### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Class Note for MATH 3331 with Professor He at UH 2

### View Full Document

## 15

## 0

## Popular in Course

## Popular in Department

This 19 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 15 views.

## Reviews for Class Note for MATH 3331 with Professor He at UH 2

### 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: 02/06/15

Linearity 1 Linearity af lagXS a fs b gs Math 3331 Section 19470 Lecture 19 March 9 2009 2 19 Reality 2 Reality ft real gt f3 real Consequence ft complex gt Re fs CRefs Im fs Imfs Math 3331 Section 19470 Lecture 19 March 9 2009 3 19 Section 52 I yrs w Derivatives Ys yts 3 Derivatives y lts ms y0 lty ltsgt 82Yltsgt sym y 0 ykgtlts skis sk 1y0 sk Qy m yltk 1gtlto Ill Math 3331 Section 19470 Lecture 19 March 9 2009 4 19 Proof 3 Proof 3 for k 1 Use partial integration fuv dt M fu v dt T T T feistyt dt 6 Styt 8 6 Styt dt 0 0 o 6 5TyT y0 T 3estyt dt 0 For T gt 00 T 6 8TyT gt 0 f0 6 8tyt dt gt Y8 gt yX8 8Y8 210 Ill Math 3331 Section 19470 Lecture 19 March 9 2009 5 19 M ultiplication by e F8 fts 4 Multiplication by Get Ce C ectfts F8 0 Math 3331 Section 19470 Lecture 19 March 9 2009 6 19 Proof 4 Proof 4 00 ectfts O e Stectmdt foo e8ctft dt 0 F3 c Math 3331 Section 19470 Lecture 19 March 9 2009 7 19 Section 52 Multiplication by 1quot F09 ft8 5 Multiplication by tk k 012 tkft8 1kFk8 Math 3331 Section 19470 Lecture 19 March 9 2009 8 1 Proof 5 Proof 5 for k 1 Fs 2 f000 6 Stft dt gt ms few dt tfts 2 Math 3331 Section 19470 Lecture 19 March 9 2009 9 19 Basic Pro erties Examles Transforms of Functions Encountered ODEs ODEs with constant coefficients gt functions tkeCt k O12 Math 3331 Section 19470 Lecture 19 March 9 2009 3910 19 Transforms of Functions Encountered in ODEs cont Property 5 gt k qtkecms oo aedxs Property 4 gt ect8 ect18 18 C 1 S C gt tkects 1k k dk 1 dSkS C Math 3331 Section 19470 Lecture 19 March 9 2009 11 19 Section 52 Basic Pro erties Ex m39les L Transforms of Functions Encountered in ODEs cont 1 gt Special Transforms 0 160 CER gt ects o k O C iw gt memo 8 s2 l w2 COSwts 2 Reg 2 82 111 Math 3331 Section 19470 Lecture 19 March 9 2009 12 19 Section 52 Ba c Pr t e EX mles Transforms of Functions Encountered in ODEs cont 0 kOcoz i gt WWW 3 5 15 at 8 04 gt e cos ts 8a262 6at Sin ES a gkw Math 3331 Sect mn 19470 Lecture 19 March 9 2009 13 19 Section 52 Table of C Transforms Table of L Transforms f t 1 tk ect tkect cos wt sin wt 60 t cos 6t eatsin t Jiwen He University of Houston Math 3331 Section 19470 Lecture 19 ft8 1 S k 8k1 L S C k L 82w2 L 82w2 s cv s a2 2 8 002452 March 9 2009 14 IQ InClass Exercises Exercise 523 3 Using linearity and Table 1 m2 4 5s t2s 4 ts 5 1s 2 1 1 F4isii5lt 2 4 5 33 32 E 2 4S 552 s3 provided 5 gt O H Jiwen He University of Houston Math 3331 Section 19470 Lecture 19 March 9 2009 15 19 Exercise 525 5 Using linearity and Table 1 2 cos I 4 sin 3ts 2 cos ts 4 sin 3ts s 3 2 4 521 29 2ss 2 9 12s2 1 s2 1s2 9 253 1232 18S 12 52 152 9 provided 5 gt O H 9 Math 3331 Section 19470 Lecture 19 March 9 2009 16 19 i In Class Exercises Exercise 5219 19 If y 5y e z with y0 1 then My 5340 2tS yIS 5 yS S 2 saws y0 5 yltsgt S 2 Ifwe let YS ys then SYS 1 5YSS2 s 5Ys1s2 m S i S m 5 Iii Jiwen He University of Houston Math 3331 Section 19470 Lecture 19 March 9 2009 17 19 In Class Exercises Exercise 5222 22 If y y sin4t y0 0 y390 1 then letting Y s y s s2 13005 sy0 y 0 ys s2Ys 1Ys 5216 Solving for Ys s2 1Ys 1 m s2 1Ys i fg 32 20 Ys Fl Jiwen He University of Houston Math 3331 Sention 19470 Lecture 19 March 9 2009 InClass Exercises Exercise 5239 39 If y y 2y e cos 2t with y0 1 and y 0 1 then with Ys ys LU y 2ys s2 ys sy0 y 0 s ys y0 2 ys s2Ys s 1 sYs 1 2Ys s2 s 2Ys s Jiwen He University of Houston Math 3331 Section 19470 Lecture 19 Because the transform of f t cos 2t is F s ss2 4 the transform of equot cos 2t is s1 51 F 1 3 s124 s22s5 Equating 2 s1 2Y S S S S S22S5 SolvingforY 51 Ys S s2s2 32s252235 s322s5s1 s2s2s22s5 s32s26s1 32s2s22s539 Iii 1919 March 9 2009 Lecture 19 s 2 Same Pvnvemes M m Lamace Tvansmm J W H 2 Wm M WM WW M mm m KVLuNnvmmzn

### 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

#### "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."

#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

#### "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!"

#### "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.