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8.1. MathCAD: Math Soft MathCAD.
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8.1.1. MathCAD : ; ; .
. Math ().
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- Calculator () , ;
- Evaluation () ;
- Graph () ;
- Matrix () ;
- Greek ( ) ;
- Calculus () ;
- Symbolic () ;
- Boolean () ;
- Programming ( ) .
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8.1.2. .
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MathCAD . , , , . .
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< Enter > .
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8.1.3. .
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, < >, , . < Ins >.
3 + 5 * 2 = < Enter >
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( , , ..).
3 + 5 < > * 2 = < Enter >
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8.1.4. = 2,2; b = 1,3; c = 4
. (8.1)
=
:=. 2.2 ( ). < Enter >.
b:
. 1.3. .
. 4. < Enter >.
a ^ 3 < > + b <> / c 1 =
3.116.
, :=; . , , , ', _ ∞, .
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8.1.5. . (8.1)?
8.1.6. . , (8.1) ?
8.1.7. . ( ). ?
8.1.8. ( ) (8.1), . ? , , ( ) .
8.1.9. , ( , , ). Log? p?
8.1.10. . , . 0,5 ( All Trigonometric; ). ?
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8.1.11. 
. 3.921.
8.1.
1. , .
2. .
3. = , . = , , .
4. , , .. < >. < Ins >.
5. . , ( ).
6. < Enter > .
7. .
8. , ( ) .
9. , , .
8.2.
f (x) = 2 x + 5 cos2 x 2 (8.1)
[3; 4].
8.2.1. , , .
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f (x) <:> 2 < Shift +6> x < > + cos (x) < Shift +6> 2 < > 2 < Enter >
8.2.2. .
f (3) =. 3.025.
= 4. f () =. 16.136.
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, , ( ), =.
8.2.3. .
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, . ( ). -Y.
x, Y f (x). < Enter >. . , 10 +10. , . .
. X-Y : . . , , . .
8.2.4. . , Zoom Trace.
Zoom, , Zoom . Unzoom. .
Trace, . . Windows.
8.2.5. (8.1) , 0,2.
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t [3; 4] 0,2 :
t = 3, 2.8 <;> 4 < Enter > (; ..).
t = .
, f (t) =. .
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. : = 3, b: = 4, n: = 50. h = 
. t 1: = , + h <;> b. , f (t 1) =. , b n.
8.2.6. .
. t 1, f (t 1). .
, .
g (t 1) = 2 × t 1 × cos (t 1). t 1. f (t 1) g (t 1).
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8.2.7. .
cos x. 
(). cos x x, < > , < Enter >. ? 
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(8.1).
8.2.8. .
r = 2. 
= (6.557). , 2.
8.2.9. .
cos x. . cos x, x. < >, , < Enter >. ?
(8.1).
8.2.10. .
(8.1) .
. b. , < > =. (27.29).
8.2.11. .
MathCAD , .
a x 2+ b x + c =0.
a b , . root (a 1 *x 2+ b 1* x + c*x 2, x) < Enter >. ?
a 2× cos x + b 2× sin x + c =0.
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8.2.12. .
MathCAD , . .
f (x) ,
x 1 = 2. root (f (x 1), x 1) =. (2.211). , .
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root (f (x 1), x 1, 1, 0) =. (0.992).
8.2.13. .
. x 0 <:> 0 ( ). xm <:> maximize (f, x 0) ( ). xm = . f (x), minimize ( ). , x 0 3; 3 .. ? ?
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maximize minimize Solving.
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8.2.14. .
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8.3. .
8.3.1.
z (x, y) = x 2 + y 2 (8.2)
:
z (x, y):= x 2 + y 2
(3D Scatter Plot) . z .
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u (x, y) = 2 x + 3 y + 10.
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; < Shift >, . < Ctrl > / .
8.3.2.
(8.3)
x Î [3; 3], y Î [3; 3].
, , 60 ( , ):
f (x, y):= 
a 1: = 3 b 1:= 3
a 2: = 3 b 2:= 3
N:= 60 i:= 0 <;> N j:= 0 <;> N
h 1:= (b 1 a 1)/ N h 2:= (b 2 a 2)/ N
xi:= a 1 + hx i yj:= a 2 + hy j
fi,j:= f (xi, yj)
( f).
Appearance Fill Surface Colormap. . Solid Color, . . .
8.4. FRAME (), . FRAME 0 9999. , ( , ), .
8.4.1. y = sin (x + t) t.
y = sin x. , sin (x + FRAME).
(View Animate) ( Tools Animation Record MathCAD) .
. . (For Frame): (From) Frame 0; (To) Frame 20; (At: Frames / Sec) 10. (Animate). .
(Play). (Save As). avi MathCAD.
MathCAD, (View Playback) ( Tools Animation Playback). (Open AVI) .
8.4.2. 
.
, FRAME. 0; 10; 10.
8.5. .
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8.5.1. 
(1; 4; 2)
(1; 3; 0).
a:=
( ). ( 3 ´ 1 ). . .
b.
s = a * b s =. 11.
: s 1 =, 
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8.5.2. .
v =, 
. (1; 2; 7).
8.5.3. .
. a. - , =. 4.583.
8.5.4. .
, q .
8.5.5. = 
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<:> (MathCAD ).
(4 ´ 4). .
8.5.6. .
, < > =. 1128.
8.5.7. .
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8.5.8. .
-1 . :
8.5.9. 3.
<: > 3 * A.
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8.5.10. 8.5.8.
D <: > A + C.
D =. ?
8.5.11. - (0; 4; 4; 2).
G <: > A * , . < Enter >.
G =. : (4; 36; 88; 4).
8.5.12. A A -1.
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8.6.
n n :
(8.4)
8.6.1. (8.2) .
: ´ = . , ; - ; - .
1 (, ), ´ = 1 ´ = 1 ´ . - x 1, x 2, , n - x n.
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: x 1 = 0,948, x 2 = 0,94, x 3= 0,255, x 4 = 0,143.
8.6.2. (8.2), lsolve.
lsolve (, ) =
8.6.3. (8.2), .
given() find (). , . , , .
, , , Boolean Equals ( ) Boolean (). .
find, . , .
(8.2) :
x 1: = 0 x 2: = 0 x 3: = x 4: = 0
given
(8.2),
find (x 1, x 2, x 3, x 4) =
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, , find minner.
8.7. . .
:
- simplify ( , , , );
- expand ( , );
- factor ( );
- collect ;
- substitute ( )
- convert to partial fraction .
. , ( ). .
, simplify, . .
sin(2 x), expand, . .
a 2 b 2, factor, , < Enter >. .
96.
cos(x 2 1), substitute, x 2 1, t, < Enter >. .
x 2(y x + y 2)+ x (y 2+ x 2), collect, , ( x), < Enter >.
, y.
8.8. MathCAD (Programming). Add Line , , . , -. - ( ), . .
Add Line . , , , . , Add Line. , , .
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: (if, otherwise), (for), (while).
8.8.1. , . .
. (8.5)
. if. , , , .
f (x):=. Add Line. , if. sin(x), x < 0. 
otherwise. , =, . .
8.8.2. , . .
, (8.6)
g (x):=. Add Line. , (8.5). Add Line, 8.8.1.
8.8.3. .
n 1 n: n! = 123 n.
. for. , ( ) ;
p (n):=. Add Line. , , p, 1. p 1. Add Line, for. i, 1 <;> n. , p, p i. p.
p , .
0 7 1.
k = 7, n:= 0 <;> k, < Enter >.
n =, p (n) =. k, .
8.8.4. , m.
. while. , .
m:= , 100. n:=. Add Line. , , s, 0. Add Line, , n, 1. Add Line. while. s £ m, Add Line. Add Line, , s, s + n. Add Line, , n, n + 1. n 2.
. n = 13.
m .
-8.1. -6.1 8.2. .
-8.2. -6.2 .
-8.3. -6.3.
-8.4. -6.4 .
-8.5. .
| 1. | tg2 x / sin x | a 3 b 3 | sin 4 x |
| 2. | ln(x 5) / ln5 | a 3 + b 3 | tg 3 x |
| 3. | sin(p /3) sin(p /6) | a 4 b 4 | ln(3 x 3) |
| 4. | (cos2(p /6) sin2(p /6)) / sin(p /3) | ln(5 x) + ln(3 x 3) | sin(x + 2) |
| 5. | (a 3 + b 3)/(a + b) | sin(2 x + 3) | cos(x 3) |
| 6. | (a 3 b 3)/(a b) | cos(2 x + 3) | ln(5 x 2) |
| 7. | (a 4 b 4)/(a 2 b 2) | tg(2 x + 3) | cos 3 x |
| 8. | tg2 x (cos2 x sin2 x) | cos2 x sin2 x | sin(2 x + 4) |
| 9. | 2ctg2 x / (cos2 x sin2 x) | a 4 + b 4 | ln(2 x 4) |
| 10. | (a 3 + b 3)/(a 2 a b + b 2) | sin 4 x + sin2 x | x 2 + 3 x 4 |
-8.6.
1. ( ) (F) ( F = 1, 8 + 32).
2. (1 = 400 ).
3. (1 = 2,54 ) .
4. N. 1´ N, 2´ N, , N ´ N.
5. . .
6. , .
7. , R .
8. N 1 r. n = 1 + (n 1) r.
9. N 1 q. n = 1 q n 1.
10. . .
-8.7. .
1. , , . n = 1 q n 1.
2. , , . n = 1 + (n 1) r.
3. , .
4. , .
5. , .
6. , .
7. , .
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