo oo Erfi00 Erficnoo and the plot looks like PlotErfix x 3 3 60 As in the textbook we can expand Erfx in a Taylor Series about x0 keeping the first 10 terms SeriesErfx x 0 10 2 x 2 x3 x5 x7 x9 F 3W 5F 21W 108V This is the approximation for xltltl ox11 The asymptotic series in the book can be considered a Taylor series about on as SeriesErfx x Infinity 10 2 1 1 3 15 105 1 11 O x x 23 45x5 85x7 169 This is Boas EqlO4 with some rearrangement of terms Use this series for xgtgtl 1e39K Compare to Taylor seriex of ArcTanhx about zerouc 11 911 nb 5 PlotArc39I anx x 5 5 SeriesArcTanx x 0 10 x5 X7 Kg 11 x Ox 3 5 7 9 There is an asymptotic series for this also about on that is SeriesArcTanx x Infinity 10 7r 1 l l l l l 11 O 2 X 3 x3 5 x5 7 x7 9 x9 X Finally we can apply this to the Euler Gama to get FullSimplifySeriesGammap l p Infinity 3 n n n I I 139113 1 72 O lp P 5 144 W2 25920 W2 emwmwwm m With some simplification this also reduces to Boas Eqll5 which are the first few terms of the asymptotic series expansion for S erling39s Formula We can pick out just the first term and simplify it FullSimplifyExp l Logl p p Sqrt2 Pip p gt 0 69 p9 l 2 7r With a bit of algebra this is equal to pp e399 2 that is 39ust E lll or Sterlin Is Formula 7 P J 1 9

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I made $350 in just two days after posting my first study guide."

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.