mathcad prirucnik

2

: : Mathcad-a ......3 1: Mathcad- ......................10 2: Mathcad- ..........................11 3: .............................12 4: Mathcad- ...13 5: ..........................................14 6: ...........................................14 7: ..............................16 8: ...................................................17 9: ..............................19 10: ..........................21 11: ................................................24 12: ....................31 13: ......................................32 14: ...............................................35 15: Mathcad- .................................36 .................................................................41

3

MATHCAD

: Mathcad-

Mathcad , , . , Mathcad . Mathcad- , , . , Mathcad . , , :

x=(-B+SQRT(B**2-4*A*C))/(2*A)

spreadsheet :

+(-B1+SQRT(B1*B1-4*A1*C1))/(2*A1)

Mathcad-, :

x b b2 4 a. c.

2 a.

Mathcad- . , , . Mathcad-, . 2D 3D . Mathcad- (Electronic Books) (drag and drop) . , Mathcad . Mathcad- , , , , . . . , , . Mathcad- Worldwide Web-, Mathcad . . Mathcad-

Mathcad-, . . . 1. Mathcad- Mathcad- . , . Mathcad- Insert Function, Insert Function .

4

Insert Function . 15 , Number Format, Displayed Precision . Calculator , = . 4 +, -, *, / .

1.837 10 3.100 35

2.3142353232=

.

log 1347.2( ) sin 35

.. 2.976= Mathcad- . . .

2.3 4.7i( ) 3 e 3 2i 148.613 47.498i= . . . . , Unit Insert, .

2350 km.1 hr. 652.78 m sec

1=

Insert Unit 2. := Calculator ; (:).

a 4

a a 6= , Mathcad .

f x( ) sin x( )xa

f 10( ) 0.218=

4 a :

[Backspace] :

5

3. . 3. .. Matrix - [;] . 2 z 4 . , z=, f(z)= .

z 0 .5, 2.. z

00.51

1.52

f z( )0

3.8353.3662.661.819

exp f z( )( ) z.0

23.15628.95921.44412.326

4. X-Y Plot Graph , [Ctrl]2 ; e x y . y , Mathcad x ! (,) .

6

f x( )

sin x( )

x x,10 0 10

2

0

2

4

5. Mathcad 3D (scatter) . . Graph/3D Scatter Plot Insert, Graph/Surface Plot Insert. Graph .

X Y, Z,

7

X Y, Z,

6. Calculus . , , , .

0

10

n

1n!

=

2.7182818=

0

1x1

1 x2d 0.785=

7. , 3 3 Vector and Matrix ( Matrix Insert), , .

A

4

5

7

5

0

2

1

12

8

, A^-1=.

A 10.074

0.135

0.031

0.117

0.12

0.132

0.184

0.163

0.077

=

, , |, Vector and Matrix .

A 326=

8

8. Mathcad- (root finder) . . .

t 1 . . . Mathcad .

root t2 cosh t( ) t, 1.621= 9. , x

7 1 x 1( ) x6 x5 x4 x3 x2 x 1.

0

xe x

2d 1

2.

x 1 1x

1

212

5.

12

12

5.

Symbolics . , , , , , , , , . 10. Programming Mathcad- : for while , , , . '' '' Mathcad- , , , . :

f x( ) J1 x( ) cos FRAME20

2. .. a 0 b 3.833 xn 17 rn 25 i 0 xn.. j 0 rn.. NthRoot a n, ,( ) estrt a

n 2

estrt 1 1n

estrt. an estrt n 1.

estrt n a while

estrt

(Newton) n- e :

9

rr i ab a

xni.

ss j 2 . j.

rn Xc i j, rr i sin ss j. Yc i j, rr i cos ss j. Zc i j, f rr i sin ss j. NthRoot 7 5, 10 6, 1.476=

11. Mathcad- . , Animate View, FRAME 0 20 -. Animate. - . Mathcad .

Xc Yc, Zc,

'' '' Mathcad- , . Mathcad- : , , .

1. Mathcad-

Mathcad- Mathcad- Mathcad , Mathcad- .

10

, , . Math Symbolics . Mathcad- Help.

. , tool tip :

Calculator

Graph

Vector and Matrix

Evaluation

Calculus

Boolean

Programming

Greek Symbol

Symbolic Keyword . Mathcad . , , spell checking- . , . Tool tip- . :

Resource Center, QuickSheets ('' ''), Mathcad- , , .

11

. , Formatting View. Resource Center

Mathcad- . ,

Mathcad- , , , . -- "auto" , Mathcad . Mathcad "WAIT" . Caps Lock Num Lock , . Mathcad- : ( ) . Mathcad- - , . , , , Mathcad- .

2: Mathcad-

Mathcad- , -, . . . , . . , . , . , , Resource Center-. x 100 x:100 . : -

12

. . . . . , . : , , - , . Regions View. . Mathcad- , . , y2 = 100 y ( Mathcad- -; ). Mathcad y 2 y. , !

y 10 y2 100=

. Cut Edit, Paste Edit . , . , . , , , Cut .

3:

- . : 1+

+ . Mathcad- ('' ''). , . , 2 , (=) . , [Enter], :

, Calculator. Calculator, Math.

+

2 2 4=

13

- 2 2 0=

* 2 2. 4=

/ 22

1=

^ 2 2 4= Mathcad- , , , . , - ["]. , , Mathcad . , . , . , , '''' . , . .

4: Mathcad-

Mathcad- . , . . , File/New, , . , . Formatting . , View/Toolbars/Formatting. , Heading One , , , . , Format Style. , . . , ,

14

Save As File of Type, Template. .mct. , , , . .

5:

. , : age:23

[:] ,

Calculator, Mathcad :=. (" ") Mathcad- . age , : age= age, 23 age , backspace , . [Enter], age= . , Mathcad- . Mathcad- :

age 23 age 10. 230=

, : old age 10. old 230=

( x TROSKOVI ) . [:] , [= ] .

6:

Mathcad- . , : f(x):x^2

15

, . . f x( ) , :

f x( ) x 2 . . . f x( ) .

f 10( ) 100= . . . f x( ) .

x 3 f x( ) 9=

. . . ( ) f x( ) .

a 0 3..

f a( )0149

. . . f x( ) . g y( ) f y( ) 6 g x( ) 15=

, , Mathcad- . , Function Insert ,

. Insert Function -, , .

16

. Mathcad- .

ln 26( ) 3.258=

csc 45 deg.( ) 1 2=

identity 3( )

1

0

0

0

1

0

0

0

1

=

cols identity 6( )( ) 6=

7:

( ): f(x):x+6[Spacebar]*(x^3[Spacebar]-1)

17

[Spacebar],

. , , . [Spacebar] ,

. [Spacebar] , x3

. , -1, x3. f(x):x+6*(x^3-1),

'''' '''' [Spacebar]. , , , . :

: x^2[Spacebar]

x2 , +3[Spacebar] , /5[Enter] ! [Spacebar] +3

x^1/t^2[Spacebar][Spacebar][Spacebar]/3

.

8:

Mathcad- . , :

18

f x( ) x

2 58

x3

.

. 5 , [Spacebar].

.

3 x3 , [Spacebar]. .

. , ; , . :

f x( ) x

2 58

x3

x f x( ) . .

x2 , . .

, . . !

f x( ) x2 58

x 3

5 6 , 5 , 6.

, 8 , [Backspace] , [*].

, [Spacebar] . [\].

12

x. x3 , x 3

1/2[Spacebar]*x. , Undo Edit . , , . Mathcad-. Mathcad

x 1.5

2 x 2. 32

x. 2 8.75=

19

2 x 5( ) 2. 52

x. 2 22.75=

x . . . . , x 2 x 5( ) 2 . x x-5. 2 -2. 2

, -. 3

2 . 3 5.

, . . [Backspace] . [-].

, , :

score 3

resultscore 6 1

2

score 2 3 result 0.583=

score:3[Enter] result:score+6[Spacebar]\+1/2[Spacebar] [Spacebar]/score^2[Spacebar]-3[Enter] result=[Enter]

, Mathcad- .

9:

Mathcad- . , x 0 10, x:0;10 ,

- [;], (..) . Mathcad- . Range Variable

Matrix. . Mathcad [=]

20

. x 0 5.. f x( ) 2 x 5( ) 2. 5

2x. 2

x=

x012345

f(x)=

f x( )52

31.5152.56

10.5

1 ( ), . , x 1 10 0.1, : x:1,1.1;10

, - [;] . , : x:1,1.1;1.8

x 1 1.1, 1.8.. data:-10,-8;0

data 10 8, 0.. n:202,192;102

n 202 192, 102.. ! x=

21

x1

1.11.21.31.41.51.61.71.8

data=

data108642

0

n=

n202192182172162152142132122112102

.

10:

. Mathcad, ,

22

, . Mathcad- . , v , v: Matrix Insert ( matrix Vector and Matrix )

. , 3 1 . Insert. . [Tab]

, .

v3.3

1.2

8

, subscript, ( [ ), Matrix. 0: v[0=

v0 3.3= 1: v[1=

v1 1.2= 2, : v[2=

v2 8= z , v[2,0 , : i:0;2

i 0 2.. v[i=

vi

3.31.28

, . Mathcad- , 0. 0 Mathcad-. , : i:2;5

i 2 5.. greska[i:1

23

greska =

greska (, , ). , , . Mathcad, , . , Mathcad 0. . , :

b 9.7 a 1.1

f v( ) v 3

9 b 2.v. a

:

v3.3

1.2

8 i 0 2..

f vi

1.111.0981.131

. . : f(x):[Ctrl]4x

f x( ) x ,

Vector and Matrix.

v3.3

1.2

8

=

f v( ) 10.1=

Vector and Matrix, :

greska i 1

gresk

0 0 1 1 1 1

=

24

[Shift]8 v w.

[Ctrl]8 v w

| M

[Ctrl]6 M 2< > ( M. , 0) Mathcad . , M :

M7

6

5

9

8

7

1

2

3

cols M( ) 3= rows M( ) 3= max M( ) 9=

eigenvals M( )

11.526

11.463

1.938

=

11:

Mathcad x-y . , , , sin(x), X-Y Plot

Graph, X-Y Plot Insert/Graph. [Enter] ! :

25

0.999982

0.999982

sin x( )

1010 x

10 5 0 5 10

1

0.5

0.5

1

! x. y^2[spacebar]-3*y, @ ( x-y ). Mathcad . :

1. z cos z( ). 2. 1

1 x2

, Mathcad . . , : . , :

f(x):-x^2[Spacebar]+8*x-27 f x( ) x2 8 x. 27

. : x:0;10

x 0 10.. , @ x-y x

f(x) . [Enter].

:

26

f x( )

x

0 5 10

50

40

30

20

10

f x( ) . , x x 0 0.1, 10.. . , , Mathcad . x-y , ( Graph Format) - . - , , , , , , , . x-y . Mathcad- -- , , , , . - .

x 0 0.1, 10..

f x( )

x

0 5 10

50

40

30

20

10

troskovi. Matrix Insert ; 8 1 .

27

-, (a) troskovi () . (a), : i:0;7

i 0 7.. [@] troskovi[i

y , i x . :

. (), , , dan:

2 3 6 8 11

12.5 14 17

troskovi i

dan

1 2 3 5 7 8

10 12

28

: @, troskovi

y , dan

x . :

0 5 10 15

5

10

15

20

"points" . . . , . , , . : . f(x):x^2

f x( ) x 2 . x: [Ctrl]M , - Insert Matrix (, 5 1 ), OK. .

2

3

6

8

11 12.5

14

17

=

troskovi

dan

29

x

2.2

0

3.56

9.9

13 . i:0;4

i 0 4.. @ y x f xi x i. :

f xi

xi

5 0 5 10 15

50

100

150

200

( 1, 2, 3, ..., 10). . . ,

1z

z 2 .

@: 1/z [Spacebar] , z^2 @ [Enter] :

30

1z

z2

z z,

10 5 0 5 10

10

5

5

10

, . . f(x):sin(x)

f x( ) sin x( ) g(t):t^3

g t( ) t3 x:-10,-9.9;10

x 10 9.9, 10.. t:-2,-1.9;2

t 2 1.9, 2.. , @ . , x,t. , f(x),g(t). [Enter]. :

31

f x( )

g t( )

x t,

10 5 0 5 10

10

5

5

10

, --- (,). .

12:

. , Formatting Mathcad- . ( Formatting , , Formatting View.) - . :

x 1 1.1, 10.. , .

f x( ) 2 x 5( ) 2. 52

x. 2

, "" Courier 12-point bold-. Times New Roman 12-point bold italic. f(x).

f x( )

x0 5 10

40

20

0

20

32

, . . : "" .

. Formatting ,

bold, italic, . Text Format. Formatting . , Style Format. , . . , File New Template. , Mathcad ( ) (), . Formatting Equation Format . Mathcad . (highlight) . Properties/Highlight Region Format . , Color Format.

13:

, , Mathcad-. : P:500

P 5000 r:.07

r .07 n:365

n 365 A t , . A(t) A(t):P*(1+r/n)^n*t

A t( ) P 1 rn

n t..

t A(3)=

A 3( ) 6.168 10 3=

33

. Mathcad ( ) 1000 , . . : (A(3)=), Number Format. - Number Format. Exponential Threshold 3 6 ( > 3). Displayed Precision 3 2. OK. A 3( )

A 3( ) 6168.27=

-- ., A 3( ) . , . Number Format. Exponential Threshold . Displayed Precision . OK. Number Format, , , : (, , ) . , , - (), Graph Format. : f(x):sin(x)

f x( ) sin x( ) g(y):cos(y)

g y( ) cos y( ) x:-10,-9.9;10

x 10 9.9, 10.. y:-2,-1.9;2

y 2 1.9, 2..

34

f x( )

g y( )

x y,

10 5 0 5 10

1

0.5

0.5

1

: @ . , x,y . , f(x),g(y). [Enter]. . , X-Y Plot Format. -

Graph/X-Y Plot Format Format.

Traces. trace 1, Color green (). trace 2 Line dadot (). OK. . , . . .

2 1 0 1 2

1

1

. . . . . .

35

2 1 0 1 22

0

2

( ), , , , . Trace Zoom Graph. , , .

14:

Mathcad- . , kilometers km. : r:6370*km

r 6370 km. A(r):4*p[Ctrl]g*r^2

A r( ) 4 . r 2. ( Calculator Greek Symbols.) , : A(r)=

A r( ) 5.099 10 14 m 2=

SI. (hectares), . - Insert Unit. .

4 . r 2. 5.099 10 14 m 2=

4 . r2. 5.099 1010 hectare= Mathcad- , , . Mathcad, Unit Insert.

w 100 joule. w 100 m N=

36

m 10 6 m. smoot 5.23 ft. smoot 1.594 10 6 m= m 6.273 10 7 smoot=

. , (newtons) ( ) . . .

a 10 msec.

F 20 s newton=

seconds. ,

a sec 1.

15: MathCad- ( Mathcad Professional)

. Mathcad- , -, , , .

?

. .

, :

, .

, .

mas 2 k.

F mas a .

37

":". Math Programming

.

"Add Line" ].

( ). , "z"

. ( z . . Mathcad- ":=", . "

38

: . Math Programming

. "If" Shift+]. "if". , boolean . "Add Line" . "otherwise". "otherwise". . :

"if" "otherwise" , "otherwise" .

( ) . : "For" . "While"

. , .

"FOR"

"for" .

"for" "for" . Math Programming

. "for" Ctrl+". "for". "e", . "e", (

, , , ).

"Add Line" . , "while" .

"WHILE"

"while" . . Esc.

39

"while" : "while" . Math Programming

. "while" Ctrl+]. "while". "while", boolean . "Add Line" Programming

. "while", . "Add

Line" . "While" . , "for" .

"BREAK"

"break" .

"break" : "break". Math Programming

. "break" Ctrl+{. "break". Mathcad "break" for while :

1. . 2. .

. , . , continue. "continue" :

40

"continue". Math Programming

. "continue" Ctrl+[. "continue". continue, , ,

.

, . , return.

"return" : "return". Math Programming

. "return" Ctrl+|. "return". "return", . "Return" .

, on error

:

41

"on error". Math Programming

. "on error" Ctrl+'. "on error". "on error", ,

. "on error",

. "Add Line" .

. , .

: :

1. , 2. . : f(n+1) f(n), f(0), f. , , , , . .

:

1.

(1) .

2.

(2) Ctrl + .

Mathcad-, . Mathcad- : ToolTips QuickSheets ('' '') On-line Help - World Wide Web MathSoft

42

. ToolTips , tooltip :

Mathcad- . Resource Center QuickSheets , Mathcad- '' ''-QuickSheets. QuickSheets . 300 QuickSheets. QuickSheets , QuickSheets Resource Center-. On-line Help

on-line Help , Mathcad-, . [F1] , Help Topics Help, Help . - - Mathcad- Help Mathcad- . , , , Mathcad- [Shift][F1] Help . World Wide Web MathSoft , World Wide Web MathSoft Mathcad- , , . Web browser- (. Netscape Navigator, Microsoft Internet Explorer, .) MathSoft- http://www.mathsoft.com/. MathSoft Collaboratory Collaboratory MathSoft- File . . , The Mathcad Treasury, . (Paul R. Lorczak), Mathcad-. Resource Center. Mathcad- , . , , , Mathcad- .

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mathcad prirucnik