Giao trinh Mathcad

GIO TRNH Mathcad

CHNG I: GII THIU Mathcad 2001i

CHNG I GII THIU Mathcad 2001i

I.

CC THAO TC CN THITI.1. Khi ng Mathcad 2001i khi ng Mathcad 2001i, c th thc hin theo cc cch sau: Nhp p vo biu tng . Nhp vo nt Start/Mathsoft Apps/Mathcad 2001i professional.

I.2. Thot khi Mathcad 2001i thot khi Mathcad 2001i, c th thc hin theo cc cch sau: Trn thanh menu : chn File/Exit. T bn phm : nhn Alt+F+X. . Nhp vo nt iu khin

I.3. Lu trI.3.1. Lu Worksheet vi tn mi

Khi va khi ng Mathcad 2001i, khi mun lu tr li hoc t file c mun lu tr li vi tn mi, bng cc cch sau: Trn thanh menu T bn phm : chn File/Save As : nhn t hp Alt+F+A

Mathcad 2001i s m ra hp thoi Save As (hnh 1.1) cho php t tn v chn ni lu tr, trong :KS. HUNH VNG THU MINH - Trang 4 -

GIO TRNH Mathcad


Mc Save in Mc File name Mc Save as type

: chn th mc cn lu tr (hnh 1.1) chn th mc Mathcad 2001i. : ni t tn cho Worksheet. : cho php lu tr Worksheet theo cc phin bn ca Mathcad hoc dng Template,

Hnh 1.1. Hp thoi Save As

Sau , nhp vo nt Save (hoc g Enter) hon tt vic lu tr. I.3.2. Lu Worksheet c tn sn : nhp vo biu tng . : nhn t hp Ctrl+S (hoc Alt+F+S). : chn File/Save.

Trn thanh cng c chun T bn phm Trn thanh menu

I.4. M mt WorksheetI.4.1. M mt Worksheet hon ton mi : nhp vo biu tng . : nhn t hp Ctrl+N (hoc Alt+F+N). : chn File/New.

Trn thanh cng c chun T bn phm Trn thanh menu

Sau , hp thoi New xut hin ( hnh 1.2)

KS. HUNH VNG THU MINH

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Hnh 1.2. Hp thoi New I.4.2. M mt Worksheet c sn

Trn thanh cng c chun : nhp vo biu tng . T bn phm : nhn t hp Ctrl+O (hoc Alt+F+O). Trn thanh menu : chn File/Open. Sau , xut hin Hp thoi Open nh hnh 1.3 Mc Look in : chn th mc c cha fie cn m. Mc File name : tn file cn m. Mc Files of type : c th m cc tp tin ca Mathcad vi cc ui *.mcd (cac Worksheet); *.mct (cac Template); *.hbk (sch gip ca Mathcad); *.* (hien th tat ca cac tap tin). Sau chn Open hon tt vic m mt tp tin.

Hnh 1.3. Hp thoi OpenKS. HUNH VNG THU MINH - Trang 6 -

GIO TRNH Mathcad


II. GII THIU GIAO DIN Mathcad 2001iII.1. Thanh tiu (Title bar) ( hnh 1.4)V tr : nm trn nh mn hnh, cho bit chng trnh ang chy l Mathcad 2001i, trang ang lm vic l [Untitled:1] (i vi tp tin cha c tn), [Tn tp tin] i vi tp tin c tn. Nt iu khin mn hnh : nm bn phi mn hnh Thanh Menu .

Thanh Tiu

Thanh cng c Math Thanh nh dng

Thanh Cng c chun

Vng son tho v tnh ton

Crosshair

Thanh Trng thi

Cc thanh cun

Hnh 1.4 Giao din Mathcad 2001i


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II.2.

Thanh thc n (menu bar) ( hnh 1.4 )

Trn thanh thc n (menu bar) c nhiu trnh n, khi mt trnh n c chn, th ngay lp tc mt thc n th (Full Down menu) (hnh 1.5) xut hin cho php chn lnh k tip. File : ngoi cc lnh tng t nh WORD, EXCEL, cn c cc lnh giao tip vi cc ngi dng Mathcad khc trn th gii thng qua mng Internet (Collaboratory) (hnh 1.5). Edit : im ni bt trong ny l xut hin cc mc Links, Object gip ngi s dng Mathcad c th trao i d liu vi cc i tng khc (hnh 1.6).

Full Down menu

Hnh.1.5. Chn trnh File trn thanh menu


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Hnh.1.6. Chn trnh Edit trn thanh menu Insert mc sau: Graph : chn vo cc loi th. Matrix : chn vo mt Vct hoc Ma trn. : chn vo nhng hm s c lp sn Function chn hn nh: sin, cos Unit : chn n v. Picture : chn vo mt hnh v. Math Region : chn mt vng trng nhp cng thc ton. Text Region : chn mt vng trng nhp vn bn. Page Break : chn ng phn trang. Reference : to mt lin kt vi mt tp tin Excel, Mathcad khc. Component : to mt lin kt vi mt tp tin Excel, Mathcad Oject : chn nh. Format : nh dng Text, Equation, th (hnh 1.8) Equation : nh dng cc dng thc ton hc v kiu ch, kch thc, mu sc, : Trong menu ny (hnh1.7) Mathcad cho php chn cc

Hnh.1.7


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Text di, Result

: nh dng cho vn bn v kiu ch, kch c, ch s trn, ch s : nh dng kt qu (hnh 1.9)

Properties Properties/Display : t mu vng c chn. Properties/Calculation/Disable Evaluation : xut hin hnh ch nht mu en pha trn, s khng th hin kt qu. Properties/Calculation/EnableOptimization : xut hin du sao , kch vo s th hin kt qu (hnh 1.10). Separate regions : tch ri cc vng chng ghp. Align Regions : canh hng ngang hng dc. Headers/Footers : to ta u trang v cui trang Hnh.1.8

Hnh 1.9. nh dng kt qu


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Hnh.1.10. Hp thoi Properties Math (hnh 1.11) Calculate : tnh mt biu thc khi c chn. Chc nng ny ch s dng khi khng nh du vo Automatic calculate trn thanh Math. Calculate Worksheet : cp nht ho tt c cc kt qu tnh ton hay v khi thay i bin cho ton b Worksheet. Automatic Calculate : t ng cp nht ho tt c cc kt qu khi thay i bin. Optimization : nh gi c lng, phn tch biu thc hoc chng trnh. Options : thay i cc tham s ca chng trnh. V d: Tnh biu thc vi bin x c cho nh sau:x:= 4 a:= (x+1)2 - (x-1)2*

Nhp p du hoa th ta thy dng n gin hn ca biu thc.

Symbolics (hnh 1.12) Cc php ton v Symbolics: thiu k chng 3.

Cc lnh ny s c gii

Hnh.1.12 Window (hnh 1.13) Cascade : cc ca s xp chng ln nhau. Hnh.1.13KS. HUNH VNG THU MINH - Trang 11 -

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Tile Horizontal Tile Vertical

: cc ca s xp thnh hng ngang k tip nhau. : cc ca s xp thnh hng dc k tip nhau. Help (hnh 1.14) Nhp vo tng mc, xut hin cc phn gip , c th m Resource Center xem cc Quicksheet, cc bng tin ch hoc m sch tra cu

Hnh.1.14


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II.3.

Thanh cng c chun (Standard Toolbar) (hnh 1.15)

Hnh.1.15. Thanh cng c chun (Standard Toolbar) Thanh cng c chun chun (Standard Toolbar) cho php thc hin cc thao tc bng biu tng (hnh 1.15) nh sau: : canh hng ngang, hng dc cc vng. : lit k tt c cc hm s c th chn vo Worksheet. : lit k tt c cc n v c th chn vo Worksheet. : lin kt mt Worksheet ca Mathcad vi nhng d liu ngun khc nh Word, Excel : to mt mi lin kt vi cc ngun ti liu khc do ngi s dng t lp nn. Khi s dng, ch cn kch p vo t no ca ti liu tc khc s xut hin ti liu khc c lin quan n n.

II.4.

Thanh nh dng (Formatting Toolbar) (hnh 1.16)

Hnh.1.16. Thanh nh dng (Format bar) Cho php nh dng i tng v: Kiu ch (Font), kch c (size), canh hng ngang, dc, ch s trn, di,

II.5.

Thanh cng c Math (Math Toolbar)Calculator toolbar Graph toolbar Matrix toolbar Boolean toolbar Programming toolba Greek toolbar Symbolic toolbar

Hnh 1.17.Thanh Math

Evaluation toolbar Calculus toolbar

Thanh cng c Math chuyn dng tnh ton (hnh 1.17), khi nhp vo mi biu tng trn thanh cng c Math th xut hin ln lt cc bng sau:KS. HUNH VNG THU MINH - Trang 13 -

GIO TRNH Mathcad


S hc (Calculator Tollbar). Bng la chn cc dng th (Graph Tollbar). Vc t v Ma trn (Vector and Matrix Tollbar). Bng cc ton t quan h (Evaluation Tollbar and Boolean Tollbar). Bng cc php ton v o hm, tch phn, gii hn,(Caculus Tollbar). Bng cc t kho lp chng trnh (Programming Tollbar). Bng cc mu k t Hy Lp (Greek Symbol Tollbar). Bng cc t kho Symbolic (Symbolic keyword Tollbar).

Hnh 1.18. Bng tnh thc hin cc php ton t thanh Math

II.6.

Thanh trng thi (Status bar) (hnh1.19 )

Hnh 1.19. Thanh trng thi

II.7. Vng son tho v tnh ton (region), hnh ch thp (crosshair) (hnh 1.4)Vng son tho v tnh ton (mc nh). : c dng hnh ch nht mu trng


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Hnh ch thp mu (Crosshair) tng trn mn hnh.

: th hin v tr trnh by mt i


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III. NH DNG TRANG V INIII.1. nh dng trang in

nh dng trang in, t thanh menu chn File/Page Setup xut hin hp thoi Page Setup (hnh 1.20).

Hnh 1.20. Hp thoi Page Setup Ti mc Paper size Orientation Portrait Orientation Landscape Margins v l inches (1in = 2.54cm). : chn kh giy. : chn kiu in trang ng. : chn kiu in trang ngang. : canh l tri, phi, trn, di. Mc nh n

III.2. In t Mathcad in trong Mathcad, thc hin theo cc cch sau: T thanh menu T bn phmKS. HUNH VNG THU MINH

: chn File/Print : nhn t hp Ctrl+P.- Trang 15 -

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Xut hin hp thoi Print (hnh 1.21). Hp thoi ny cho php chn my in, chn kiu in nh ( in tt c), (in trang hin hnh). (chn trang in), (in phn c chn),

Hnh 1.21. Hp thoi Print


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CHNG II: NHP K T V CNG THC

CHNG II NHP K T V CNG THC TRN Mathcad 2001i

I.I.1.

NHP K TLa chn thuc tnh cho k tTrn thanh menu : chn Format/Style, xut hin hp thoi Text Style (hnh 2.1).

Hnh 2.1. Hp thoi Text Style C th chn New t tn cho mt ln la chn (nu mun s dng nhiu kiu ch - Style), hoc nu mun mc nh th chn Normal/Modify xut hin hp thoi Define Style (hnh 2.2).

Hnh 2.2. Hp thoi Define StyleKS. HUNH VNG THU MINH - Trang 16 -

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Trong hp thoi Define Style Format (hnh 2.3).

: chn

, xut hin hp thoi Text

Hnh 2.3. Hp thoi Text Format Trong hp thoi Text Format cho php la chn cc thuc tnh cho k t, sau chn OK/Close hon tt cng vic. Khi trn thanh nh dng (Formatting Toolbar) s thay i (hnh 2.4).

Hnh 2.4. Thanh Formatting Toolbar sau khi nh dng Style

I.2. To vng k tMun to vng k t, thc hin theo cc bc sau: Kch con tr chut ti v tr mun t k t. Trn thanh menu Hoc t bn phm : nhn Insert/Text Region. : nhn .

Khi khung k t hin trn mn hnh , tin hnh nhp k t, mun xung dng th nhn Enter, mun thot nhn tr chut ngoi khung k t (hnh 2.5).

Hnh 2.5. Khung k tKS. HUNH VNG THU MINH - Trang 17 -

GIO TRNH Mathcad


Lu : thao tc c nhanh, ch cn kch tr chut ti vng mun th hin k t, nh bnh thng cui cng s dng thanh Spacebar, chui k t t ng chy vo khung k t.

II. X L K TII.1. Sao chp k t

Sau khi chn i tng, thc hin vic sao chp theo cc cch sau: Trn thanh menu Trn thanh cng c chun T bn phm : chn Edit/Copy. : nhp vo biu tng : nhn t hp Ctrl+C. .

II.2.

Ct k t

Sau khi chn i tng, thc hin vic ct k t theo cc cch sau: Trn thanh menu Trn thanh cng c T bn phm : chn Edit/Cut. : nhp vo biu tng : nhn t hp Ctrl+X. .

II.3.

Dn k t

Sau khi chn v tr cn dn i tng, thc hin theo cc cch sau: Trn thanh menu Trn thanh cng c T bn phm : chn Edit/Pase. : nhp vo biu tng : nhn t hp Ctrl+V. .

II.4.

Xo chui k t

Kch chn khung k t cn xo: Xo k t nm bn tri im chn Xo k t nm bn phi im chn Xo tt c cc khung k t : nhn Bksp ( : nhn Delete. : chn Edit/Select All (nhn trl+A). ).


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II.5.

Mun ghi chng k t

Kch tr chut ngay bn tri ca k t u tin mun ghi chng: Nhn phm Insert bt u nhp ni dung mi. Nhn li phm Insert tr li ch mc nh ban u.

II.6.

Chn cng thc vo chui k t

Kch tr chut ti ni mun chn cng thc, sau c th thc hin theo cc cch sau: Trn thanh menu : chn Insert/Math Region. T bn phm : nhn t hp Ctrl+Shift+A.

Xut hin khung trng nhp cng thc, kch chut vo mt ch bt k trong vng vn bn tr v ch nhp k t.

II.7.

Kt ni

Mun kt ni mt tp tin bt k, thc hin theo cc bc sau: Chn i tng mun kt ni. Trn thanh menu : chn Insert/Hyperlink (hoc nhn Ctrl+K), xut hin hp thoi Insert Hyperlink (hnh 2.6). Chn tm file cn kt ni.

Mun file kt ni dng Pop-up th kch vo mc Display as pop-up document. Mun s dng a ch tng i, kch vo mc Use relative path for hyperlink. Mun th hin ch thch thanh trng thi, nh vo mc Message that appears Cui cng chn OK.


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Hnh 2.6. Hp thoi Insert Hyperlink Khi mun m file kt ni, ch cn kch p vo i tng c kt ni.

II.8.

Tm v thay th

II.8.1. Tm k t Thc hin theo cc cch sau: Trn thanh menu T bn phm : chn Edit/Find : nhn t hp Ctrl+F

Xut hin hp thoi Find (hnh 2.7)

Hnh 2.7. Hp thoi Find Trong khung Find what nhp chui k t cn tm. Nhn Find Next thc hin vic tm k t.


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II.8.2. Thay th k t Thc hin theo cc cch sau: Trn thanh menu T bn phm : chn Edit/Replace : nhn t hp Ctrl+F

Xut hin hp thoi Replace (hnh 2.8)

Hnh 2.8. Hp thoi Replace Trong khung Find what Trong khung Replace with Th Replace Th Replace All Th Find Next : nhp chui k t mun tm. : nhp chui k t mun thay th. : ch thay th mt k t hin hnh. : thay th ton b k t hin hnh. : tm k t k tip thay th.

II.9.

Kim tra li chnh t

Thc hin theo cch sau: Chn k t mun kim tra li. Trn thanh menu : chn Edit/Check Spelling

Xut hin hp thoi Check Spelling (hnh 2.9)


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Hnh 2.9. Hp thoi Check Spelling Trong khung Not Found Trong khung Change To Lu : Trng hp t thay th trong t in b thiu, c th thm t mi vo t in. : xut hin t b li. : xut hin t thay th.

II.10.

Son tho ni dung ca phn trang tnh dnh nhp s liu

Mi loi s liu nn nhp vo mt bng ring hoc mt phn ring trn trang tnh. Trong trang ny nn c cc s hoc hnh v gii thch ngha ca cc s liu c nhp. to cc hnh v, c th s dng AutoCAD hay Paint chn vo trang tnh ca Mathcad.

II.11.

Son tho ni dung ca phn trang tnh dnh xut kt qu

Cch son tho ni dung trang tnh dnh xut kt qu cng ging nh khi son tho trang tnh dnh nhp s liu. Kt qu xut ra cng cn phn loi v xp vo tng bng theo nhm ngha d theo di. Km theo bng kt qu nn c cc hnh v minh ho, c th s dng phn ho trong Mathcad v bng s liu thc. Nh vy khi s liu thay i th gi tr v biu hnh v s thay i theo. Hoc c th dng AutoCAD hay Paint, nhng n ch thun tu l hnh v minh ho ch khng m t c kt qu thc.

II.12.

Son tho ni dung trang tnh dnh lu tr c s d liu

Trong qu trnh tnh ton c th s dng nhng bng tra, hoc bng s liu t Excel, th c son sn... tt c c xem l c s d liu dng tra cu, ni suy hay c s liu


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Nu khng mun lu tr c lp vi Mathcad, c th chp n vo trang nm bn phi trang in trong Mathcad. Khi khng cn nh dng trang ny v n s khng c in. Trng hp c mt s cng thc tnh ton hoc lp trnh khi khng mun cho ngi s dng phn mm nhn thy hoc khng mun in ra, thc hin theo cc bc nh sau: Chn Insert/Area chn vng cn kho (lock). Kch nt phi chut vo vng cn kho xut hin menu th v chn Lock Trong hp thoi Lock Area, g vo Password. Chn OK hon tt vic kho.

III. NHP CNG THCt con tr chut ti ch bt u g cng thc, sau t bn phm c th g cc k t, con s hoc cc ton t nh cng (+), tr (-), nhn (*), chia (/), hoc c th dng thanh cng c Math ( c gii thiu chng 1). Khi nhp cng thc tnh ton, ta s thy chng nm trong khung cng vi ng ch mu xanh bit theo di l k t no ang c x l.

III.1.

Chn cc k hiu ton t

chn ton t vo biu thc: Kch vo biu thc mun chn. Nhn phm Ins di chuyn im chn sang tri. Nhn phm ton t mun chn.

III.2.

Xo cc k hiu ton t

xo cc k hiu ton t: Kch vo biu thc mun xo. Nhn phm Ins chuyn im chn sang tri. Nhn phm BkSp ( ).

III.3.

Xo ton b cng thcKch chn cng thc mun xo. Trn thanh menu : nhn Edit/Delete.


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III.4. Thm du ngoc n vo biu thc ng ngoc mt i tng duy nht: t con tr chut trc hoc sau i tng. T bn phm : nhn du nhy n ().

ng ngoc nhiu i tng: t con tr vo trc i tng v nhn phm du ngoc m ( ( ). t con tr chut vo sau i tng v nhn phm du ngoc ng ( ) ).

III.5.

Nhp cc con s

a. Nhp cc s ln hn 999 Khi nhp cc con s ln hn 999, khng c dng du phy (,) hoc du chm (.) phn cch cc con s m phi nh lin tc. V d: 10000 hoc 200000 b. Nhp s thp phn Khi nhp cc s thp phn, dng du chm (.) phn bit s thp phn. c. Nhp con s tng theo bi s 10 Nhp s cn tng theo bi s ca 10. T bn phm : nhn a*10^ s xut hin a 10 . Trong khung trng hnh ch nht, nh con s tng ng vi bi s 10.d. Nhp s o nhp s o: nh s thc. nh i hoc j ngay sau cc s . Lu : Nu mun th hin s o l i hoc j ta phi nh l 1i hoc 1jsau s 1 s bin mt. Nu ch nh i hoc j th n hiu l mt bin ch khng phi s o.


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III.6. nh ngha bin trnh nhm ln cc tn bin, tt nht nn chn tn bin ging nh tn bin cn tnh ton. V d: Tnh h s bin ng Cv (trong tnh ton Thy vn)Cv := ( ki 1) n12

Nh vy lc ny Cv l mt bin trong Mathcad.

III.7. nh ngha hmBn cht ca hm trong Mathcad cng ging nh hm trong ton hc. Trong Mathcad c tt c cc tnh nng nh mt chng trnh ton hc. Do tnh c hm thc hin theo cc bc sau: Khai bo bin. Khai bo hm. Kt qu. V d:Khai bao bien : Khai bao ham : Ket qua :q := 0.5 T m L := 10m L RB := q 2 RB = 2.5T

L RA := q 2 RA = 2.5T

III.8.

Bng k mt s t hp phm bm ca MathcadHin th e i % Ch gii V cng S Pi C s e S o i Phn trm

Phm bm Ctrl+Shift+Z Ctrl+Shift+P e 1i %

Thao Tc Trn Cc Ca S V WorksheetsPhm bm Ctrl+F4 Ctrl+F6 Ctrl+O Alt+F4 Hin th Ch gii ng Worksheet Qua ca s k tip M Worksheet That- Trang 25 -


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Ctrl+Q F1 F5 F6 F7 F9 Shift+F1 Esc

That M ca s gip M Worksheet Lu Worksheet To Worksheet mi Tnh mt biu thc c chn M hoc thot ca s gip Thot ca s gip

Phm Tt Cho Son ThoPhm bm Enter Delete Ctrl+F5 Shift+F5 Alt+BkSp Ctrl+C Ctrl+V Ctrl+X Ctrl+U Hin th Ch gii Chn mt hng trng Xa hng trng Tm chui t li chui Phc hi li son tho sau cng Copy Dn Ct Chn hp thoi n v

To Php TanPhm bm ! $ & ' ( ) * + , ; < > ?[ \KS. HUNH VNG THU MINH

Hin th !

Ch gii Giai tha Tng dy Tch phnDu ngoc M ngoc ng ngoc Nhn Cng Tch cc i s ca hm s Cho dy s Du tr Nh hn Ln hn o hm cp 1Thnh phn ca vc t hoc ma trn Cn bc hai- Trang 26 -

d

( )

( ) . +, ..

< >d d

GIO TRNH Mathcad


^ | Ctrl+1 Ctrl+3 #Ctrl+4 Ctrl+9 Ctrl+0 Ctrl+8 Ctrl+Ctrl+= Ctrl+6 Ctrl+Shift+4Ctrl+Shift+3 Ctrl+Shift+? Ctrl+\ Ctrl+Enter

T

Ly tha Gi tr tuyt i, nh thc ma trn Php hon chuyn Khng bng Tch mt dyTng cc thnh phn ca vctNh hn hoc bng Ln hn hoc bng Tch c hng Vct ha Bng Trch ct ca ma trn TngTch o hm cp n Cn bc n Xung dng (nu dng tnh qu di)

=

=

d d...

+

Cc Php Ton SymbolicPhm bm Ctrl+I Ctrl+L Ctrl+Shift +A Ctrl+Shift +B Hin th

d

Ch gii Nguyn hm Gii hn

lim lim

+

Gii hn bn phi Gii hn bn tri

lim

Phm To Mt VngPhm bm @ Ctrl+5 Ctrl+7 Ctrl+2 Hin th Ch gii V th trong mt phng V contour V trong ta cc V b mt ma trn- Trang 27 -


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Ctrl+G Ctrl+M Ctrl+ Shift +P Ctrl+ Shift +Z

i k t Roman sang Hylap v ngc li To ma trn hoc vc t Chn k hiu s Pi Chn k hiu v cc

IV. N V O LNG TRONG MATHCADTrong Mathcad n v mc nh l h SI (International System of Units). Mathcad c kh nng tm n v tiu chun khi tnh ton v t ng thay i n v tnh ton. Cho nn khng c g ngc nhin khi bn nh ngha n v ca bin l Tone (tn) th trong qu trnh tnh ton Mathcad t ng chuyn qua n v l Kilogram (kg). Nu bn mun kt qu c th hin bng n v l T, thc hin nh sau: Kch vo kt qu c n v mun iu chnh, s xut hin khung ch nht mu en ngay sau n v. G vo n v mun c th hin. V d:

Kt qu:q := 0.5 T m L := 10m RA = 2.5T T 1000kg .

L RA := q 2

Lu : Trc phi nh ngha:


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CHNG III: MATHCAD VI I S V S HC

CHNG III MATHCAD VI I S V S HCI. TNH TON VI SYMBOLICS T THANH CNG C CHUN

Hnh 3.1. Trnh n Symbolics trn menu bar Symbolics/Evaluate/Symbolically : xut gi tr biu thc di dng k hiu. V d: Tnh (2a-1) + 3a Chn biu thc T thanh cng c chun : nhn Symbolically/Evaluate/Symbolically (hoc nhn Shift + F9). Kt qu : 5a-1 Symbolics/Evaluate/foating Point: xut gi tr biu thc di dng s thc ng. V d: Tnh 1 +1 3

Chn biu thc. Chn Symbolically/Evaluate/Foating Point, xut hin hp thoi Floating Point Evaluation (hnh 3.2).


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2

Trong th Floating Point Precision mc nh l 20, c th thay i tu thch, sau chn OK. Kt qu : 1.33333333333333333333. Symbolics/Evaluate/Complex : xut gi tr biu thc di dng s phc. V d: Tnh 2i + 1

Chn biu thc T thanh cng c chun Kt qu Symbolics/Simplify Symbolics/Expand V d: :

: nhn Symbolics/Evaluate/Complex

: n gin biu thc. : khai trin biu thc c chn.

Symbolics/Factor nhn t. V d:

: khai trin biu thc c chn, phn tch thnh

Symbolics/Collect V d:

: sp xp theo lu tha ca bin.

z2 - xz + x2z2 + 2z -1 cho kt qu (x2+1)z2+(-x+2)z-1 Symbolics/Polynomial Coefficient V d: (1-x)(x2+2) -3x -1 cho kt qu: : tm cc h s ca a thc.

Lu : Sau khi n gin biu thc n s sp xp cc h s theo th t t di ln trn. Symbolics/Variable/Solve V d:KS. HUNH VNG THU MINH Trang - 29 -

: giai phng trnh.

GIO TRNH Mathcad


Symbolics/Variable/Substitute V d:

: tnh biu thc theo biu thc con.

Tnh U2 +U vi U= x+1 Cho kt qu (x-1)2 + x -1 Symbolics/Variable/ Differentiate V d: : tnh o hm.

Symbolics/Variable/Integrate : tnh nguyn hm. V d:

Symbolics/Variable/ Expand to series V d:

: khai trin chui.

Symbolics/Variable/Convert to Partial Fraction : phn tch cc phn thc n gin hn c mu bc nht. V d:


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GIO TRNH Mathcad


II. TNH TON VI SYMBOLICS T THANH CNG C MATH

Hnh 3.3. Bng Symbolics t thanh Math : Symbolics Evaluation V d:

: Symbolics Keyword Evaluation (g biu thc km t kho).: la chn cc iu kin b sung t bng Modifier (hnh 3.4).

Hnh 3.4. Bng Modifier : cho kt qu l s thc vi phn thp phn tu chn. V d:

: cho kt qu l s phc. : to gi thuyt cho bin. : gii phng trnh cho kt qu dng Symbolics.


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GIO TRNH Mathcad


V d:

: n gin mt biu thc. V d:

: tnh mt biu thc theo mt biu thc con. V d:

: phn tch thnh nhn t ca mt biu thc. V d:

: khai trin mt biu thc di dng lu tha, tch, tng. V d:

: trch cc h s ca a thc theo bin la chn. V d:


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GIO TRNH Mathcad


: sp xp a thc theo bin chn. V d:

: khai trin thnh chui Taylor cc hm s. V d:

: phn tch mt biu thc thnh cc tng phn s n gin hn. V d:

: khai trin hm s dng fourier. : khai trin hm s dng laplace. : khai trin dng z- transform ca mt hm s. : bin i ngc dng fourier. : php bin i ngc dng laplace. : php bin i ngc dng z- transform.

III. LM TON TRN SYMBOLICS MENU V MATH PALETTEIII.1. Khai trin biu thc

Mathcad cho php bn khai trin biu thc s hoc ch. V d: Khai trin biu thc Cch 1: Kch chn biu thc mun khai trin. T thanh cng c : nhn Symbolics/Expand. Kt quKS. HUNH VNG THU MINH( 1 + x)4

:

1 + 4 x + 6 x + 4 x + x

2

3

4

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GIO TRNH Mathcad


Lu : Theo mc nh, kt qu khai trin s nm bn di biu thc c khai trin. Nu mun kt qu khai trin nm ngang vi biu thc thc hin theo cch sau: T thanh cng c : nhn Symbolics/Evaluation Style/ Hrizontally, xut hin hp thoi Evaluation Style (hnh 3.5). Th hin du bng nhn (Shift+) hoc nhn Insert/Text Region v g vo du bng (=). Kt qu :( 1 + x)4 2 3 4 = 1 + 4 x + 6 x + 4 x + x

Hnh 3.5. Hp thoi Evaluation Style Cch 2: Kch chn biu thc mun khai trin T thanh Math : kch vo biu tng (hnh 3.3). T bng Symbolics : kch vo nt lnh Kt qu qu. :4

, xut hin bng symbolics

( 1 + x) expand 1 + 4 x + 6 x + 4 x + x

2

3

4

Lu : nu mun thay i biu thc ang tnh th ch c cch 2 l cp nht kt

III. 2.tnh V d:

Rt gn biu thc

Rt gn biu thc (Simplify), tng t nh khai trin biu thc cng c 2 cch2 2 2

a. Rt gn biu thc Kt qu cch 1 Kt qu cch 2 b. Rt gn biu thc

: : :( x + 1)2

sin ( x) + cos ( x)2

sin ( x) + cos ( x)2

=1

sin ( x) + cos ( x) simplify 1

2

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Chn biu thc cn rt gn T bng Symbolics : kch voKS. HUNH VNG THU MINH

GIO TRNH Mathcad

CHNG III: MATHCAD VI I S V S HC( x + 1)2

simplify

Kt qu

:

x+ 1 assume , x > 0

III. 3.

Trc cn thc mu

trc cn thc mu, s dng hm factor. V d:1

Trc cn thc Kt qu cch 1 Kt qu cch 2

: : :

3+ 3+

4+ 1 4+

5

35

= 22

3 3 22

1 11

3 5 + 1 11

2 11

+

1 22 2 11

5 + 1 22 5

1 3+ 4+ 5

factor

3

3 5 +

IV. CC PHP TNH GII HN, O HM V TCH PHNKch chn thanh Calculus t thanh cng c Math (Hnh 3.6)

Hnh 3.6.Thanh Calculus : o hm cp 1 V d: Tnh o hm cp 1 ca hm f(x) = 2x3 + 3x

: o hm cp n V d: Tnh o hm cp 2 ca hm f(x) = 2x3 + 3x

: tnh gii hn V d:

: tnh gii hn bn phi


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V d:

: tnh gii hn bn tri V d:

, V d:

: tnh tch phn gii hn v tch phn suy rng

: tnh tng nhiu s V d:

: tnh tch nhiu s V d:

BI TP CHNG 31. n gin cc biu thc sau:x2 3 4 + 2x 5 x4

2. Khai trin biu thc sau:


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3. n gin biu thc c iu kin: a.

(a 1)2

a2

, iu kin a>1

b.

( x 1) 2 ( x 1) 2 , iu kin x0 8. Tnh gii hn cc hm s sau:


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CHNG IV: VC T V MA TRN

CHNG IVVC T V MA TRNI.I.1.

TO MT VC T V CC PHP TNH VC TTo mt Vc t

Vc t l mt dy sp xp ngay ngn (hay Ma trn ch c mt ct). to mt Vc t trong Mathcad, thc hin theo cc cch sau: Trn thanh menu Trn thanh Math T bn phm : chn Insert/Matrix : nhp vo biu tng : nhn t hp Ctrl+M

Xut hin hp thoi Insert Matrix (hnh3.1).

Hnh 3.1. Hp thoi Insert Matrix Trong khung Rows chn s dng tng ng. Trong khung Columns chn s ct tng ng. Chn OK, xut hin , nhp s cn thit vo s c mt Vc t

mong mun.


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I.2.

Tnh ton vi vcta. Tch ca hai Vc t (Dot product) Tnh v hng ca hai Vc t Kch vo biu tng V d:1 u := 2 3 4 v := 5 6u v = 32

(hnh 3.4), xut hin

Nhp tn hai Vc t mun tnh.

Tnh c hng ca hai Vc t Kch vo biu tng V d: (hnh 3.4), xut hin


b. Giao ca hai Vc t (Cross product) Kch vo biu tngV d:1 u := 2 3 4 v := 5 6 3 u v= 6 3

(hnh 3.4), xut hin


c. Tng ca mt Vc t (vector sum) Kch vo biu tng (hnh 3.4), xut hin Nhp tn Vc t mun tnh. V d:4 v := 5 6

.

v = 15


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I.3.

Tnh kch c ca VctHm length (v) Hm last (v) V d: : cho bit Vc t c bao nhiu phn t. : cho bit th t ca phn t cui cng.

1 v := 2 3 length ( v) = 3 last ( v) = 3

I.4.

To mt bng gi tr ca hm sV d:Cho ham so: low := 1 n := 15 r := low , low r =1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f ( j ) := j + 1 high := 15 low high n1 f ( r) =2 5 10 17 26 37 50 65 82 101 122 145 170 197 226

2

.. high


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V d: To bng gi tr cc khong chia khng theo mt th t no.i := 1 .. 5 xi := 1 1.2 0.5 3.5 2.5 Mi := xi + 2 Mi =3 3.2 2.5 5.5 4.5

Lu : Kt qu ln mn hnh ch th hin ti a 15 phn t. Trng hp ln hn 15 phn t khi kch p vo bng gi tr, xut hin bng tr s s dng thanh trt s thy tt c cc kt qu.

II. TO MT MA TRN V TNH TON VI MA TRNII.1. To mt Ma trn

Thc hin ging nh cch to mt Vc t nu Ma trn c t hn 10 dng v 10 ct hoc thc hin theo cch sau:V V1, 1 2, 1

:= 0 := 3

V V

1, 2 2, 2

:= 1 := 4

V V

1, 3 2, 3

:= 2 := 5 V=

0 1 2 3 4 5

Lu : Mathcad s t gi tr 0 cho tt c cc phn t m bn khng nh ngha. V d:V2, 1

:= 3

V

2, 2

:= 4

V

2, 3

:= 5

V=

0 0 0 3 4 5

Tuy nhin cch trn khng tin, mt nhiu thi gian nhp s liu. Khi Ma trn c nhiu hn 100 phn t, thc hin theo cc cch sau:


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Ni cc mng nh li vi nhau. c t tp tin d liu. Dng bin chy. To bng d liu nhp. V d: To mt Ma trn bng cch dng bin chy.i := 0 .. 3 Xi , j := i +2

j := 0 .. 3 j 2 1 2 5 1.5 2.5 5.5

0 1 X= 4 9

0.5 1.5 4.5

9.5 10 10.5

V d: To mt Ma trn vi cc gi tr ca hm s.f ( x , y) := x + y2 2

- Nhap iem au va iem cuoi cua day bien xlow := 2 ylow := 1 xhigh := 2 yhigh := 2

- Nhap so chia day cac phan t xn := 5 i := 1 .. xnj := 1 .. yn

yn := 6 xind i := xlow + i yind j := ylow + j

xhigh xlow xn 1yhigh ylow yn 1

Mi , j := f xind i , yind j

(

)2.96 1.96 2.96 5.96 5 4 5 7.76 6.76 7.76

1.16 0.16 M = 1.16 4.16 9.16

1.04 1.64 0.04 0.64 1.04 1.64 4.04 4.64

8 10.76

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CHNG IV: VCT V MA TRN

II.2

Hiu chnh Ma trn

II.2.1. Xo ct (hoc hng) ca Ma trn xo mt ct (hoc hng) hay nhiu ct (hoc nhiu hng) ca Ma trn, thc hin nh sau: Kch vo phn t ct (hoc hng) mun xo. T hp thoi Insert Matrix (hnh 3.1) ch r s ct (hng) mun xo. Kch nt Delete. V d: Cho Ma trn sau:

1 3 C := 5 7

2 4 6 8

xo ct u tin ca Ma trn C : ti mc Rows chn gi tr 0, ti mc Columns chn gi tr 1 (hnh 3.2).

Hnh.3.2. Hp thoi Insert Matrix xo dng th hai ca Ma trn C : ti mc Rows chn gi tr 2, ti mc Columns chn gi tr 0 (hnh 3.3).

Hnh 3.3


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II.2.2. Thm ct (hoc hng) vo Ma trn thm mt ct (hoc hng) hay nhiu ct (hoc hng) vo Ma trn, thc hin nh sau: Kch vo phn t trong ct (hoc hng), im chn s nm bn phi (i vi ct) v bn di (i vi hng). G s ct (hoc hng) mun chn vo. Chn Insert. II.3. Tnh ton vi Ma trn s xut hin cc la chn tnh ton

T thanh Math, kch vo biu tng cho Ma trn v c Vc t (hnh 3.4).

Hnh 3.4 a. Subscripts (ch s di) Xc nh tr s di ca Ma trn. Cho Ma trn M. xc nh cc ch s di. Kch vo biu tng1 2 3 M := 4 5 6 7 8 9M M1, 1 2, 1

=1 =4

M M

1, 2 2, 2

=2 =5

M M

1, 3 2, 3

=3 =6

Thay i ch s di ca Ma trn.:= 0

M

1, 1

0 2 3 M = 4 5 6 7 8 91

b. Ma trn nghch o (Inverse) Kch vo biu tng , xut hin Nhp tn Ma trn mun th hin.0 2 3 M := 4 5 6 7 8 91

.

M

1 1 2 2 7 4 = 1 4.667 2.667


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c. Tnh nh thc ca Ma trn (Determinant) Kch vo biu tng , xut hin Nhp tn Ma trn mun tnh nh thc.0 2 3 M := 4 5 6 7 8 9

M =3

d. Trch mt ct t mt Ma trn (Matrix column) Kch vo biu tng , xut hin . Nhp tn Ma trn v ct mun trch ra.0 2 3 M := 4 5 6 7 8 91

M

0 = 4 7

. Ma trn chuyn v (Matrix transpose) Kch vo biu tng , xut hin Nhp tn Ma trn mun tnh.0 2 3 M := 4 5 6 7 8 9 0 4 7 M = 2 5 8 3 6 9T T

III. X L MNGIII.1. Ni cc mng

Hm stack (A,B,C) dng ni hai hay nhiu Ma trn vi nhau theo hng t trn xung di. Hm augment (A,B,C) dng ni hai hay nhiu Ma trn vi nhau theo hng t tri qua phi. V d:

1 7 1 M := 5 8 2 6 9 3

1 2 A := 3 7 4 9

1 2 B := 3 7 4 9


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1 3 4 stack( A , B) = 1 3 4III.2. Tch cc mng

2 7 9 2 7 9

1 7 1 1 2 augment M , A) = 5 8 2 3 7 ( 6 9 3 4 9

Hm submatrix (M,ir,jr,ic,jc) dng tch nh cc mng. Trong : - M l Ma trn. - ir l s dng bt u tch. - ij l s dng kt thc tch. - ic l s ct bt u tch. - jc l s ct kt thc tch. V d:

1 7 1 5 8 2 M := 6 9 3 1 2 3 4 5 5III.3.

4 4 3 3 2 3 4 3

1 7 1 submatrixM , 1 , 2 , 1 , 3) = ( 5 8 2

6 8

Tnh kch c ca Ma trnHm rows (M) Hm cols (M) : cho bit Ma trn c bao nhiu hng. : cho bit Ma trn c bao nhiu ct.

V d:

1 2 3 4 M := 5 6 7 8 9 10 11 12 rows ( M) = 3 cols ( M) = 4

III.4.

Cc hm tnh cc tr ca Ma trn- Trang 46 -


GIO TRNH Mathcad


Hm max(A,B,C) Hm min(A,B,C) V d:

: cho bit phn t ln nht trong cc Ma trn. : cho bit phn t nh nht trong cc Ma trn.

1 2 A := 3 4 5 6

2 3 B := 4 5 6 7

3 4 C := 5 6 7 8

max ( A , B , C) = 8 min ( A , B , C) = 1

III.5.

Hm dng to mt mng miHm matrix (m,n,f)

Trong : - m l s dng ca Ma trn. - n l s ct ca Ma trn. - f l hm s ca hai bin. V d:F ( x , y) := x + y m := 102 2

n := 12

M := matrix m , n , F) (1 1 2 3 4 5 6 7 8 9 10 0 1 4 9 16 25 36 49 64 81 2 1 2 5 10 17 26 37 50 65 82 3 4 5 8 13 20 29 40 53 68 85 4 9 10 13 18 25 34 45 58 73 90 5 16 17 20 25 32 41 52 65 80 6 25 26 29 34 41 50 61 74 7 36 37 40 45 52 61 72 85 8 49 50 53 58 65 74 9 64 65 68 73 80 10 81 82 85 90 97

M=

89 106

85 100 117 98 113 130

89 100 113 128 145

97 106 117 130 145 162


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III.6.

Mt s hm tm kimHm lookup(z,M,N) Hm vlookup(z,M,c)

Hm hlookup(z,M,r) Trong : - z l gi tr ca phn t thuc ct (hoc hng) u tin. - M, N l Ma trn. - c, r l gi tr phn t c tr v t ct (hoc hng) tng ng. V d:

11 M := 6 11

2 7

3 8

4 2

4 10

12 13 14 15

0 N := 6 11

2 1

3

4

4 10

13 4

19 17 14 15

M1 := hlookup( 4 , M , 3) M2 := vlookup( 11 , M , 4) M3 := lookup( 12 , M , N)

14 M1 =

15 14

4 M2 =

M3 = ( 19 )

IV. HIN TH MA TRN V VC TKt qu khi x l s liu Ma trn thng c th hin theo hai dng sau: - Nu mng c t hn 100 phn t, kt qu c hin th di dng Ma trn thng thng. - Nu mng c nhiu hn 100 phn t, kt qu c hin th di dng bng c thanh trt, kch vo thanh trt xem nhng phn t b che khut. Tuy nhin nu mun th hin kt qu di dng bng trong trng hp c t hn 100 phn t, thc hin nh sau: T thanh menu Format (hnh 3.5). Chn th Chn OK. . : chn Format/Result, xut hin hp thoi Result

Ti mc Matrix display style chn Table.


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Hnh 3.5. Hp thoi Result Format V d:

1 Cho Ma tran B := 4 7Ket qua0 1 4 2 6

2 3 5 6 8 9

Tnh

M := B 2

M=

0 1 2

2

8 10 12 14 16 18

V.

THAY I MC NH

Hnh 3.6. Math OptionsKS. HUNH VNG THU MINH - Trang 49 -

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Trong mt Vc t hay Ma trn, phn t u tin trong Mathcad c bt u bng phn t 0. phn t u tin bt u l 1 thc hin theo cch sau: T thanh cng c : chn Math/Options, xut hin hp thoi Math Options (hnh 3.6). Chn th Built-In Variables. Trong mc Text box Array Origin (ORIGIN) chn s 1. Chn OK.


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BI TP CHNG 41. Cho ma trn A v B nh sau:

Tch t ma trn A ra ma trn C

C th ni kt hai ma trn A v B theo th t t trn xung di v t tri qua phi c hay khng? Nu c th xut kt qu nu khng th gii thch? 2. Gii h phng trnh tuyn tnh a v dng Ma trn a.

b.


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CHNG V: CC HM S TRONG MATHCAD

CHNG V CC HM S TRONG MATHCADI. CC HM S TRONG MATHCAD

Mathcad lp sn mt s hm dng trong tnh ton k thut thng dng v chuyn su. c c mt hm s ta c th thc hin theo hai cch sau: T thanh menu T bn phm : chn Insert/Function (hnh5. 1). : g chnh xc tn hm.

Hnh 5.1. Hp thoi Insert Function Sau y s lit k mt s hm thng s dng trong tnh ton k thut:

I.1.

Hm BesselHm Bessel thay i I0(x) K0(x) Hm Airy Ai(x) Bi(x)- Trang 51 -

I1(x) K1(x)

In(m,x) Kn(m,x)


GIO TRNH Mathcad

CHNG V: CC HM S TRONG MATHCAD

Hm Bessel Kelvin Bei(n,x) ber(n,x)

Hm Spherical Bessel is(n,x) ys(n,x) - Trong x l tp hp s thc v khng c th nguyn.

I. 2.

Hm iu kin khng lin tcif(cond,x,y) : tr v x nu cond l TRUE, ngc li tr v y.

(m,n) - Kronecker delta : tr v 1 nu m=n, ngc li tr v 0. sign(x) : tr v 0 nu x=0, tr v 1 nu x>0, tr v -1 vi nhng trng hp cn li. x l s thc. (i,j,k) (x) : hon tt hm s khng i xng Tensor. : hm s bc. Tr v 0 nu x9 : Trm A v Trm B c tng quan, ngc li khng tng quan.


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CHNG IX: MATHCAD NG DNG

CHNG IX MATHCAD NG DNGI. NG DNG TRONG TNH TON KT CU-------------------------------------------------------------------------

I.1. Cho mt dm n gi hai u nh hnh 9.1. Tnh cc phn lc gi ti A v B.P P1

l1

l2

l3

Hnh 9.1 nh ngha:


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------------------------------------


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I.2. Cho dm nh hnh 9.2. Tnh cc phn lc ti gi.q := 1.2T m1

P := 10T

L1 := 5m

L2 := 2m

Hnh 9.2

I.3. Cho mt dm n gi hai u nh hnh 9.2. Tnh v v biu lc ct v moment cho dm.

l

Hnh 9.31. Nhap so lieu l := 10m q := 1.2 T m

2. Tnh toan a. Tnh cac phan lc goi tai A va BRA := q l 2 RB := q l 2

RA

RB


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b.Tnh va ve lc cat tai iem x bat ky tren damx := 0 .. l Q ( x) := RA q x


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I.4. Cho s o ket cau ban ay cng (tnh theo phng phap dam ao) hnh 9.4

Hnh 9.4 Cho cc s liu sau: q=30kG/m ; l=10m ; M1=M2=300kGm Giai:


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II. NG DNG MATHCAD TRONG O C----------------------------------------------------------------------

II.1. Tnh ton b tr tim cu (hnh 9.5)

Hnh 9.5 S liu cho nh sau: x = 200.000m - im khng ch A: A y B = 200.00m x = 378.31m B: B y B = 340.02m


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x = 400.000 m - im cn b tr 1 : 1 y1 = 400.00m xc nh c im cn b tr cn xc nh c gc bng A _ 1 , B _ 1

Phn tnh tnh ton c du bng lnh kho (lock).

II.2. Bnh sai ng chuyen kinh v khep kn


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III. NG DNG TRONG TNH TON THU VN----------------------------------------------------------------------------

III.1.Cho hai Trm Thu vn A v B nm trn cng mt con sng, c s liu nh bng sau:STT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Nm 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 Trm A_M(m3/s.km2) 4.8 4.1 5.3 5.0 6.3 6.0 6.3 3.3 6.2 4.8 7.1 5.5 4.1 9.2 Trm B_M(m3/s.km2) 6.9 7.2 5.9 6.4 6.2 5.3 6.8 8.0 8.7 7.8 8.5 5.6 8.9 6.5 9.5 7.0 -

Yu cu: - Cho bit hai trm A v B c tng quan vi nhau hay khng? - Vit phng trnh tng quan gia 2 trm b sung s liu gia hai trm. - V ng tng quan gia hai trm.


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Gii: 1. Nhp s liu:

2. Tnh ton


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a. Kim tra iu kin tng quan

b. Vit phng trnh tng quan b sung s liu cho trm thiu


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3. V ng thng tng quan


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IV. NG DNG MT S HM TRONG MATHCAD--------------------------------------------------------------------------------

V biu triu


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Vit hm ni suy tm Rn v Ra ca Btng cho trong bng sau:Mc Btng 150 200 250 300 Cng chu nn Rn, kG/cm2 6.5 90 110 130 Cng chu ko Ra, kG/cm2 5 7.5 8.3 10

C nhiu cch ni suy tm Rn v Ra ca Btng, y xin nu ln 2 cch: Cch 1:


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Cch 2:


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V. NG DNG TNH TON CA VAN----------------------------------------------------------

Xc nh v tr t dm chnh


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