### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Mechan Engineering Analysis ME 391

MSU

GPA 3.57

### View Full Document

## 17

## 0

## Popular in Course

## Popular in Mechanical Engineering

This 101 page Class Notes was uploaded by Princess Rolfson on Saturday September 19, 2015. The Class Notes belongs to ME 391 at Michigan State University taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/207538/me-391-michigan-state-university in Mechanical Engineering at Michigan State University.

## Reviews for Mechan Engineering Analysis

### 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: 09/19/15

ML 5010 LV VS I NOTEf llZEo397 W TN I39ZA W W W M W pram an oL fwxabmf koq Hm wwwmwi 0 W4 QHJ MJwWaQ 59 baa HM aka7M in M7 coyzfd W M W e QWW fM d P ohvtwac avk W UW Q OCXAL39 TB 05 warW Fww W deoj gulf mum fax HM Wm M w Ntw LA x40 44 Q G E m CLJU NOTE Io2qo7 whot if M of a MM K L V d eo bVl39d Ij39 Tm MEZKEPCA lechRoQg 1k014moxf Man WONQM Rem 0 WJQM WCWCJQMWJLM g Mg m CLAS NQTKJ ZS 37 a ill 3 TE 36 Si b2 Huff MK I J Cb CccwP W w QQCQ g E 3amp6 NKwQIVQ w g TQ n uni bxixf WankXOQHNW CAT na x in G wmgfnmrgj uh iqC H DOC pximbw umOQ u XM xx 93 Q 536 E yl F 67 c17 7 jya Lyffoo a R jevl J 52 4 3739 6 C er q 70 7 6963 Wr H 7 3f amp27ltf39l L 7f 3b y 4911 e W f EL 7914 EU H 4 jfoy0 j 5Y01yw r 7G 5234 67 m 70 2454quot YO 2 1 29 55 55 jQ J 39 Cr 39 6 39 J fig w 239 61 46 Cl yue 439 2 9 JV 6 c a Q E t4 ix d arfg cf 6 PVbiIbrj A 5 7 gtlt o y 2 16 J gtCt 746 SX 1I M SVG y0 SyCr j Z 9X0 4 72y lt5 IXy fZ39 y SVJ 2gt5XUJ O J 5Xf q4lj7r 39 Z Y W3MMWMMXQJWVO X9 5425 7j I245 39 C I Q ywxEtp CBkat SCoj3fj xx 7 Qm3t Bzmyt CHAP FQK 397 VECTorL Q4 2d IQcbv V quotP bu7 6CXIylgt X x I COMEM 0W for o 2 Q11a1gt 2 3m 5 aicrf vw make 390 EUR 33 mwa uxmsci 33 g 33 T3375 um 33 23 d uaumg hxwmguxmxfwwx m3 3ng 343V o u NLU m i6 b iw iigv B um m 26 33 t u v wing ABEQ 20 um 33 93723 M u A 4 10807 KW w 5 Hquot K 9827 CLAS J NoTEJ Aside Noquot oUth o rL EXamPQQf O39F LiYquLJ L Evva cng V U 0 3 g 39L X 33 X 3 oy Q Z ok 0310107 lfNQaJ L ODE CL wwxx 4m 00 no 941027 HQ 9 CVuLaEl O h to l39b39 lt9th 7Lahvn yr X othZ er Z r Fig7 2 2 X okx hx Rx by d2 L w l dy I39D y0konatm JLMcJDE C3 3 f2y4exso St o J M QXW ODE 5m 4 NH 591 NOTE 09 7 3 V7 23 Solution Curves without a Solution Definition Critical Point A critical point or equilibrium point or stationary point of the differential equation dydxfx is a point yo such that fyo0 yyo is a constant or equilibrium solution of the above differential equation 5amp2 heft poilt2 k QXGWP QQ it C Q Q 312 Homogeneous Equations dn ly dquoty an an1x anx1aoxygx If gx0 homogeneous equation If gx 0 then n l dquoty d d anx anlxdx nl anx7d x Za0xy 0 is called the associated homogeneous equation Definition A set of n linearly independent solutions of a linear ODE Ly0 is a fundamental set of solutions Theorem The general solution of the homogeneous ODE LyO is yC1y1C2yz Cnyn where yj s comprise a fundamental set and 01 s are constants 09943 CLAU Example 37 4 C 0 Wm 0t COM WNJC NUTES OM J oW m D yEO ol o aCojo 4 BE AKOH G39Z SoMO ff yg ax yt OxQquotOLX y oj QQ 0 X aofax O amp na aQ Jomz 3y lCe x Kfm pa aw C 0 l 91 PMVL M Cajg TN t a Dry gtan OfSO eAAe W 7 JCO 101 C22 cu I Cgt6 K C 39Z W ka v e 0 chrxutmm 0 50Mmj Exact Analytical Rare but very useful Approximate Analytical More advanced very useful Geometrical Useful typically generated via computer Numerical Powerful but very speci c NEE EON Raye ho JUMCW Eu 512l39lo RQIVwgtVQJKLbn 50W RM TM OU buf M b Ex y x y 3 y 020 IVP V0 0 gt 0 o h H l 3 y39 X o Lr Q M H m ym j girk f z w mhftkwa SM W Examples Population Dynamics TkOMOj i798 ASSUImp I TW 3 025 Ola Pome inou k Wt a CMWM Hm I Pmpomw b He W popw mm god 0 1 d dp Kgto 0 29 PO 6 gawk7 w a in quotle 50 Cmsa okenohm faahjsbj Llce MMjT labo39rx mana 39m aim 1M4 S HU UPQcX 7am W02 Ql39itq MohawkQ gMbAHx t AE cal ECW Q E Assumptions Express assumptions in terms gt Mathematical of differential equations formulation i If necessary alter assumptions Solve the DEs of the model or increase resolution l T Check model lt Display model predictions lt Obtain solutions 931a El LL EXERCISE 14 9 L58 lowILleJli 27 33 3 ExgulsE ii 9 Z ylz 1L J I J Ex uf 1 e 9 math6 CHAPTER 2 FIRST ORDER DIFFERENTIAL EQUATIONS 21 Solution curves without a solution 22 Separable Variables 23 Linear Equations 24 Exact Equations 21 To be covered after 22 23 and 24 Qgt 7 L E m8 mvn muh SnNa w9nWwQNQ9Q 04m okx un p q f HUM 61 yew cu let 1W lt1 13W C C FCI 4 c2 010 ME 39 LECTURE NoTEr b1 lt2 ha 3 a 5 L939 mo IIIIII L a I39IIIIIII be in DC 11 076 7 LLEL u 3 7quot 39 Z 339 3 x 4 0 I quot2 X1 2 WC YxX39L 7C3 2054 by fwm Suir4c u 0h 8X31 3 33quot Z7X39gt3 DJ XL33 f 2Xf21 LXX1 3gtggtz2 a gt62 2 Z Z 5 XZ x ZQ w V1 OQOAOJLm J 03rng 1 2b En amaze 392 x gtCerrPrX 1 XIXZHXH q lt3 I x 4xz4u44X 4Fhl b 1 2 EL F9 1 quot39 tj lt H 31 20 El Fm 93 53 3 39ZJHLP F5 IL 2 1 A QJ l MOOy 1 5 m 547 L AC5 51 9504 C Owl 1 56m 52 amp A 1 E352 ijQf15 CSf5j 55 52 SEMI MZ C n Yr Ca an 5hl 39 Q5 aoj PFY39LC W PU v urj QQ 95 75 39 ALQ 2 arr ya 65 AMI PU yw iquot g G CJ 040 PO h

### 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

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

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "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.