r o f a 23 H e z e k i a h : L o y a l t o G o d O F T H E Ordinary Men and Women... Super Ordinary Power

Size: px
Start display at page:

Download "r o f a 23 H e z e k i a h : L o y a l t o G o d O F T H E Ordinary Men and Women... Super Ordinary Power"

Transcription

1 H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 23 H z k a h : L o y a l t o G o d H r o s o f t h F a t h C u r r c u l u m No part of ths currculum may b rpublshd wthout prmsson. Plas fl fr to copy for classroom us.

2 23 H z k a h : L o y a l t o G o d Mmory Vrs: Whovr trs to lv rght and b loyal fnds lf, succss, and honor. (Provrbs 21:21 NCV) Lsson Goals: #1 - Undrstand how ordnary Hzkah was #2 - Dscovr what fath ld Hzkah to do #3 - Dsr to lt God do xtraordnary thngs n th lf of th ordnary studnt Audnc: Young, un-churchd larnrs Adaptabl for all ags, ncludng adults (S For mor tranng on Actvts pag) Scrptur to Study: 2 Kngs Chroncls Isaah Provrbs 25 Matthw 1:9-10 Hzkah: Loyal to God / pag 2

3 23 H z k a h : L o y a l t o G o d 2 Kngs 18:1-8, 2 Chroncls 29-32, Isaah 38:1-8 Who can tll m what a hro s? A hro s somon who s couragous and brav and compassonat. Thr ar hros and hrons n th Bbl. All of thm ar brav and couragous and mor, but not n th way you would xpct. Our hro: Hzkah Hs Hroc Fat: Is Loyal to God Loyalty to God may not sound vry hroc, but lt s look at th facts and s what you thnk whn you hav hard th whol story Do you rmmbr that, snc Kng Solomon, all of Isral s kngs hav bn compard to Kng Davd? Thr was a kng, many yars aftr Kng Ahab, who ddn t follow Kng Davd s xampl. H dd not do what th Lord hs God sad was rght. (2 Kngs 16:2b NCV) Hs nam was Ahaz. H snt th tmpl trasurs to thr nms and usd othr thngs from th tmpl of God to worshp hs own, fals gods. Whn Kng Ahaz dd, hs son, Hzkah, bcam kng aftr hm. Hzkah was twnty-fv whn h bcam kng. Instad of followng hs fathr s xampl, Kng Hzkah followd Kng Davd s xampl. Hzkah trustd n th Lord, th God of Isral. Thr was no on lk hm... thr bfor hm or aftr hm. Hzkah was loyal to th Lord and dd not stop followng Hm; h obyd th commands th Lord had gvn Moss. (2 Kngs 18:5-6 NCV) On of th frst thngs Hzkah dd as kng was to rddcat and rpar th tmpl and rmov th thngs that hs fathr had usd n dol worshp. You s, th doors of th tmpl had bn closd and th tmpl sat unusd. Hzkah also calld th Lvts back so that thy could mak thmslvs rady to srv n th tmpl. And thn, Hzkah dd somthng that hadn t bn don snc th tm of Kng Solomon; h prpard for th clbraton of th Passovr. Whn God nsttutd th Passovr, t was to b clbratd vry yar. Many yars had passd snc th last clbraton, so Hzkah snt out nvtatons to th Passovr as wll as a rmndr to rturn to God. Many of th popl laughd at Hzkah and rfusd to com, but som wr sorry for thr sns and plannd to com to clbrat th Passovr. Thos who clbratd th Passovr rmovd th altars n Jrusalm whr othr gods wr worshppd. Thy clbratd for svn days and prasd th Lord vry day wth loud musc. (2 Chroncls 30:21b NCV) Aftr th Passovr clbraton, th popl gav gfts for th tmpl and th tmpl bgan to b usd as t had yars bfor. Hzkah trd to oby God n hs srvc of th tmpl of God, and h trd to oby God s tachngs and commands. H gav hmslf fully to hs work for God. So h had succss. (2 Chroncls 31:21 NCV) Hzkah: Loyal to God / pag 3

4 Aftr Hzkah dd ths thngs, n th fourtnth yar of hs rgn, th ladr of Assyra cam to attack. Hs nam was Snnachrb. H told Hzkah and th popl that thr confdnc n God was msplacd. H rdculd God. H vn sad God had snt hm to march aganst th country. Whn Kng Hzkah hard th mssag, h tor hs cloths and put on rough cloth to show how sad h was. Thn h wnt to th Tmpl of th Lord. (2 Kngs 19:1 NCV) Hzkah prayd to God and God answrd. God assurd Hzkah that th battl was Hs. Hzkah ddn t nd to worry. God dlvrd Hzkah and th country from th Assyrans But rght aftr that, Hzkah got vry ll. In fact, h was dyng. And just lk h had all through hs lf, Hzkah turnd to God. H prayd, Rmmbr, Lord, how I hav walkd bfor you fathfully and wth wholhartd dvoton and hav don what s good n your ys. (Isaah 38:3 NIV) God hard Hzkah s prayr and addd fftn yars to hs lf. God gav a sgn to Hzkah that h would kp Hs proms, I wll mak th shadow cast by th sun go back th tn stps t has gon down on th starway of Ahaz. So th sunlght wnt back th tn stps t had gon down. (Isaah 38:8 NCV) Wh rgh lf or. NC Who s ths God who fought battls for Hzkah, gav hm fftn mor yars of lf and vn causd th shadow cast by th sun to back up? H s th God, th only On, who dsrvs our loyalty. Hzkah s lf was blst bcaus of hs loyalty to God. How about you? Ar you loyal to God? N x t W k Josah Y O U c a n b a h r o, t o o Whn you lv a lf of fath n Jsus Chrst, you don t hav to lap tall buldngs to b a hro. Hzkah was loyal to God. Our mmory vrs says, Whovr trs to lv rght and b loyal fnds lf, succss, and honor. (Provrbs 21:21 NCV) I m sur w would all agr that w want lf, succss and honor. Ar you wllng to follow Hzkah s xampl of loyalty to God? Followng Hzkah s xampl bgns wth a rlatonshp wth th Allpowrful God of th unvrs. H snt Hs own Son to d for th sns you hav commttd. Wll you surrndr to Hm today? Hzkah: Loyal to God / pag 4

5 p r - s c h o o l l s s o n Who can tll m what a hro s? A hro s somon who s couragous and brav and compassonat. Thr ar hros and hrons n th Bbl. All of thm ar brav and couragous and mor, but not n th way you would xpct. Our hro: Hzkah Hs Hroc Fat: Is Loyal to God Loyalty to God may not sound vry hroc, but lt s look at th facts and s what you thnk whn you hav hard th whol story W mt a nw kng, today. Hs nam was Hzkah. H was twnty-fv whn h bcam kng. Bcaus hs dad had bn a bad xampl, Hzkah chos not to follow hs xampl. Instad, Hzkah obyd God. Hzkah was loyal to God. On of th frst thngs Hzkah dd as kng was to rpar th tmpl. You s, Hzkah s fathr had takn thngs from th tmpl and gvn thm away to thr nms. H ddn t tak car of th tmpl. Th doors of th tmpl had bn closd and th tmpl wasn t usd. Hzkah cland th tmpl. H got rd of th thngs that wr for othr gods. Hzkah also calld th Lvts back to work. Thy wr spcal popl who srvd n th tmpl. Thn Hzkah rddcatd th tmpl to God. Thy gav th anmal sacrfcs that God usd to rqur. Thn thy sang and blw trumpts. All th popl worshpd, th sngrs sang, and th trumptrs blw thr trumpts untl th burnt offrng was fnshd. (2 Chroncls 29:28 NCV) Thy vn usd Psalms from Kng Davd to pras God. What do you do at church? Do you brng gfts to God? Do you sng to Hm and play nstrumnts? Do you rad from th Psalms? Hav you vr thought about hlpng to clan at church? Ar you carful wth how you trat thngs at church? You can b loyal to God th way Hzkah was. Hzkah: Loyal to God / pag 5

6 a c t v t s Mmory Vrs Actvty - Prnt ach word, and th rfrnc, on sparat pcs of colord papr. Practc placng th vrs n th corrct ordr, practcng as you go. Contnu addng hros nams and hroc fats to your Hros Bannr. Lstn to Mchal Card s Thn Thy Wll Know. Sng Th Battl Blongs to th Lord, I Wll, Mghty to Sav, Our God or othr pras songs rlatd to th lsson. Mak a lst of chors for your Bbl study ara. Encourag your studnts to voluntr for spcfc tasks. For mor tranng: Rad Matthw 1, focusng on vrss Talk about Hzkah s loyalty and hs plac as an ancstor of Jsus. For mor tranng: Rad Provrbs 25. Rvw th hghlghts of our lsson on Solomon. Dscuss how ths vrss cam to b n th Bbl (s v. 1). For mor tranng: Rad and dscuss Isaah 39. (Ths wll lad us nto th lssons on Josah, Danl, and Shadrach, Mshach and Abd-ngo.) For mor tranng: Rad Isaah Compar and contrast Snnachrb s mssag to God s mssag. Hzkah: Loyal to God / pag 6

7 Whovr trs to lv rght and b loyal fnds lf, succss, and honor. Provrbs 21:2 Hzkah: Loyal to God / pag 7

8 H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr H r o n T r a n n g Hzk ah: Loyal to God H r o s o f t h F a t h C u r r c u l u m No part of ths currculum may b rpublshd wthout prmsson. Plas fl fr to copy for classroom us.

9 h r o t r a n n g Scrptur: 2 Kngs 18:1-8, 2 Chroncls 29-32, Isaah 38:1-8 Mmory vrs: Whovr trs to lv rght and b loyal fnds lf, succss, and honor. (Provrbs 21:21 NCV) Our Hro: What dd our hron do that was so hroc? What can you do to b a Hro of th Fath? HS What powr do Hros of th Fath possss? Do you hav th powr? Rad Isaah 38: What dos Hzkah know about God? Lst thm blow. Hzkah: Loyal to God / pag 9

10 h d d n m s s a g Can you crack th cod to fnd th Hddn Mssag? Usng th ky blow, fll n th blanks to complt th mmory vrs A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Whovr trs to lv rght and b loyal fnds _ a n d _ Provrbs 21:21 Hzkah: Loyal to God / pag 10

11 w o r d s a r c h B S I C K N E S S S G D E D P H L I F G I E S F I L R E O E N V I D N T O N I H E L A E V S D N L L O T E L O N V A R E A O L L S Z S M E E R A N C R O T E E A P D H M E N H T W H N K C A T T A Y M E N E T O I A S E E S N M R O D S T A N S M T R E Y I C D O S H O O P R P E H B N A E E G J V L S Y T D E I V H T U T E E A Y F A S D I U I O N R N S B I E V O D P F H T B U I L F T E G P L E - Hzkah - followd Davd - cland tmpl - Passovr - nmy attack - Snnachrb - God n control - scknss - fftn yars Hzkah: Loyal to God / pag 11

12 h Answr Pag d d n m s s a g Can you crack th cod to fnd th Hddn Mssag? Usng th ky blow, fll n th blanks to complt th mmory vrs A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Whovr trs to lv rght and b loyal fnds... l f s u c c s s a n d h o n o r Provrbs 21:21 Hzkah: Loyal to God / pag 12

13 w o r Answr Pag d s a r c h B S I C K N E S S S G D E D P H L I F G I E S F I L R E O E N V I D N T O N I H E L A E V S D N L L O T E L O N V A R E A O L L S Z S M E E R A N C R O T E E A P D H M E N H T W H N K C A T T A Y M E N E T O I A S E E S N M R O D S T A N S M T R E Y I C D O S H O O P R P E H B N A E E G J V L S Y T D E I V H T U T E E A Y F A S D I U I O N R N S B I E V O D P F H T B U I L F T E G P L E - Hzkah - followd Davd - cland tmpl - Passovr - nmy attack - Snnachrb - God n control - scknss - fftn yars Hzkah: Loyal to God / pag 13

r o f a 24 T h e E i g h t Y e a r O l d K I n g O F T H E Ordinary Men and Women... Super Ordinary Power

r o f a 24 T h e E i g h t Y e a r O l d K I n g O F T H E Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 24 T h E g h t Y a r O l d K I n g H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum may

More information

r o f a 11 J o s h u a S e r v e s t h e L o r d O F T H E Ordinary Men and Women... Super Ordinary Power

r o f a 11 J o s h u a S e r v e s t h e L o r d O F T H E Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 11 J o s h u a S r v s t h L o r d H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum may

More information

r o f a O F T H E Ordinary Men and Women... Super Ordinary Power H e r o e s o f t h e F a i t h C u r r i c u l u m

r o f a O F T H E Ordinary Men and Women... Super Ordinary Power H e r o e s o f t h e F a i t h C u r r i c u l u m H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 36 T h C n t u r o n s G r a t F a t h H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum

More information

r o f a O F T H E Y e a r O l d A b r a h a m H a s a S o n Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E Y e a r O l d A b r a h a m H a s a S o n Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 5 1 0 0 Y a r O l d A b r a h a m H a s a S o n H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths

More information

r o f a O F T H E G i d e o n W i n s B a t t l e W i t h O n l y M e n Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E G i d e o n W i n s B a t t l e W i t h O n l y M e n Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 14 G d o n W n s B a t t l W t h O n l y 3 0 0 M n H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of

More information

r o f a 13 D e b o r a h L e a d s I s r a e l O F T H E Ordinary Men and Women... Super Ordinary Power

r o f a 13 D e b o r a h L e a d s I s r a e l O F T H E Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 13 D b o r a h L a d s I s r a l H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum may

More information

r o f a O F T H E T i m o t h y - A n E x a m p l e f o r B e l i e v e r s Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E T i m o t h y - A n E x a m p l e f o r B e l i e v e r s Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 47 T m o t h y - A n E x a m p l f o r B l v r s H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths

More information

r o f a O F T H E P h i l i p - a f a i t h f u l w i t n e s s Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E P h i l i p - a f a i t h f u l w i t n e s s Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 46 P h l p - a f a t h f u l w t n s s H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum

More information

r o f a 15 J e s u s D e f e a t s D e a t h O F T H E Ordinary Men and Women... Super Ordinary Power

r o f a 15 J e s u s D e f e a t s D e a t h O F T H E Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 15 J s u s D f a t s D a t h H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum may b rpublshd

More information

r o f a O F T H E N e h e m i a h F e a r l e s s i n H i s e f f o r t s t o R e b u i l d W a l l o f J e r u s a l e m

r o f a O F T H E N e h e m i a h F e a r l e s s i n H i s e f f o r t s t o R e b u i l d W a l l o f J e r u s a l e m H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 29 N h m a h F a r l s s n H s f f o r t s t o R b u l d W a l l o f J r u s a l m H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org

More information

r o f a O F T H E C a l e b E x p l o r e s t h e P r o m i s e d L a n d Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E C a l e b E x p l o r e s t h e P r o m i s e d L a n d Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 10 C a l b E x p l o r s t h P r o m s d L a n d H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths

More information

r o f a O F T H E E s t h e r R i s k s H e r L i f e t o S a v e H e r P e o p l e Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E E s t h e r R i s k s H e r L i f e t o S a v e H e r P e o p l e Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 28 E s t h r R s k s H r L f t o S a v H r P o p l H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of

More information

r o f a O F T H E J o h n... S o n o f T h u n d e r! Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E J o h n... S o n o f T h u n d e r! Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 35 J o h n... S o n o f T h u n d r H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum may

More information

r o f a O F T H E N o a h b u i l d s b o a t o n d r y l a n d Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E N o a h b u i l d s b o a t o n d r y l a n d Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 3 N o a h b u l d s b o a t o n d r y l a n d H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum

More information

r o f a O F T H E J e s u s - R e t u r n i n g K i n g Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E J e s u s - R e t u r n i n g K i n g Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 48 J s u s - R t u r n n g K n g H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum may

More information

r o f a 43 S i l a s T r a v e l s w i t h P a u l O F T H E Ordinary Men and Women... Super Ordinary Power

r o f a 43 S i l a s T r a v e l s w i t h P a u l O F T H E Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 43 S l a s T r a v l s w t h P a u l H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum

More information

r o f a O F T H E M o r d e c a i H a l t s P l o t A g a i n s t t h e K i n g Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E M o r d e c a i H a l t s P l o t A g a i n s t t h e K i n g Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 27 M o r d c a H a l t s P l o t A g a n s t t h K n g H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part

More information

r o f a O F T H E S a m s o n : A T r a g i c S t o r y Ordinary Men and Women... Super Ordinary Power

r o f a O F T H E S a m s o n : A T r a g i c S t o r y Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 16 S a m s o n : A T r a g c S t o r y H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum

More information

r o f a 7 J o s e p h S a v e s E g y p t O F T H E Ordinary Men and Women... Super Ordinary Power

r o f a 7 J o s e p h S a v e s E g y p t O F T H E Ordinary Men and Women... Super Ordinary Power H s O F T H E r o f a t H Ordnary Mn and Womn... Supr Ordnary Powr 7 J o s p h S a v s E g y p t H r o s o f t h F a t h C u r r c u l u m 2 0 1 2 www.mssonarlngton.org No part of ths currculum may b rpublshd

More information

Summer Reading Activities!

Summer Reading Activities! HOOT FLUSH SCAT CHOMP From Bstslling Author Summr Rading Activitis! Flush Word Find Can you find all 14 words in th puzzl blow? S W I M E N J L P H S P A R R D A Z A G A Z E I B H O T L V S C N U D H I

More information

Want to go a-courtin but not allowed to dance? Well then, try this once popular party game as a way to get to know each other.

Want to go a-courtin but not allowed to dance? Well then, try this once popular party game as a way to get to know each other. fiddl, piano party gam, circl danc Want to go a-courtin but not allowd to danc? Wll thn, try this onc popular party gam as a way to gt to know ach othr. Ky G, first not do(g) Squar/Circl Danc d d d d d

More information

Lucas Test is based on Euler s theorem which states that if n is any integer and a is coprime to n, then a φ(n) 1modn.

Lucas Test is based on Euler s theorem which states that if n is any integer and a is coprime to n, then a φ(n) 1modn. Modul 10 Addtonal Topcs 10.1 Lctur 1 Prambl: Dtrmnng whthr a gvn ntgr s prm or compost s known as prmalty tstng. Thr ar prmalty tsts whch mrly tll us whthr a gvn ntgr s prm or not, wthout gvng us th factors

More information

Higher order derivatives

Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of

More information

Alpha and beta decay equation practice

Alpha and beta decay equation practice Alpha and bta dcay quation practic Introduction Alpha and bta particls may b rprsntd in quations in svral diffrnt ways. Diffrnt xam boards hav thir own prfrnc. For xampl: Alpha Bta α β alpha bta Dspit

More information

ECE602 Exam 1 April 5, You must show ALL of your work for full credit.

ECE602 Exam 1 April 5, You must show ALL of your work for full credit. ECE62 Exam April 5, 27 Nam: Solution Scor: / This xam is closd-book. You must show ALL of your work for full crdit. Plas rad th qustions carfully. Plas chck your answrs carfully. Calculators may NOT b

More information

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim. MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function

More information

I Will Pass Over You [===========================[

I Will Pass Over You [===========================[ I Will Pass Ovr You F G 7 4 x x h x x h 1 hrist our r-dm-r did on th cross; did for th sin-nr, paid all his du 2 hif st of sin nrs Y-shu a will sav; all has prom-isd, that will do 3 O grat com-pas-sion,

More information

ph People Grade Level: basic Duration: minutes Setting: classroom or field site

ph People Grade Level: basic Duration: minutes Setting: classroom or field site ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:

More information

3 2x. 3x 2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

3 2x. 3x 2.   Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Math B Intgration Rviw (Solutions) Do ths intgrals. Solutions ar postd at th wbsit blow. If you hav troubl with thm, sk hlp immdiatly! () 8 d () 5 d () d () sin d (5) d (6) cos d (7) d www.clas.ucsb.du/staff/vinc

More information

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula 7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting

More information

CS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages:

CS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages: CS 6353 Compilr Construction, Homwork #1 1. Writ rgular xprssions for th following informally dscribd languags: a. All strings of 0 s and 1 s with th substring 01*1. Answr: (0 1)*01*1(0 1)* b. All strings

More information

SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy.

SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy. LTNY OF TH SNTS Cntrs Gnt flwng ( = c. 100) /G Ddd9/F ll Kybrd / hv Ddd9 hv hv Txt 1973, CL. ll rghts rsrvd. Usd wth prmssn. Musc: D. Bckr, b. 1953, 1987, D. Bckr. Publshd by OCP. ll rghts rsrvd. SMPL

More information

Propositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018

Propositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018 Propositional Logic Combinatorial Problm Solving (CPS) Albrt Olivras Enric Rodríguz-Carbonll May 17, 2018 Ovrviw of th sssion Dfinition of Propositional Logic Gnral Concpts in Logic Rduction to SAT CNFs

More information

MA 262, Spring 2018, Final exam Version 01 (Green)

MA 262, Spring 2018, Final exam Version 01 (Green) MA 262, Spring 218, Final xam Vrsion 1 (Grn) INSTRUCTIONS 1. Switch off your phon upon ntring th xam room. 2. Do not opn th xam booklt until you ar instructd to do so. 3. Bfor you opn th booklt, fill in

More information

MEMORIAL UNIVERSITY OF NEWFOUNDLAND

MEMORIAL UNIVERSITY OF NEWFOUNDLAND MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS Midtrm Examination Statistics 2500 001 Wintr 2003 Nam: Studnt No: St by Dr. H. Wang OFFICE USE ONLY Mark: Instructions: 1. Plas

More information

Roadmap. XML Indexing. DataGuide example. DataGuides. Strong DataGuides. Multiple DataGuides for same data. CPS Topics in Database Systems

Roadmap. XML Indexing. DataGuide example. DataGuides. Strong DataGuides. Multiple DataGuides for same data. CPS Topics in Database Systems Roadmap XML Indxing CPS 296.1 Topics in Databas Systms Indx fabric Coopr t al. A Fast Indx for Smistructurd Data. VLDB, 2001 DataGuid Goldman and Widom. DataGuids: Enabling Qury Formulation and Optimization

More information

Discrete Shells Simulation

Discrete Shells Simulation Dscrt Shlls Smulaton Xaofng M hs proct s an mplmntaton of Grnspun s dscrt shlls, th modl of whch s govrnd by nonlnar mmbran and flxural nrgs. hs nrgs masur dffrncs btwns th undformd confguraton and th

More information

Add sodium hydroxide solution

Add sodium hydroxide solution , :::.l9 &30 ~!fjrkh:+l. ~ S/::T..:=4... A studnt has four solutons lablld A, B, C and D. Each soluton contans on compound from th followng lst: FCh Th studnt dos som smpl tsts to dntfy th compounds prsnt.

More information

(1) Then we could wave our hands over this and it would become:

(1) Then we could wave our hands over this and it would become: MAT* K285 Spring 28 Anthony Bnoit 4/17/28 Wk 12: Laplac Tranform Rading: Kohlr & Johnon, Chaptr 5 to p. 35 HW: 5.1: 3, 7, 1*, 19 5.2: 1, 5*, 13*, 19, 45* 5.3: 1, 11*, 19 * Pla writ-up th problm natly and

More information

The following information relates to Questions 1 to 4:

The following information relates to Questions 1 to 4: Th following information rlats to Qustions 1 to 4: QUESTIN 1 Th lctrolyt usd in this ful cll is D watr carbonat ions hydrogn ions hydroxid ions QUESTIN 2 Th product formd in th ful cll is D hydrogn gas

More information

The Hyperelastic material is examined in this section.

The Hyperelastic material is examined in this section. 4. Hyprlastcty h Hyprlastc matral s xad n ths scton. 4..1 Consttutv Equatons h rat of chang of ntrnal nrgy W pr unt rfrnc volum s gvn by th strss powr, whch can b xprssd n a numbr of dffrnt ways (s 3.7.6):

More information

1 Minimum Cut Problem

1 Minimum Cut Problem CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms

More information

Differentiation of Exponential Functions

Differentiation of Exponential Functions Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of

More information

First derivative analysis

First derivative analysis Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points

More information

Gradebook & Midterm & Office Hours

Gradebook & Midterm & Office Hours Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r-1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing

More information

Review - Probabilistic Classification

Review - Probabilistic Classification Mmoral Unvrsty of wfoundland Pattrn Rcognton Lctur 8 May 5, 6 http://www.ngr.mun.ca/~charlsr Offc Hours: Tusdays Thursdays 8:3-9:3 PM E- (untl furthr notc) Gvn lablld sampls { ɛc,,,..., } {. Estmat Rvw

More information

PHA 5127 Answers Homework 2 Fall 2001

PHA 5127 Answers Homework 2 Fall 2001 PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring

More information

SCIENCE Student Book. 3rd Grade Unit 2

SCIENCE Student Book. 3rd Grade Unit 2 SCIENCE Studnt Book 3rd Grad Unit 2 Unit 2 PLANTS SCIENCE 302 PLANTS Introduction 3 1. Plant Parts...4 Roots 6 Stms 8 Lavs 10 Food Storag Parts 11 Slf Tst 1 15 2. Plant Growth... 17 Watr and Minrals 18

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 401 Digital Signal Procssing Prof. Mark Fowlr Dtails of th ot St #19 Rading Assignmnt: Sct. 7.1.2, 7.1.3, & 7.2 of Proakis & Manolakis Dfinition of th So Givn signal data points x[n] for n = 0,, -1

More information

In the table below, write the coordinates of each point in the figure. Point x-coordinate y-coordinate A 0 3 B 3 3 C 3 5 D 3 8 E 5 5 F 6 3 G 3 1

In the table below, write the coordinates of each point in the figure. Point x-coordinate y-coordinate A 0 3 B 3 3 C 3 5 D 3 8 E 5 5 F 6 3 G 3 1 1 TASK 1.1.1: PATTY PAPER TRANSFORMATIONS Solutions 10 D C E A B F G -5 5 10 - - In th tabl blow, writ th s of ach pot th figur. x- y- A 0 3 B 3 3 C 3 5 D 3 E 5 5 F 3 G 3 1 1. On patty papr, trac th figur

More information

Learning All About. Mary. Creative. Communications. Sample

Learning All About. Mary. Creative. Communications. Sample Larnng All Abu Mary Hal Mary... Yu v prbably hard hs wrds a l. Mayb yu say hs prayr. Bu hav yu vr wndrd why w say? Wha abu all h sngs, saus and fas days ddcad Mary? Why d w hnr Mary s much? Frs, hnk abu

More information

That is, we start with a general matrix: And end with a simpler matrix:

That is, we start with a general matrix: And end with a simpler matrix: DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES Eduard N. Klnov* Rostov-on-Don, Russia Th articl considrs phnomnal gomtry figurs bing th carrirs of valu spctra for th pairs of th rmaining additiv

More information

Electrochemistry L E O

Electrochemistry L E O Rmmbr from CHM151 A rdox raction in on in which lctrons ar transfrrd lctrochmistry L O Rduction os lctrons xidation G R ain lctrons duction W can dtrmin which lmnt is oxidizd or rducd by assigning oxidation

More information

Sundials and Linear Algebra

Sundials and Linear Algebra Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.

More information

Consider a system of 2 simultaneous first order linear equations

Consider a system of 2 simultaneous first order linear equations Soluon of sysms of frs ordr lnar quaons onsdr a sysm of smulanous frs ordr lnar quaons a b c d I has h alrna mar-vcor rprsnaon a b c d Or, n shorhand A, f A s alrady known from con W know ha h abov sysm

More information

Aim To manage files and directories using Linux commands. 1. file Examines the type of the given file or directory

Aim To manage files and directories using Linux commands. 1. file Examines the type of the given file or directory m E x. N o. 3 F I L E M A N A G E M E N T Aim To manag ils and dirctoris using Linux commands. I. F i l M a n a g m n t 1. il Examins th typ o th givn il or dirctory i l i l n a m > ( o r ) < d i r c t

More information

EECE 301 Signals & Systems Prof. Mark Fowler

EECE 301 Signals & Systems Prof. Mark Fowler EECE 301 Signals & Systms Prof. Mark Fowlr ot St #21 D-T Signals: Rlation btwn DFT, DTFT, & CTFT 1/16 W can us th DFT to implmnt numrical FT procssing This nabls us to numrically analyz a signal to find

More information

Chapter 3 Exponential and Logarithmic Functions. Section a. In the exponential decay model A. Check Point Exercises

Chapter 3 Exponential and Logarithmic Functions. Section a. In the exponential decay model A. Check Point Exercises Chaptr Eponntial and Logarithmic Functions Sction. Chck Point Erciss. a. A 87. Sinc is yars aftr, whn t, A. b. A A 87 k() k 87 k 87 k 87 87 k.4 Thus, th growth function is A 87 87.4t.4t.4t A 87..4t 87.4t

More information

A Propagating Wave Packet Group Velocity Dispersion

A Propagating Wave Packet Group Velocity Dispersion Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to

More information

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0

Function Spaces. a x 3. (Letting x = 1 =)) a(0) + b + c (1) = 0. Row reducing the matrix. b 1. e 4 3. e 9. >: (x = 1 =)) a(0) + b + c (1) = 0 unction Spacs Prrquisit: Sction 4.7, Coordinatization n this sction, w apply th tchniqus of Chaptr 4 to vctor spacs whos lmnts ar functions. Th vctor spacs P n and P ar familiar xampls of such spacs. Othr

More information

Week 3: Connected Subgraphs

Week 3: Connected Subgraphs Wk 3: Connctd Subgraphs Sptmbr 19, 2016 1 Connctd Graphs Path, Distanc: A path from a vrtx x to a vrtx y in a graph G is rfrrd to an xy-path. Lt X, Y V (G). An (X, Y )-path is an xy-path with x X and y

More information

orbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the

orbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly

More information

A central nucleus. Protons have a positive charge Electrons have a negative charge

A central nucleus. Protons have a positive charge Electrons have a negative charge Atomic Structur Lss than ninty yars ago scintists blivd that atoms wr tiny solid sphrs lik minut snookr balls. Sinc thn it has bn discovrd that atoms ar not compltly solid but hav innr and outr parts.

More information

Lecture 14. Relic neutrinos Temperature at neutrino decoupling and today Effective degeneracy factor Neutrino mass limits Saha equation

Lecture 14. Relic neutrinos Temperature at neutrino decoupling and today Effective degeneracy factor Neutrino mass limits Saha equation Lctur Rlc nutrnos mpratur at nutrno dcoupln and today Effctv dnracy factor Nutrno mass lmts Saha quaton Physcal Cosmoloy Lnt 005 Rlc Nutrnos Nutrnos ar wakly ntractn partcls (lptons),,,,,,, typcal ractons

More information

Computing and Communications -- Network Coding

Computing and Communications -- Network Coding 89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc

More information

5. B To determine all the holes and asymptotes of the equation: y = bdc dced f gbd

5. B To determine all the holes and asymptotes of the equation: y = bdc dced f gbd 1. First you chck th domain of g x. For this function, x cannot qual zro. Thn w find th D domain of f g x D 3; D 3 0; x Q x x 1 3, x 0 2. Any cosin graph is going to b symmtric with th y-axis as long as

More information

Basic Polyhedral theory

Basic Polyhedral theory Basic Polyhdral thory Th st P = { A b} is calld a polyhdron. Lmma 1. Eithr th systm A = b, b 0, 0 has a solution or thr is a vctorπ such that π A 0, πb < 0 Thr cass, if solution in top row dos not ist

More information

Jones vector & matrices

Jones vector & matrices Jons vctor & matrcs PY3 Colást na hollscol Corcagh, Ér Unvrst Collg Cork, Irland Dpartmnt of Phscs Matr tratmnt of polarzaton Consdr a lght ra wth an nstantanous -vctor as shown k, t ˆ k, t ˆ k t, o o

More information

y = 2xe x + x 2 e x at (0, 3). solution: Since y is implicitly related to x we have to use implicit differentiation: 3 6y = 0 y = 1 2 x ln(b) ln(b)

y = 2xe x + x 2 e x at (0, 3). solution: Since y is implicitly related to x we have to use implicit differentiation: 3 6y = 0 y = 1 2 x ln(b) ln(b) 4. y = y = + 5. Find th quation of th tangnt lin for th function y = ( + ) 3 whn = 0. solution: First not that whn = 0, y = (1 + 1) 3 = 8, so th lin gos through (0, 8) and thrfor its y-intrcpt is 8. y

More information

Preview. Graph. Graph. Graph. Graph Representation. Graph Representation 12/3/2018. Graph Graph Representation Graph Search Algorithms

Preview. Graph. Graph. Graph. Graph Representation. Graph Representation 12/3/2018. Graph Graph Representation Graph Search Algorithms /3/0 Prvw Grph Grph Rprsntton Grph Srch Algorthms Brdth Frst Srch Corrctnss of BFS Dpth Frst Srch Mnmum Spnnng Tr Kruskl s lgorthm Grph Drctd grph (or dgrph) G = (V, E) V: St of vrt (nod) E: St of dgs

More information

Derangements and Applications

Derangements and Applications 2 3 47 6 23 Journal of Intgr Squncs, Vol. 6 (2003), Articl 03..2 Drangmnts and Applications Mhdi Hassani Dpartmnt of Mathmatics Institut for Advancd Studis in Basic Scincs Zanjan, Iran mhassani@iasbs.ac.ir

More information

Shortest Paths in Graphs. Paths in graphs. Shortest paths CS 445. Alon Efrat Slides courtesy of Erik Demaine and Carola Wenk

Shortest Paths in Graphs. Paths in graphs. Shortest paths CS 445. Alon Efrat Slides courtesy of Erik Demaine and Carola Wenk S 445 Shortst Paths n Graphs lon frat Sls courtsy of rk man an arola Wnk Paths n raphs onsr a raph G = (V, ) wth -wht functon w : R. Th wht of path p = v v v k s fn to xampl: k = w ( p) = w( v, v + ).

More information

Atomic energy levels. Announcements:

Atomic energy levels. Announcements: Atomic nrgy lvls Announcmnts: Exam solutions ar postd. Problm solving sssions ar M3-5 and Tusday 1-3 in G-140. Will nd arly and hand back your Midtrm Exam at nd of class. http://www.colorado.du/physics/phys2170/

More information

UNTYPED LAMBDA CALCULUS (II)

UNTYPED LAMBDA CALCULUS (II) 1 UNTYPED LAMBDA CALCULUS (II) RECALL: CALL-BY-VALUE O.S. Basic rul Sarch ruls: (\x.) v [v/x] 1 1 1 1 v v CALL-BY-VALUE EVALUATION EXAMPLE (\x. x x) (\y. y) x x [\y. y / x] = (\y. y) (\y. y) y [\y. y /

More information

Einstein Equations for Tetrad Fields

Einstein Equations for Tetrad Fields Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for

More information

(Upside-Down o Direct Rotation) β - Numbers

(Upside-Down o Direct Rotation) β - Numbers Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg

More information

Where k is either given or determined from the data and c is an arbitrary constant.

Where k is either given or determined from the data and c is an arbitrary constant. Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is

More information

INTEGRATION BY PARTS

INTEGRATION BY PARTS Mathmatics Rvision Guids Intgration by Parts Pag of 7 MK HOME TUITION Mathmatics Rvision Guids Lvl: AS / A Lvl AQA : C Edcl: C OCR: C OCR MEI: C INTEGRATION BY PARTS Vrsion : Dat: --5 Eampls - 6 ar copyrightd

More information

4. (5a + b) 7 & x 1 = (3x 1)log 10 4 = log (M1) [4] d = 3 [4] T 2 = 5 + = 16 or or 16.

4. (5a + b) 7 & x 1 = (3x 1)log 10 4 = log (M1) [4] d = 3 [4] T 2 = 5 + = 16 or or 16. . 7 7 7... 7 7 (n )0 7 (M) 0(n ) 00 n (A) S ((7) 0(0)) (M) (7 00) 8897 (A). (5a b) 7 7... (5a)... (M) 7 5 5 (a b ) 5 5 a b (M)(A) So th cofficint is 75 (A) (C) [] S (7 7) (M) () 8897 (A) (C) [] 5. x.55

More information

Hardy-Littlewood Conjecture and Exceptional real Zero. JinHua Fei. ChangLing Company of Electronic Technology Baoji Shannxi P.R.

Hardy-Littlewood Conjecture and Exceptional real Zero. JinHua Fei. ChangLing Company of Electronic Technology Baoji Shannxi P.R. Hardy-Littlwood Conjctur and Excptional ral Zro JinHua Fi ChangLing Company of Elctronic Tchnology Baoji Shannxi P.R.China E-mail: fijinhuayoujian@msn.com Abstract. In this papr, w assum that Hardy-Littlwood

More information

10/7/14. Mixture Models. Comp 135 Introduction to Machine Learning and Data Mining. Maximum likelihood estimation. Mixture of Normals in 1D

10/7/14. Mixture Models. Comp 135 Introduction to Machine Learning and Data Mining. Maximum likelihood estimation. Mixture of Normals in 1D Comp 35 Introducton to Machn Larnng and Data Mnng Fall 204 rofssor: Ron Khardon Mxtur Modls Motvatd by soft k-mans w dvlopd a gnratv modl for clustrng. Assum thr ar k clustrs Clustrs ar not rqurd to hav

More information

A=P=E M-A=N Alpha particle Beta Particle. Periodic table

A=P=E M-A=N Alpha particle Beta Particle. Periodic table Nam Pr. Atomic Structur/Nuclar Chmistry (Ch. 3 & 21) OTHS Acadmic Chmistry Objctivs: Undrstand th xprimntal dsign and conclusions usd in th dvlopmnt of modrn atomic thory, including Dalton's Postulats,

More information

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x "±# ( ).

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x ±# ( ). A. Limits and Horizontal Asymptots What you ar finding: You can b askd to find lim x "a H.A.) problm is asking you find lim x "# and lim x "$#. or lim x "±#. Typically, a horizontal asymptot algbraically,

More information

Thomas Whitham Sixth Form

Thomas Whitham Sixth Form Thomas Whitham Sith Form Pur Mathmatics Unit C Algbra Trigonomtr Gomtr Calculus Vctor gomtr Pag Algbra Molus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv

More information

CHAPTER 33: PARTICLE PHYSICS

CHAPTER 33: PARTICLE PHYSICS Collg Physcs Studnt s Manual Chaptr 33 CHAPTER 33: PARTICLE PHYSICS 33. THE FOUR BASIC FORCES 4. (a) Fnd th rato of th strngths of th wak and lctromagntc forcs undr ordnary crcumstancs. (b) What dos that

More information

Cramér-Rao Inequality: Let f(x; θ) be a probability density function with continuous parameter

Cramér-Rao Inequality: Let f(x; θ) be a probability density function with continuous parameter WHEN THE CRAMÉR-RAO INEQUALITY PROVIDES NO INFORMATION STEVEN J. MILLER Abstract. W invstigat a on-paramtr family of probability dnsitis (rlatd to th Parto distribution, which dscribs many natural phnomna)

More information

Problem Set 6 Solutions

Problem Set 6 Solutions 6.04/18.06J Mathmatics for Computr Scinc March 15, 005 Srini Dvadas and Eric Lhman Problm St 6 Solutions Du: Monday, March 8 at 9 PM in Room 3-044 Problm 1. Sammy th Shark is a financial srvic providr

More information

Physics 256: Lecture 2. Physics

Physics 256: Lecture 2. Physics Physcs 56: Lctur Intro to Quantum Physcs Agnda for Today Complx Numbrs Intrfrnc of lght Intrfrnc Two slt ntrfrnc Dffracton Sngl slt dffracton Physcs 01: Lctur 1, Pg 1 Constructv Intrfrnc Ths wll occur

More information

ON THE COMPLEXITY OF K-STEP AND K-HOP DOMINATING SETS IN GRAPHS

ON THE COMPLEXITY OF K-STEP AND K-HOP DOMINATING SETS IN GRAPHS MATEMATICA MONTISNIRI Vol XL (2017) MATEMATICS ON TE COMPLEXITY OF K-STEP AN K-OP OMINATIN SETS IN RAPS M FARAI JALALVAN AN N JAFARI RA partmnt of Mathmatcs Shahrood Unrsty of Tchnology Shahrood Iran Emals:

More information

Introduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013

Introduction to Arithmetic Geometry Fall 2013 Lecture #20 11/14/2013 18.782 Introduction to Arithmtic Gomtry Fall 2013 Lctur #20 11/14/2013 20.1 Dgr thorm for morphisms of curvs Lt us rstat th thorm givn at th nd of th last lctur, which w will now prov. Thorm 20.1. Lt φ:

More information

Hydrogen Atom and One Electron Ions

Hydrogen Atom and One Electron Ions Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial

More information

Minimum Spanning Trees

Minimum Spanning Trees Mnmum Spnnng Trs Spnnng Tr A tr (.., connctd, cyclc grph) whch contns ll th vrtcs of th grph Mnmum Spnnng Tr Spnnng tr wth th mnmum sum of wghts 1 1 Spnnng forst If grph s not connctd, thn thr s spnnng

More information

SCHUR S THEOREM REU SUMMER 2005

SCHUR S THEOREM REU SUMMER 2005 SCHUR S THEOREM REU SUMMER 2005 1. Combinatorial aroach Prhas th first rsult in th subjct blongs to I. Schur and dats back to 1916. On of his motivation was to study th local vrsion of th famous quation

More information

ORDER OF PLAY START OF ROUND

ORDER OF PLAY START OF ROUND ORDER OF PLAY 6 7 Playrs will start a round by rplnishing th markt cards and qust or. (Pag 9) Thy will thn mov ovrsrs in th min to collct rsourcs. (Pag 0) Nxt, thy will rarrang playr ordr basd on positions

More information

A general N-dimensional vector consists of N values. They can be arranged as a column or a row and can be real or complex.

A general N-dimensional vector consists of N values. They can be arranged as a column or a row and can be real or complex. Lnr lgr Vctors gnrl -dmnsonl ctor conssts of lus h cn rrngd s column or row nd cn rl or compl Rcll -dmnsonl ctor cn rprsnt poston, loct, or cclrton Lt & k,, unt ctors long,, & rspctl nd lt k h th componnts

More information

Differential Equations

Differential Equations Prfac Hr ar m onlin nots for m diffrntial quations cours that I tach hr at Lamar Univrsit. Dspit th fact that ths ar m class nots, th should b accssibl to anon wanting to larn how to solv diffrntial quations

More information

Heisenberg Model. Sayed Mohammad Mahdi Sadrnezhaad. Supervisor: Prof. Abdollah Langari

Heisenberg Model. Sayed Mohammad Mahdi Sadrnezhaad. Supervisor: Prof. Abdollah Langari snbrg Modl Sad Mohammad Mahd Sadrnhaad Survsor: Prof. bdollah Langar bstract: n ths rsarch w tr to calculat analtcall gnvalus and gnvctors of fnt chan wth ½-sn artcls snbrg modl. W drov gnfuctons for closd

More information