1. Intrinsic Mathcad Functions

Transcription

1 . Intrinsi Mth Fntions Mth hs myri of mthmtil fntions. Yo h lry s srl of thm hih r ill on th lltor tool pltt. Srl ommon fntions r fon in th tl lo. Yo n s ll th fntions ill, s ll s sription of h, y th insrt --> f(x) mn Fntions Dsription xp(x), x Th nmr ris to th por of x. log(x,[]) Bs logrithm of x. (= y flt) ln(x) Ntrl logrithm of x x! Ftoril of x. mx(,,, ) Th l of th lrgst rgmnt. min(,,, ) Th l of th smllst rgmnt. mn(,,, ) Th rg of,,, floor(x) Th lrgst intgr lss thn or ql to x. il(x) Th smllst intgr grtr thn or ql to x. Th nmr x ron to n iml pls. If n is omitt, x is ron(x,n) ron to th nrst intgr. If n<, x is ron to th lfts of th iml point. trn(x) Th intgr prt of x mo(x,y) Th rminr of iiing x y y if(onition,tr,fls) If onition is tr (non-ro), rtrns tr. If onition is fls, rtrns fls. (lls toolr) n i f ( i), smmtion (lls toolr) n f ( i), prot i Prti. Cllt th folloing: floor of π, il of π, th rminr of iiing π y. floor( π) il( π) mo( π ).. Ron π to iml pls.

2 ron( π ).. Lt x =. n llt th folloing: x, log (x), log (x), ln(x) x. x. log( x). log( x ). ln( x). Trigonomtri Fntions All trigonomtri fntion r ill n r otin y typing th nm follo y ()'s. x is ssm to in rins nlss spifi othris.. Usr-Dfin Fntions sin π. On of th porfl ftrs of Mth is th ility to fin yor on fntions. This is ry hlpfl hn oing nginring lltions n ill s oftn. Syntx To rt fntion:. Typ th sir fntion nm. Typ (x) hr x is th ril of th fntion.. Typ : to gi yo :=. Dfin th xprssion in trms of x. Not: yo n s mor thn on ril in fntion, simply sprt h ith omm. Prti: rit fntions of on n to rils, thn lt th fntions sing ls for th rils f( x) x f( ) f( ) x f( x). Th if fntion g( xy ) x y y x gxy ( ) g ( ) Syntx if(onition, tr, fls) Tr n fls n fntions, txt, lttrs, nmrs, t. Dirnt onitions n fon on th Booln tool pltt.

3 Prti: rit n solt l fntion sl( x) if( x x x ) sl( ) sl( ) Compon Logil Exprssions Oprtor Symol on Tool Pltt Dsription An ^ Rtrns if oth x n y r non-ro (tr). othris. Or Rtrns if ithr x or y r non-ro (tr). othris. Exlsi or, xor Rtrns if x or y, t not oth, r non-ro. othris. Not Rtrns if x is ro (fls). Rtrns othris Lss thn Rtrns if x < y, othris Grtr thn Rtrns if x > y, othris Eql to = Rtrns if x + y, othris Not Eql to Rtrns if x os not ql y, othris Dmonstrtion Imgin tht th tmprtr of th rtor mst kpt o C to kp th rtion going n lo C to prnt xssi prssr from forming in th ssl. Writ simpl logil fntion to trmin if th rtion tmprtr is in th orrt rng. hk_rtor( t) if [( t ) t "hlp" "rtor is OK" ] hk_rtor( ) "rtor is OK" hk_rtor( ) "hlp" hk_rtor( ) "hlp" Arrys, Vtors, Mtris. Crting Mtris Thr r srl ys to rt mtrix A. Th "Insrt Mtrix" Wino (<Ctrl>M)

4 B Ky Point Rfr to mtrix si y ros x olmns Us th t ky to mo tn pl holrs. B. Pst mtrix from lshr (sh s xl or txt fil) Typ ril nm in Mth Opn n Exl fil. Slt som t Copy Pst into th plholr of th ril C C. Insrt tl M Slt Insrt/Dt/Tl from th Insrt mn Clik n thn right lik th ppr-lft ll Slt "Import" from th mn Us th rosr to fin th fil ontining th t (mtrix.txt) Clik OK Gi th tl ril nm Ky Points Do NOT rt th ril nm first! Mk sr to import th tl y right liking Ni to s this for ig tls (sroll rs). Rfrning Arrys Iniil lmnts r rfrn ith ssripts y typing th [ ky. Prti

5 B B B B Ky Points Mth gins onting mtrix inis t Yo n hng th strting inx y fining ORIGIN Prti ORIGIN B Prti Yo n rt mtris sing inx nottion D. D D. D.. Prti. Crt th folloing mtrix sing ssript (inx) nottion. E E E E E E. Wht is th l of th th ro, r olmn of M?. Eiting Mtrix M Yo n or lt ros n olmns to xisting mtris. It is triky. To ro/olmn:. Pl rsor o ros n to th lft of th ros n olmns to.. Opn th Insrt Mtrix ino.. Typ th nmr of ros n olmns to n lik Insrt. To lt ro/olmn:. Pl rsor in th pprmost ro n lftmost olmn of th ros n olmns to rmo.. Opn th Insrt Mtrix ino.

6 . Typ th nmr of ros n olmns to lt n lik Dlt. Dmonstrtion A ro olmns B B B Dlt olmns, ro y first olmn ro n thn olmn ros. B B B B B B Ky Point Noti tht to ro in th mil of B, yo ro n olmns.. Soling Systms of Linr Eqtions Explntion Rll tht mtrix mth n s sol systms of linr qtions. A systm of linr qtions is on in hih th rils (x, y, ) ppr only to th por of. x y = x y = A systm of linr qtions n rittn th folloing mtrix form. AX = B

7 hr x A = X = B = y Th systm of linr qtions rittn in this form hs th folloing soltion. A AX = A B IX = A B X = A B Th orr of th mltiplition mttrs. Th soltion is A - B not BA - Dmonstrtion A B A B lsol( AB ) Ky Points Mth n otin th nsrs in to ys, sing n inrs or sing lsol Both r orrt. lsol ss fstr lgorithm hih my om importnt for lrg mtris.. Oprtions With Mtris S Mtrix Toolr for mny mtrix oprtions Bsi Mtrix Mth Ri Aition n strtion To mtris n n strt only if thy r th sm si. Aition n strtion is on lmnt y lmnt to rt mtrix of th sm si Mltiplition To mtris n mltipli if thir innr imnsions r th sm. Exmpl: x * x not x * x.

8 Exmpl: x * x not x * x Th otr imnsions tll th si of th mtrix. Exmpl: x * x ill pro x mtrix Rmmr tht orr mttrs ith mtrix mltiplition! Error s innr imnsions on't mth Diision Thr is not mtrix iision! Mltiply y th inrs to mo mtris ross = signs. Othr Mtrix Oprtions Fntions ros(a) ols(a) smtrix(a, ir, jr, i, j) gmnt(a, B, C, ) stk(a, B, C, ) Dsription Rtrns th nmr of ros in mtrix A Rtrns th nmr of olmns in mtrix A Crts n mtrix hih is portion of rry A. Th portion onsists of th lmnts in ros ir throgh jr n in olmns i throgh j. Crts singl mtrix ompris of tors A, B, C, ll ith th sm nmr of ros, ontnt from lft to right. Crts singl mtrix ompris of tors A, B, C, ll ith th sm nmr of olmns, ontnt from top to ottom. Extrts th nth olmn of mtrix s olmn tor. Tks th inrs of mtrix. Tks th trminnt of th mtrix. Th tor ot n ross prot.

9 stk s t s t gmnt r s t r s t smtrix r s t Prti. Fin soltion to th folloing st of qtions. x y =.. y =.x. = x y = x A.... x A x..... For th mtris fin lo, prform th rqst oprtions (if possil). If prtilr oprtion is not possil, n yo gi th rson hy? A X Y Z i. XY, YX, XZ, ZX ii. AX, XA, AA, A - A iii. X+Y, Y+X i. A T, X T, Z T. Y-Z, Y-X i. A, X, Y, Z

10 i. XY YX XZ Z*X hs inorrt innr imnsions iii. XA XA AX AA AA A A A i. X Y Y X. YZ YX i. A A Y Z Z X.

11 Us th mtrix tool on th pltt to fin th folloing x mtrix: A A ro ontining th ntris [ ] ftr th son ro to form th folloing mtrix: A A n itionl olmn to th mtrix ith th ntris [ ] to form th folloing x mtrix: A Rng Vrils Rng rils r sfl for fining rrys n orking ith fntions n plots Us th ; to fin th rng: Typ: "i:;" Typ: "i:,.;"

12 i x i.i i x..... f( x).....

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