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MathCAD 15
2013
2
681.3.06
, . . MathCAD
[] / . . . : , 2013. 114 .
.
2 10.02.13
MathCAD 15.
,
.
.
, ,
.
.
, ..
.
, .. -
. -
.
.
-
.
3
.................................................................................................................. 7
MathCAD ...................................................................... 9
1 Mathcad ................................................................................................... 9
1.1 Mathcad ............................................................................................. 9
1.2 ........................................................................................................ 10
1.3 ........................................................................................... 11
2 , ............ 14
2.1 Mathcad .................................................................................................. 14
2.2 ................................................................... 15
2.3 .......................................................................................... 16
2.4 ....................................................................................... 16
2.5 ....................................................................................... 17
2.6 ............................................................................. 19
2.7 .......................................................................................... 20
2.8 . ....................................................... 22
2.9 ......................................................................................... 22
2.10 . ................................................. 23
2.9 ........................................................................................ 24
3 . ................................................................... 25
3.1 ............................................................................ 25
3.2 ............................................................................................................ 26
4 ............................................................................................ 27
4.1 ........................................................................................ 27
4.2 .......................................................................................... 28
4.3 ................................................................................... 28
4.4 ....................................................................... 29
4.5 ............................................................. 30
4.6 ........................................................................................... 30
4.7 ........................................................... 31
4.8 ....................................................................... 33
4
. ................................................................................................ 34
1 .................................................................................................. 34
1.1 ....................................................................... 34
2.2 ............................................................................. 35
2.3 ........................................................................... 35
2.4 ORIGIN ......................................................................... 36
2.5 .................................................. 36
2.6 .......................................... 38
2.7 ....................................................................................... 39
2.8 ........................................................................... 40
2.9 ......................................................................................... 41
2.9.1 ............................................................................. 41
2.9.2 ................................................................ 41
2.9.3 , ...................................................... 42
2.9.4 , ,
....................................................................................................................... 42
2.9.5 ..................................................................................... 45
.................................................................................................. 46
1 ............................................................................ 46
2 ............................................................................ 46
3 .............................................................................. 47
4 ................................................................................... 49
5 ....................................... 51
5.1 ...................... 52
5.2 ( ) 54
6 ........................................................................... 55
6.1 ................................................................ 55
6.2 Given Find . 56
7 ............................................................... 57
................................................. 58
1 ......................................................... 58
1.1 .............................................................. 60
5
1.2 ................................................................................ 64
1.3 ................................................. 65
3 ........................................................................ 68
3.1 ............................................................. 69
4 ..................................................................................... 70
5 ................................................................................... 71
6 ........................................................................................ 72
7 .................................................................................. 73
8 ......................................................................................... 73
.............................................................. 75
1 .......................................... 75
1.1 ....................................................................................................... 76
1.1.1 .................................................................................... 76
1.1.2 - ....................................................................................... 77
1.2 ............................................................................................................... 79
1.2.1 ...................................................................................... 81
1.2.2 ........ 85
1.3 .......................................................................................... 87
............................................................................ 89
1.1 .............................................................................................. 89
1.1.1 .................................................................................... 89
1.1.2. ..................................................................... 90
1.2 if ........................................................................................... 91
1.3 .................................................................................................. 94
1.3.1 while ................................................................................................... 94
1.3.2 for ....................................................................................................... 96
1.3.3 break, continue, return ..................................................................... 97
1.4 ......................................................... 98
1.5 - ...................................................................................... 98
1.6 ................................................................................................ 99
1.7 ........................................................... 100
2 ............................................................................................................... 103
6
2.1 ............................................................................................ 103
...................................................................................................... 106
1. Mathcad ............................................................. 106
1 .............................................................................................................. 106
2 ................................................................................... 107
3 ...................................................................................................... 107
2. ................................................................. 108
................................................................................................... 114
7
Mathcad -
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1.1 Mathcad
Untitled:1 (:1), -
Normal () Mathcad, -
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of the day ( ) Mathcad Resource ( Mathcad). -
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at startup ( ) Close (-
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1.2
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1 2 3 4 5 6 7 8 9 10
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1. Mathcad.
2. File () , , , -
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5. Insert () .
6. Format () , -
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11
1.3
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12
Formatting ()
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Matrix ( )
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2. [ = ].
x 1 3 20
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y1
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18
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20
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2. (Font),
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System Ms Sans Serif.
2.7
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2. ,
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3.
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22
2.8 .
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23
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This variable is not definited above
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2.10 .
:
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:= 0..5, -
= 0, 1, 2, 3, 4, 5.
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: min, min ..maxx , min , (-
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,
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24
2.9
Mathcad ,
. Mathcad 20 ,
.
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Result Format ( ), Number
Format ( ). :
General ()
.
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Expo-
nential threshold ( -
).
Scientific ()
: 1,22105.
Decimal (-
) : 12,2564.
Engineering () ,
3: 1,22106.
Fraction () :
/ 1
.
(Level of accuracy)
(Use fixed number).
( ) -
( Set as default ( )).
1.3
25
3 .
1. :
2. :
3. :
4. :
5. n- :
n 3
6. :
3.1
1. .
1.1 :
1.2 :
a 23.4 b 78
=a b 101.4 =a b 54.6
=.a b 1.825103 =
a
b0.3
=a 4.837
=b 8.832
=a
1
n2.86
=b
1
n4.273
=ab6.29310
106
x 3.34
=sin( )x 0.197 =cos( )x 0.98
=sec( )x 1.02 =csc( )x 5.073
=tan( )x 0.201 =cot( )x 4.974
26
2. .
2.1 :
2.2 :
3.2
1. 10.
10 -
.
1.1 :
1.2 :
1.3 10:
2.
-
.
2.1 :
2.2 :
2.3 :
x 300 x .xdeg
=sin( )x 0.866 =cos( )x 0.5
=sec( )x 2 =csc( )x 1.155
=tan( )x 1.732 =cot( )x 0.577
x 5.67
=ln( )x 1.735
=log( )x 0.754
x 12.78
b 2
logb( ),b xln( )x
ln( )b
=logb( ),b x 3.676
27
4
4.1
Simplify ()
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:
23 3 21 1 3
9 1 3
x x x
x x
:
1. , -
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2. , -
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3. .
4. .
13 x 3 x
2
9x 1
1 32x
3x
13
3
3 x 3 x2
9 x 1
28
4.2
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:
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4.3
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3 2
2 3 1
2 9 18
x x
x x x
:
1. .
x5
25 x4
250 x3
1250x2
3125x 3125
29
2. .
.
:
124678488
:
1. .
2. .
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4.4
Collect ( ) , -
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:
:
2 3 2 2 32 3 8 6 15 50 10x x x x x x x
:
1. .
2. .
.
x 1( ) 2 x2
2 x 1 x 3( ) x 3( ) x 2( )
23
3 11 347 1361
13 x3
24 x2
8 x 50
30
4.5
-
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.
:
b:
3 2 3( )a b c
:
1. .
2. -
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4.6
Mathcad
:
1. , -
Calculus (), -
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2. lim.
3. lim ,
, .
4. .
a9
3 a6
c2
3 a3
c4
c6
6 a3
c2
3 a6
3 c4
3 a3
3 c2
1
31
5. Mathcad Symbolics Evaluate Symbolical-
ly ( ). Mathcad
, .
.
:
:
2 2lim
3 6
x
xx
:
3. .
4. -
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4.7
Symbolics -
:
1. , -
, ,
. Symbolics Variable Differen-
tiate ( ) Symbol-
ics Variable Integrate ( -
).
2. Calculus () -
.
Symbolics Evaluate Symbolically ( -
).
1
3
32
:
2
(5 3 7)x x dx :
1. .
2. .
.
:
10
3
1
( 3 5)x x dx
:
1. .
2. -
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(=).
:
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cos( )sin
xx
x
x5x2
3x 7
d5 x
3
3
3 x2
2 7 x
1
10
xx3
3x 5
d10773
4 2.693 10
3
33
:
1. .
2. -
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:
1. .
2. Symbolics Variable Convert to
Partial Fraction ( -
- ).
Mathcad ,
.
:
2
3 2
2 3 1
2 9 18
x x
x x x
:
1. .
5.
- .
.
xsin x( )
cos x( )
x
d
dcos x( )
cos x( )
x2
sin x( )
x
1
3 x 3( )
3
x 2
14
3 x 3( )
34
.
1
:
1. , -
, ( 100 ).
2. . ,
.
3. .
1.1
1. , .
2. Vector and Matrix
Toolbar ( ),
Matrix or Vector ( ).
Mathcad Insert Matrix ( )
[Ctrl]+[m].
3. (Rows)
(Columns), .
.
2.1
4. ,
.
. ,
, .
35
2.2
, :
1. . -
.
2. -
[Ctrl]+[m]. ,
.
3. Insert () Delete (),
. , -
1, 0 Insert Delete.
Mathcad -
, ,
.
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[Delete] ( ) Cut -
Mathcad ( ). -
Cut ,
.
Mathcad
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2.3
,
.
Xn Subscript ( ), [ [ ]
( ),
.
( ), -
. :
36
1. .
2. Matrix and Vectors Tool-
bar ( )
Matrix Column
( ).
3. .
2.2
2.4 ORIGIN
-
ORIGIN. ORIGIN=0,
, .
, -
( ) ORIGIN:=l.
ORIGIN . -
Tools Worksheet Options ( -
), Built-in Variables
( ) Array Origin (ORIGIN)
. ORIGIN ,
.
Matrix. ORIGIN
, .
Mathcad ,
, , mean (
) fft ( ). ORIGIN:=l -
, .
2.5
M2
4
3
2
1
0V1
< >M
0 =V12
4
V2< >M
1
=V23
2
37
Mathcad -
:
, :
rows(M) ;
m() min() -
;
, :
cols(M) ;
tr(M) , -
.
, :
last(M) ;
length(M) ;
V
Matrix;
2.3
2.4
2.5
M
2
4
5
1
3
2
n rows( )M =n 3
m cols( )M =m 2
V
4
1
7
SV V =SV 2
ORIGIN 1 V
4
3
1
5
K last( )V
=K 4
38
2.6
2.7
2.8
2.6
-
:
augment(A, ) .
.
2.9
stack(A, ) . -
.
2.10
V
4
3
1
5
n length( )V =n 4
V
1
4
2
1
MV max( )V
MV min( )V
=MV 4
=MV 2
M
2
3
8
4
2
2
1
7
3
=tr( )M 3
M11
1
0
4
5
2M augment( ),M1 M2 =M
1
1
0
4
5
2
2
4
3
3
1
1
M1 1 2 3( )
M2 4 5 6( )M stack M1 M2( ) M
1
4
2
5
3
6
39
submatrix(A, irows, jrows, icols, jcols) ,
. A,
irows jrows, icols jcols.
2.11 ,
2.7
Mathcad . -
, 100
. , -
augment stack.
-
- .
2.12
M
1
6
11
16
21
2
7
12
17
22
3
8
13
18
23
4
9
14
19
24
5
10
15
20
24
M1 submatrixM 1 3 1 3( ) M1
7
12
17
8
13
18
9
14
19
ORIGIN 1
n 5 m 5
i 1 n j 1 m
xi
0.1i yj
0.2j
fi j
sin xi
yj
f
0.02
0.04
0.06
0.08
0.1
0.04
0.08
0.12
0.159
0.199
0.06
0.12
0.179
0.238
0.296
0.08
0.159
0.238
0.315
0.389
0.1
0.199
0.296
0.389
0.479
40
2.8
Mathcad -
:
sort(V) ;
2.13
reverse(V) ;
2.14
csort(M, i)
i- ;
2.15
rsort(, i) -
i- .
2.16
V
5
2
4
1
3
V sort V( ) V
1
2
3
4
5
V
1
2
3
4
5
V reverse V( ) V
5
4
3
2
1
M
3
4
6
4
5
8
5
1
2
6
2
1
M csort M 2( ) M
4
6
3
5
8
4
1
2
5
2
1
6
M
3
4
6
4
5
8
5
1
2
6
2
1
M rsort M 2( ) M
6
2
1
5
1
2
3
4
6
4
5
8
41
2.9
2.9.1
,
, .
:
1. .
2. .
3. Matrix () -
, .
.
( -
), ,
, -
.
2.17
2.9.2
Matrix -
||, :
2.18
V
2
3
1
VTTV =VT 2 3 1( )
M
1
5
9
2
6
10
3
7
11
4
8
12
M MT
M
1
2
3
4
5
6
7
8
9
10
11
12
M2
1
3
2NM M =NM 1
42
2.9.3 ,
, , -
X-1
Matrix.
.
.
Mathcad identity(n),
n .
2.19
2.9.4 , , -
.
A, -
B C, ij j ijc a bi
2.20
M
1
8
2
1
3
5
1
2
4
4
4
9
6
2
6
1
M M1
M
0.223
0.389
0.068
0.055
0.109
0.055
0.021
0.032
0.192
0.404
0.053
0.134
0.035
0.017
0.127
0.07
M1 identity 4( ) M1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
A
2
4
7
8
3
1
5
8
6
B
7
2
1
6
5
7
4
8
7
A B
9
6
8
14
8
8
9
16
13
A B
5
2
6
2
2
6
1
0
1
43
( ). Mathcad-
.
2.21
. -
, .
View Multiplication as (
).
.
,
,
.
,
, (mn) (nk) = (mk) (
).
, ,
.
-
, .
2.22
A
2
4
7
8
3
1
5
8
6
B
7
2
1
6
5
7
4
8
7
A B
35
42
57
87
95
89
107
96
78
A
B
0.306
0.204
0.673
0.796
1.803
2.116
1.449
1.034
1.946
A
1
3
4
1
2
2
1
3
1
1
3
4
3
2
2
3
A A2
A
14
15
21
29
16
17
19
21
18
16
22
28
18
21
26
26
44
, -
.
2.23
,
, 1
n
i ii
UV U V n
, cos( )UV U V .
2.24
, X Y ,
sin( )XY X Y
, X Y .
Matrix X Y ,.
2.25
.
V
1
4
3
V1 V =V1
1
4
3
V
0.5
0.2
0.7
V V10 V
5
2
7
V1
2
3
5
V2
3
2
1
C .V1V2 =C 7
V1
2
3
5
V2 ( )3 2 1 M .V1V2 =M
6
9
15
4
6
10
2
3
5
V1
1
2
3
V2
4
5
6
P V1 V2 =P
3
6
3
45
2.9.5
Mathcad , -
.
. -
:
1. .
2. ( )f M . -
;
3. [ = ].
2.26
Mathcad -
, . , V ,
cos(V)= .
2.27 -
M
8
3
3
4
2
4
2
3
cos M( )
0.924
0.5
0.707
1
0.707
0
1
1
V
0
30
45
60
90
180
cos V deg( )
1
0.866
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6.1
100
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102
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103
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106
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107
2
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Ins
108
2.
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109
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110
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111
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112
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113
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114
1. Mathcad (+ CDROM): , ,
2009 . 384 .
2. Mathcad 11/12/13 . (+ CDROM): . . -
, , 2007 . 960 .
3. Mathcad 12. : ,
, 2005 . 464 .
4. Mathcad 12. (+ CDROM):
, , 2005 . 566 .
5. Mathcad 12: . . , . . ,
, 2005 . 352 .
6. Mathcad 14 . : -
, , 2009 . 512 .
7. Mathcad: ..
, 2006 . 264 .
8. . 1. MathCAD: . . -
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9. Mathcad 12,
MATLAB 7, Maple 9: . . , . . , , 2006
. 496 .
10. Mathcad (+ CDROM): . . -
, , 2004 . 512 .
11. Mathcad. : . .
, , 2005 . 752 .