(R, XLISP-STAT (C, C++, Java, Fortran, Ruby, Perl, Python, Scheme,... Microsoft Office Open Office 1.2 KNOPPIX/Math DVD (1) DVD KNOPPIX/Math DVD Windo
|
|
|
- やすはる いちぞの
- 7 years ago
- Views:
Transcription
1 KNOPPIX/Math KNOPPIX/Math Klaus Knopper KNOPPIX(OS Linux) KNOPPIX/Math Windows KNOPPIX/Math KNOPPIX/Math DVD KNOPPIX/Math DVD KNOPPIX/Math Windows Windows 1.1 KNOPPIX/Math (platex2e, AMS-TeX, AMS-LaTeX, Prosper, Kile (Axiom, Maxima, Risa/Asir) (Scilab, FreeMat, ATLAS, BLAS, LAPACK, Octave) (KSeg, GeoGebra, KidsCindy) (Geomview, Qhull, Surf, Surface Evolver, XaoS, Yorick (GAP (PARI/GP (Singular, Macaulay2 (SnapPea 1
2 (R, XLISP-STAT (C, C++, Java, Fortran, Ruby, Perl, Python, Scheme,... Microsoft Office Open Office 1.2 KNOPPIX/Math DVD (1) DVD KNOPPIX/Math DVD Windows DVD KNOPPIX/Math DVD (2) KNOPPIX Linux (3) Linux KNOPPIX 6.2 (4) ( ) Windows K KNOPPIX DVD CD return key DVD, USB 1.3 KNOPPIX/Math USB Windows USB USB USB K 2
3 USB USB USB 1.4 KNOPPIX/Math Maxima(Mathemtica ) KSeg( ) (1) KNOPPIX/Math (KnmxLauncher) (KNOPPIX-Math-Start) (2) K xmath (KnmxLauncher) (KNOPPIX- Math-Start) xmaxima wxmaxima Math 2 Id (1) Ctrl Alt Delete (2) Id Enter (3) Maxima(wxMaxima) maxima wxmaxima KSeg kseg KSEG(.exe) 3
4 KSeg file Choose Language C apps kseg kseg_ja.qm KSeg KSeg (1) (2) 3 Maxima 3.1 Maxima CD-R win maxima exe ( Windows windows version (maxima exe.exe ) 3.2 Maxima(Windows ) Maxima wxmaxima, xmaxima, maxima (1) wxmaxima maxima wxmaxima (2) (version ) wxmaxima(version /* wxmaxima Maxima Using Lisp GNU Common Lisp (GCL) GCL (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. ; Shift Enter Enter Enter 4
5 ; Shift Enter (3) (%i1) (input) (%o1) (output) %o1 % (4) % Simplify ratsimp(%); ratsimp, trigsimp 3.3(6) (tr) 3.3 Maxima (1) + - * / ( ) Mathematica * (x+1)*(x+2), 2*x^2+3*x*y ^ (2) = : y:(x+1)*(x+2) (3) := f(x):=3*x+1 (4) π %pi x 4 x^4 x**4 sqrt( ) e %e 4! 4! abs( ) inf realpart( ) exp( ) i %i imagpart( ) log( ) sin( ), cos( ), tan( ) asin( ), acos( ), atan( ) sinh( ), cosh( ), tanh( ) 5
6 (5) ev(n*(n+1)/2 n=10) n=10 n*(n+1)/2 float(%pi) %pi 16 fpprec:20; bfloat( %pi ); %pi 20 b sum(i^2 i 3 9 ) 9i=3 i 2 nusum(i^2, i, 1, n) ni=1 i 2 (= n(n + 1)(2n + 1)/6) limit( (1+n)/n, n, inf ) lim n (1 + n)/n (= 1) (6) expand( (x+2)^3 ) factor( x^3-1 ) ratsimp( 1/(x-1)+1/(x+1) ) (rational function) trigsimp(sin(x)^2+cos(x)^2) (trigonometric function) radcan( ) trigreduce( ) trigexpand(sin(x+y)) (7) solve( ) solve([ 1 2,...] [ 1 2,...]) (8) diff( 2*x^2+3*x*y, x ); x 2 diff( 2*x^2+3*x*y, x, 2 ); x taylor( sin(x), x, 0, 5 ) x x = 0 5 (9) integrate( 3*x^2+6*x*y, x ); x integrate( 3*x^2+6*x*y, x, 0, 2 ); x 0 2 romberg( 2*cos(x^2+3*x), x, 1, %pi); x 1 π (10) 1 ode2(,, ) 6
7 %c, %k1, %k2 1. ode2( diff(y, x)=2*y, y, x) 1 ic1(, xval, yval) 2 ic2(, xval, yval, dval) xval, yval, dval 2. ic1(ode2( diff(y, x)=2*y, y, x), x=0, y=y0) 3. ic2(ode2( diff(y,x,2)=y,y,x),x=0,y=y0, diff(y,x)=d0) 4. ode2( diff(y, x)=2*y, y, x) ic1(%, x=0, y=y0) (11) desolve(, ) 1. x (t) = 2x(t) desolve( diff(x(t), t, 2)=2*x(t), x(t)) 2. x (t) = y, y (t) = x(t) desolve([ diff(x(t), t)=y(t), diff(y(t), t)=-x(t)],[x(t),y(t)]) atvalue(y(x), xval, yval)) atvalue( diff(y(x),x), xval, dval)) xval, yval, dval 3. y (x) = y(x) y(0) = 1, y (0) = 0 atvalue(y(x), x=0, 1); atvalue( diff(y(x),x), x=0, 0); desolve( diff(y(x),x,2)=-y(x),y(x)); (11) (x1, y1, z1) [x1, y1, z1] [x1, y1, z1].[x2, y2, z2] x1 y1 z1 x2 y2 z2 matrix([x1, y1, z1],[x2, y2, z2],[x3, y3, z3]) x3, y3 z3 A A A B transpose(a) A^^-1 A.B 7
8 [x1, y1, z1] 1 x1 [x1, y1, z1][1]. A A : matrix([x1, y1, z1],[x2, y2, z2],[x3, y3, z3]) A (1,2) A[1,2] x = x1 x:matrix([x1],[x2]) x2 Mathematica [ ] ( ) % 3.4 Maxima Maxima 2 3 gnuplot 3 gnuplot graph option 2 plot2d(f(x),[x,a,b]) f(x) a x b 3 plot3d(f(x,y),[x,a,b],[y,c,d]) f(x, y) a x b, c y d 3.1 plot2d( [parametric, cos(t), sin(t), [t, 0, 2*%pi], [nticks, 50]] ) γ(t) = (cos(t), sin(t)) 0 t 2π plot3d ([cos(x)*(3 + y*cos(x/2)), sin(x)*(3 + y*cos(x/2)), y*sin(x/2)], [x, -%pi, %pi], [y, -1, 1], [grid, 50, 15]); [grid, x, y ] 3.3 plot3d([cos(t), sin(t),2*t],[t,-%pi,%pi],[s,-1,1],[grid,50,50]); 1 gnuplot graph 2 plot2d, plot3d wxplot2d, wxplot3d wxplotsize wxplotsize 8
9 wxplot2d, wxplot3d wxplotsize:[400,500]; 3 wxmaxima Plot 2D, Plot 3D Format inline wxplot2d, wxplot3d 4 KSeg 4.1 KSeg kseg zip CD-R win kseg zip Windows kseg-0.401(.zip) kseg C Program Files kseg KSEG(.exe) KSeg file Choose Language kseg_ja.qm kseg kseg_help_ja.html 4.2 KSeg (1) 2 (2) (3) (4) (5) (6) A,B,C,... C 1,C 2,... S 1,S 2, KSeg 4.1 (1) KSeg ( ) (2) A 9
10 (3) SHIFT B SHIFT A (4) New/Circle By Center And Point ( / ) A B A B (5) B SHIFT A (6) New/Circle By Center And Point ( / ) B A ( ) (7) SHIFT (8) New/Intersection Points ( / ) (9) A A A SHIFT B 1 3 New/Segment ( / ) A,B 1 (10) KSeg 4.4 (1) Sift (2) BAC BAC Ctrl Z 10
11 View Pan( ) Zoom( ) ( ) Zoom to Fit Original Zoom 100% ( ) ( ) ( ) (/) OK 11
12 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 4.2 (0) (1) (2). A A. (3). A A. (4) 4.3 (0) (1) 3 Shift 3 (2) (3).... (4).... (5).. 12
13 (1) (2) Shift 3 (180 ) (3) (4) : 1 (1) 2 (5) (6) (2) (7) y x (3) (8) (4) (9) OK 4.6 (5) (9) (5) (6) (7) / (8) / (9) OK 4.6 Ctrl Ctrl Ctrl Ctrl 13
14 4.7 (1) AB C (2) A AC C CB 1 P (3) C,P C AB P (1) AB C (2) 2 A,C AC CB (3) AC D CB E (4) 2 1 P (5) 2 C,P AC AC 4.9 (1) 2 A B (2) A B (3) C D (4) CD E (5) CD E CD (6) (5) D 4.7 (construction) 4.10 (1) File/New Construction ( / ) (2) 3 A,B,C 14
15 (3) A,B,C Construction/Make Given ( / ) (Given) (4) AB BC D,E (5) D AB E BC F (6) F A (7) A,B,C Edit/Hide Objects ( / ) A,B,C (8) File/Save as ( / ) (9) File/New Sketch ( / ) 3 3 Play/Untitled ( / ) (.sec) (9) 3 (3) 4.11 (1) File/New Construction ( / ) (2) 3 A,B,C (3) AB BC D,E (4) DE F (5) A,B,C ( ) Construction/Make Given ( / ) (Given) (6) A,D,F ( ) Construction/Recurse ( / ) (7) F,E,C ( ) Construction/Recurse ( / ) (8) 4 A,B,C,F Edit/Hide Objects ( / ) (9) File/Save as ( / ) (.sec) (10) ( File/New Sketch ( / ) ) 3 3 Play ( ) (6)(8) (5) 15
16 5 (1) 2010 KNOPPIX/Math DVD knoppix_v6.2-math-dvd ja.iso (2) Windows win windows PDF KSeg_example.seg,.sec KSeg.html InternetExplorer 6 (1) Maxima 2006 ISBN Maxima Maxima (2) Scilab( ) GNU Octave FreeMat (3) KidsCindy (4) GRAPES (5) TeX 16
17 Maxima (1) 5+7; (2) 3^100; (3) float(%); % (4) fpprec:50;bfloat(sqrt(10)); 50 (5) (3+4*%i)^10; (6) expand(%); (7) factor( ); (8) factor(x^2+5*x+6); (9) ratsimp(1/(x+1)+1/(x-1)); (10) trigsimp(sin(x)^3+sin(x)*cos(x)^2); (a u)(a v) (b u)(b v) (11) x 1 =, x 2 = a b b a x1:sqrt((a-u)*(a-v)/(a-b)); x2:sqrt((b-u)*(b-v)/(b-a)); ratsimp(x1^2/(a-u)+x2^2/(b-u)); (12) plot2d(sin(exp(x)),[x,0,%pi]); x 1 2 a v + x 2 2 b v sqrt( ) : GNU (13) plot2d([parametric,2*cos(t),sin(t),[t,0,2*%pi]]); (14) plot3d(sin(x+sin(y)),[x,-3,3],[y,-3,3]); (15) plot3d([u*sin(t),u*cos(t),t/3],[t,0,10],[u,-1,1]); (16) wxplot3d([u*sin(t),u*cos(t),t/3],[t,0,10],[u,-1,1]); (17) integrate(sin(x),x); (18) integrate(sin(x),x,0,%pi); (19) romberg(sin(x),x,0,%pi); (20) solve(x^3-x^2-x-15=0,x); (21) solve([x+y=1,x-2*y=2],[x,y]); KSEG 1 (1) 4.1(p.9) KSEG (2) (3) (1) 2 17
18 (p.13) 5 4.9(p.14) C (6) (6) (5) AD F (7) D F AF+FC=AF+FD=AD C 7 Bezier (p.15) 8 Deltoid (1) AB O (2) C (3) C,O,A (4) O (5) B D ( DOB = 2 COA) (6) CO (1) C E (7) C CE (8) CD (7) FG (9) CD FG C 9 (1) A B C (2) A (3) D (4) CD E (5) CD E CD (6) (5) D 10 (6) (6) D (7) (5) (6) F (8) D F CF=FD (p.14) 18
19 12 (1) A, B (2) C D (3) D CD (4) (3) D 13 2 (1) A,B AB C (2) AC, BC (3) AC D BC E (4) 2 1 P (5) 2 C,P D,E C AB (1) A, B (2) C D (3) D CD (4) (3) D C Deltoid2 (1) AB O (2) C (3) C,O,A (4) O (5) B D ( DOB = 2 COA) (6) C OC E (7) E EC (8) CD (7) C F (9) CD F C 16 2 P 1, P 2, P 3,..., Q 1, Q 2, Q 3,... P 1, Q 1 P 2, Q 2 P 3, Q 3... (1) (2) 4 A,B,C,D (3) 2 A,C AC (4) C AC ( E ) (5) 19
20 (6) 2 B,D BD (7) D BD ( F ) (8) (9) 2 E,F (10) Shift 4 A,B,C,D (11) (12) Shift 4 C,D,E,F (13) (14) (15) 2 (l, m (16) l 2 A,C (17) m 2 B,D (18) Shift 4 A,B,C,D / 17 KSEG 18 KSEG 19 KSEG 20 20
2011 v (1) Mathematica, Maple (2) MATLAB (3) CabriGeometry II Plus 1
2011 v111 sugahara@ccosaka-kyoikuacjp 1 11 (1) Mathematica, Maple (2) MATLAB (3) CabriGeometry II Plus 1 (1) Maxima http://maximasourceforgenet/ Maxima 2006 ISBN 9784777512010 (2) Scilab( Home Page) http://scilabna-inetjp/
いつでも どこでも スマホで数学! サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行当時のものです.
いつでも どこでも スマホで数学! サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/001201 このサンプルページの内容は, 初版 1 刷発行当時のものです. 0 i Maxima on Android SNS Web Maxima Android Linux, Windows, MacOS
. KNOPPIX cloop, 700MB CD 1.8GB. DVD, KNOPPIX DVD 12GB.,.,,,. *2, KNOPPIX. 2.1 Windows Mac CD/DVD, Windows PC KNOPPIX. Apple Mac,, Mac Intel CPU
KNOPPIX/Math KNOPPIX/Math Project 1 Maxima [1],,,.., KNOPPIX/Math *1. CD/DVD PC,. KNOPPIX/Math/2007 2000, 100. KNOPPIX/Math,,. KNOPPIX/Math.,,., CD/DVD,. USB,. KNOPPIX/Math,. 2 KNOPPIX KNOPPIX/Math KNOPPIX
topics KNOPPIX/Math DVD maxima KSEG GeoGebra Coq 2011 July 17 - Page 1
KNOPPIX/Math ( ) 2011/07/17 topics KNOPPIX/Math DVD maxima KSEG GeoGebra Coq 2011 July 17 - Page 1 (1) 2011 July 17 - Page 2 (2) 2011 July 17 - Page 3 KNOPPIX/Math KNOPPIX: Linux CD/DVD CD/DVD 1 Windows
. UNIX, Linux, KNOPPIX. C,.,., ( 1 ) p. 2
2009 ( 1 ) 2009 ( 1 ) p. 1 . UNIX, Linux, KNOPPIX. C,.,.,. 2009 ( 1 ) p. 2 , +, ( ), ( ), or PC orange2, knxm2008vm, iyokan-6 KNOPPIX/Math (DVD ) 2009 ( 1 ) p. 3 ,. Mathematica (20-30 /1 ), Maple (20 /1
種々の数学ソフトウェア
January 17, 2013 Maple, Maxima, GeoGebra,,, Knoppix/Math Maple,, : Student[Calculus1] : 30 ( 2 ) Maple Doc Maple ( ) cfep, ; ab a*b, x n xˆn x n + x m, xˆn, x n+xm Maple ( ) =, =!= f(x):=xˆ3-3*x+1;
1 1 Gnuplot gnuplot Windows gnuplot gp443win32.zip gnuplot binary, contrib, demo, docs, license 5 BUGS, Chang
Gnuplot で微分積分 2011 年度前期 数学解析 I 講義資料 (2011.6.24) 矢崎成俊 ( 宮崎大学 ) 1 1 Gnuplot gnuplot http://www.gnuplot.info/ Windows gnuplot 2011 6 22 4.4.3 gp443win32.zip gnuplot binary, contrib, demo, docs, license 5
( )
18 10 01 ( ) 1 2018 4 1.1 2018............................... 4 1.2 2018......................... 5 2 2017 7 2.1 2017............................... 7 2.2 2017......................... 8 3 2016 9 3.1 2016...............................
70 : 20 : A B (20 ) (30 ) 50 1
70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................
18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C
8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,
( ) a, b c a 2 + b 2 = c 2. 2 1 2 2 : 2 2 = p q, p, q 2q 2 = p 2. p 2 p 2 2 2 q 2 p, q (QED)
rational number p, p, (q ) q ratio 3.14 = 3 + 1 10 + 4 100 ( ) a, b c a 2 + b 2 = c 2. 2 1 2 2 : 2 2 = p q, p, q 2q 2 = p 2. p 2 p 2 2 2 q 2 p, q (QED) ( a) ( b) a > b > 0 a < nb n A A B B A A, B B A =
DVIOUT-MTT元原
TI-92 -MTT-Mathematics Thinking with Technology MTT ACTIVITY Discussion 1 1 1.1 v t h h = vt 1 2 gt2 (1.1) xy (5, 0) 20m/s [1] Mode Graph Parametric [2] Y= [3] Window [4] Graph 1.1: Discussion 2 Window
D xy D (x, y) z = f(x, y) f D (2 ) (x, y, z) f R z = 1 x 2 y 2 {(x, y); x 2 +y 2 1} x 2 +y 2 +z 2 = 1 1 z (x, y) R 2 z = x 2 y
5 5. 2 D xy D (x, y z = f(x, y f D (2 (x, y, z f R 2 5.. z = x 2 y 2 {(x, y; x 2 +y 2 } x 2 +y 2 +z 2 = z 5.2. (x, y R 2 z = x 2 y + 3 (2,,, (, 3,, 3 (,, 5.3 (. (3 ( (a, b, c A : (x, y, z P : (x, y, x
熊本県数学問題正解
00 y O x Typed by L A TEX ε ( ) (00 ) 5 4 4 ( ) http://www.ocn.ne.jp/ oboetene/plan/. ( ) (009 ) ( ).. http://www.ocn.ne.jp/ oboetene/plan/eng.html 8 i i..................................... ( )0... (
t θ, τ, α, β S(, 0 P sin(θ P θ S x cos(θ SP = θ P (cos(θ, sin(θ sin(θ P t tan(θ θ 0 cos(θ tan(θ = sin(θ cos(θ ( 0t tan(θ
4 5 ( 5 3 9 4 0 5 ( 4 6 7 7 ( 0 8 3 9 ( 8 t θ, τ, α, β S(, 0 P sin(θ P θ S x cos(θ SP = θ P (cos(θ, sin(θ sin(θ P t tan(θ θ 0 cos(θ tan(θ = sin(θ cos(θ ( 0t tan(θ S θ > 0 θ < 0 ( P S(, 0 θ > 0 ( 60 θ
Fortran90/95 [9]! (1 ) " " 5 "Hello!"! 3. (line) Fortran Fortran 1 2 * (1 ) 132 ( ) * 2 ( Fortran ) Fortran ,6 (continuation line) 1
![Fortran90/95 [9]! (1 ) 5 Hello!! 3. (line) Fortran Fortran 1 2 * (1 ) 132 ( ) * 2 ( Fortran ) Fortran ,6 (continuation line) 1](/thumbs/48/24845697.jpg "Fortran90/95 [9]! (1 ) 5 Hello!! 3. (line) Fortran Fortran 1 2 * (1 ) 132 ( ) * 2 ( Fortran ) Fortran ,6 (continuation line) 1")
Fortran90/95 2.1 Fortran 2-1 Hello! 1 program example2_01! end program 2! first test program ( ) 3 implicit none! 4 5 write(*,*) "Hello!"! write Hello! 6 7 stop! 8 end program example2_01 1 program 1!
GraphicsWithPlotFull.nb Plot[{( 1), ( ),...}, {( ), ( ), ( )}] Plot Plot Cos x Sin x, x, 5 Π, 5 Π, AxesLabel x, y x 1 Plot AxesLabel
![GraphicsWithPlotFull.nb Plot[{( 1), ( ),...}, {( ), ( ), ( )}] Plot Plot Cos x Sin x, x, 5 Π, 5 Π, AxesLabel x, y x 1 Plot AxesLabel](/thumbs/81/83602176.jpg "GraphicsWithPlotFull.nb Plot[{( 1), ( ),...}, {( ), ( ), ( )}] Plot Plot Cos x Sin x, x, 5 Π, 5 Π, AxesLabel x, y x 1 Plot AxesLabel")
http://yktlab.cis.k.hosei.ac.jp/wiki/ 1(Plot) f x x x 1 1 x x ( )[( 1)_, ( )_, ( 3)_,...]=( ) Plot Plot f x, x, 5, 3 15 10 5 Plot[( ), {( ), ( ), ( )}] D g x x 3 x 3 Plot f x, g x, x, 10, 8 00 100 10 5
40 6 y mx x, y 0, 0 x 0. x,y 0,0 y x + y x 0 mx x + mx m + m m 7 sin y x, x x sin y x x. x sin y x,y 0,0 x 0. 8 x r cos θ y r sin θ x, y 0, 0, r 0. x,
9.. x + y + 0. x,y, x,y, x r cos θ y r sin θ xy x y x,y 0,0 4. x, y 0, 0, r 0. xy x + y r 0 r cos θ sin θ r cos θ sin θ θ 4 y mx x, y 0, 0 x 0. x,y 0,0 x x + y x 0 x x + mx + m m x r cos θ 5 x, y 0, 0,
2 1 Mathematica Mathematica Mathematica Mathematica Windows Mac *1 1.1 1.1 Mathematica 9-1 Expand[(x + y)^7] (x + y) 7 x y Shift *1 Mathematica 1.12
![2 1 Mathematica Mathematica Mathematica Mathematica Windows Mac *1 1.1 1.1 Mathematica 9-1 Expand[(x + y)^7] (x + y) 7 x y Shift *1 Mathematica 1.12](/thumbs/39/20083158.jpg "2 1 Mathematica Mathematica Mathematica Mathematica Windows Mac *1 1.1 1.1 Mathematica 9-1 Expand[(x + y)^7] (x + y) 7 x y Shift *1 Mathematica 1.12")
Chapter 1 Mathematica Mathematica Mathematica 1.1 Mathematica Mathematica (Wolfram Research) Windows, Mac OS X, Linux OS Mathematica 88 2012 11 9 2 Mathematica 2 1.2 Mathematica Mathematica 2 1 Mathematica
29
9 .,,, 3 () C k k C k C + C + C + + C 8 + C 9 + C k C + C + C + C 3 + C 4 + C 5 + + 45 + + + 5 + + 9 + 4 + 4 + 5 4 C k k k ( + ) 4 C k k ( k) 3 n( ) n n n ( ) n ( ) n 3 ( ) 3 3 3 n 4 ( ) 4 4 4 ( ) n n
II 1 3 2 5 3 7 4 8 5 11 6 13 7 16 8 18 2 1 1. x 2 + xy x y (1 lim (x,y (1,1 x 1 x 3 + y 3 (2 lim (x,y (, x 2 + y 2 x 2 (3 lim (x,y (, x 2 + y 2 xy (4 lim (x,y (, x 2 + y 2 x y (5 lim (x,y (, x + y x 3y
GNUPLOT 28 3 15 UNIX Microsoft-Windows GNUPLOT 4 GNUPLOT 1 GNUPLOT 2 2 3 2.1 UNIX.......................................... 3 2.2 Windows........................................ 4 2.3..................................
sin x
Mathematica 1998 7, 2001 3 Mathematica Mathematica 1 Mathematica 2 2 Mathematica 3 3 4 4 7 5 8 6 10 7 13 8 17 9 18 10 20 11 21 12 23 1 13 23 13.1............................ 24 13.2..........................
, x R, f (x),, df dx : R R,, f : R R, f(x) ( ).,, f (a) d f dx (a), f (a) d3 f dx 3 (a),, f (n) (a) dn f dx n (a), f d f dx, f d3 f dx 3,, f (n) dn f
,,,,.,,,. R f : R R R a R, f(a + ) f(a) lim 0 (), df dx (a) f (a), f(x) x a, f (a), f(x) x a ( ). y f(a + ) y f(x) f(a+) f(a) f(a + ) f(a) f(a) x a 0 a a + x 0 a a + x y y f(x) 0 : 0, f(a+) f(a)., f(x)
(1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10)
2017 12 9 4 1 30 4 10 3 1 30 3 30 2 1 30 2 50 1 1 30 2 10 (1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10) (1) i 23 c 23 0 1 2 3 4 5 6 7 8 9 a b d e f g h i (2) 23 23 (3) 23 ( 23 ) 23 x 1 x 2 23 x
1.3 2 gnuplot> set samples gnuplot> plot sin(x) sin gnuplot> plot [0:6.28] [-1.5:1.5] sin(x) gnuplot> plot [-6.28:6.28] [-1.5:1.5] sin(x),co
![1.3 2 gnuplot> set samples gnuplot> plot sin(x) sin gnuplot> plot [0:6.28] [-1.5:1.5] sin(x) gnuplot> plot [-6.28:6.28] [-1.5:1.5] sin(x),co](/thumbs/91/107022946.jpg "1.3 2 gnuplot> set samples gnuplot> plot sin(x) sin gnuplot> plot [0:6.28] [-1.5:1.5] sin(x) gnuplot> plot [-6.28:6.28] [-1.5:1.5] sin(x),co")
gnuplot 8 gnuplot 1 1.1 gnuplot gnuplot 2D 3D gnuplot ( ) gnuplot UNIX Windows Machintosh Excel gnuplot C 1.2 web gnuplot $ gnuplot gnuplot gnuplot> exit 1 1.3 2 gnuplot> set samples 1024 1024 gnuplot>
i
i 3 4 4 7 5 6 3 ( ).. () 3 () (3) (4) /. 3. 4/3 7. /e 8. a > a, a = /, > a >. () a >, a =, > a > () a > b, a = b, a < b. c c n a n + b n + c n 3c n..... () /3 () + (3) / (4) /4 (5) m > n, a b >, m > n,
Ver ceil floor FunctionGenerator (PTZCameraSony)
RT 2011 9 18 2009 11 15 1 2009 11 20 2009 12 4 1.2 Ver.1.0.2 ceil floor 3.2.1 4 FunctionGenerator 4.1 2009 12 7 4.2 2009 12 18 1.4 - - (PTZCameraSony) 2.2 - - 4.3 - - 2009 12 27 1.1 2011 9 18 OpenRTM-aist-1.0.0
(, Goo Ishikawa, Go-o Ishikawa) ( ) 1
(, Goo Ishikawa, Go-o Ishikawa) ( ) 1 ( ) ( ) ( ) G7( ) ( ) ( ) () ( ) BD = 1 DC CE EA AF FB 0 0 BD DC CE EA AF FB =1 ( ) 2 (geometry) ( ) ( ) 3 (?) (Topology) ( ) DNA ( ) 4 ( ) ( ) 5 ( ) H. 1 : 1+ 5 2
(4) P θ P 3 P O O = θ OP = a n P n OP n = a n {a n } a = θ, a n = a n (n ) {a n } θ a n = ( ) n θ P n O = a a + a 3 + ( ) n a n a a + a 3 + ( ) n a n
3 () 3,,C = a, C = a, C = b, C = θ(0 < θ < π) cos θ = a + (a) b (a) = 5a b 4a b = 5a 4a cos θ b = a 5 4 cos θ a ( b > 0) C C l = a + a + a 5 4 cos θ = a(3 + 5 4 cos θ) C a l = 3 + 5 4 cos θ < cos θ < 4
8 i, III,,,, III,, :!,,,, :!,,,,, 4:!,,,,,,!,,,, OK! 5:!,,,,,,,,,, OK 6:!, 0, 3:!,,,,! 7:!,,,,,, ii,,,,,, ( ),, :, ( ), ( ), :... : 3 ( )...,, () : ( )..., :,,, ( ), (,,, ),, (ϵ δ ), ( ), (ˆ ˆ;),,,,,,!,,,,.,,
.5 z = a + b + c n.6 = a sin t y = b cos t dy d a e e b e + e c e e e + e 3 s36 3 a + y = a, b > b 3 s363.7 y = + 3 y = + 3 s364.8 cos a 3 s365.9 y =,
[ ] IC. r, θ r, θ π, y y = 3 3 = r cos θ r sin θ D D = {, y ; y }, y D r, θ ep y yddy D D 9 s96. d y dt + 3dy + y = cos t dt t = y = e π + e π +. t = π y =.9 s6.3 d y d + dy d + y = y =, dy d = 3 a, b
MathLibre KNOPPIX (next generation) 2012 KNOPPIX/Math MathLibre KNOPPIX , KNOPPIX 6.0, next generation. KNOPPIX/Math KDE,
MathLibre KNOPPIX (next generation) 2012 KNOPPIX/Math MathLibre KNOPPIX 20120514, 20120608 KNOPPIX 60, next generation KNOPPIX/Math 2010 KDE, lxde, 1 KNOPPIX/Math DVD Q KNOPPIX/Math A http://wwwmathkobe-uacjp/openxm/math/dojo,
0.6 A = ( 0 ),. () A. () x n+ = x n+ + x n (n ) {x n }, x, x., (x, x ) = (0, ) e, (x, x ) = (, 0) e, {x n }, T, e, e T A. (3) A n {x n }, (x, x ) = (,
[ ], IC 0. A, B, C (, 0, 0), (0,, 0), (,, ) () CA CB ACBD D () ACB θ cos θ (3) ABC (4) ABC ( 9) ( s090304) 0. 3, O(0, 0, 0), A(,, 3), B( 3,, ),. () AOB () AOB ( 8) ( s8066) 0.3 O xyz, P x Q, OP = P Q =
cpall.dvi
55 7 gnuplot gnuplot Thomas Williams Colin Kelley Unix Windows MacOS gnuplot ( ) ( ) gnuplot gnuplot 7.1 gnuplot gnuplot () PC(Windows MacOS ) gnuplot http://www.gnuplot.info gnuplot 7.2 7.2.1 gnuplot
48 * *2
374-1- 17 2 1 1 B A C A C 48 *2 49-2- 2 176 176 *2 -3- B A A B B C A B A C 1 B C B C 2 B C 94 2 B C 3 1 6 2 8 1 177 C B C C C A D A A B A 7 B C C A 3 C A 187 187 C B 10 AC 187-4- 10 C C B B B B A B 2 BC
OABC OA OC 4, OB, AOB BOC COA 60 OA a OB b OC c () AB AC () ABC D OD ABC OD OA + p AB + q AC p q () OABC 4 f(x) + x ( ), () y f(x) P l 4 () y f(x) l P
4 ( ) ( ) ( ) ( ) 4 5 5 II III A B (0 ) 4, 6, 7 II III A B (0 ) ( ),, 6, 8, 9 II III A B (0 ) ( [ ] ) 5, 0, II A B (90 ) log x x () (a) y x + x (b) y sin (x + ) () (a) (b) (c) (d) 0 e π 0 x x x + dx e
gnuplot gnuplot 1 3 y = x 3 + 3x 2 2 y = sin x sin(x) x*x*x+3*x*x
gnuplot gnuplot y = x + x y = sin x.8 sin(x) 8 7 6 x*x*x+*x*x.6.. -. -. -.6 -.8 - - - - - - - -. - -. - -.. gnuplot gnuplot> set xrange[-.:.] gnuplot> plot x**+*x** y = x x gnuolot> reset gnuplot> plot
gnuplot.dvi
gnuplot gnuplot 1 gnuplot exit 2 10 10 2.1 2 plot x plot sin(x) plot [-20:20] sin(x) plot [-20:20][0.5:1] sin(x), x, cos(x) + - * / ** 5 ** plot 2**x y =2 x sin(x) cos(x) exp(x) e x abs(x) log(x) log10(x)
() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
S I. dy fx x fx y fx + C 3 C vt dy fx 4 x, y dy yt gt + Ct + C dt v e kt xt v e kt + C k x v k + C C xt v k 3 r r + dr e kt S Sr πr dt d v } dt k e kt
S I. x yx y y, y,. F x, y, y, y,, y n http://ayapin.film.s.dendai.ac.jp/~matuda n /TeX/lecture.html PDF PS yx.................................... 3.3.................... 9.4................5..............
1 28 6 12 7 1 7.1...................................... 2 7.1.1............................... 2 7.1.2........................... 2 7.2...................................... 3 7.3...................................
211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,
IA 2013 : :10722 : 2 : :2 :761 :1 (23-27) : : ( / ) (1 /, ) / e.g. (Taylar ) e x = 1 + x + x xn n! +... sin x = x x3 6 + x5 x2n+1 + (
IA 2013 : :10722 : 2 : :2 :761 :1 23-27) : : 1 1.1 / ) 1 /, ) / e.g. Taylar ) e x = 1 + x + x2 2 +... + xn n! +... sin x = x x3 6 + x5 x2n+1 + 1)n 5! 2n + 1)! 2 2.1 = 1 e.g. 0 = 0.00..., π = 3.14..., 1
1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C
0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,
2.2 Sage I 11 factor Sage Sage exit quit 1 sage : exit 2 Exiting Sage ( CPU time 0m0.06s, Wall time 2m8.71 s). 2.2 Sage Python Sage 1. Sage.sage 2. sa
I 2017 11 1 SageMath SageMath( Sage ) Sage Python Sage Python Sage Maxima Maxima Sage Sage Sage Linux, Mac, Windows *1 2 Sage Sage 4 1. ( sage CUI) 2. Sage ( sage.sage ) 3. Sage ( notebook() ) 4. Sage
I I / 68
2013.07.04 I 2013 3 I 2013.07.04 1 / 68 I 2013.07.04 2 / 68 I 2013.07.04 3 / 68 heat1.f90 heat2.f90 /tmp/130704/heat2.f90 I 2013.07.04 4 / 68 diff heat1.f90 heat2.f90!! heat2. f 9 0! c m > NGRID! c nmax
7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6
26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7
di-problem.dvi
005/05/05 by. I : : : : : : : : : : : : : : : : : : : : : : : : :. II : : : : : : : : : : : : : : : : : : : : : : : : : 3 3. III : : : : : : : : : : : : : : : : : : : : : : : : 4 4. : : : : : : : : : :
Chap10.dvi
=0. f = 2 +3 { 2 +3 0 2 f = 1 =0 { sin 0 3 f = 1 =0 2 sin 1 0 4 f = 0 =0 { 1 0 5 f = 0 =0 f 3 2 lim = lim 0 0 0 =0 =0. f 0 = 0. 2 =0. 3 4 f 1 lim 0 0 = lim 0 sin 2 cos 1 = lim 0 2 sin = lim =0 0 2 =0.
2009 IA 5 I 22, 23, 24, 25, 26, (1) Arcsin 1 ( 2 (4) Arccos 1 ) 2 3 (2) Arcsin( 1) (3) Arccos 2 (5) Arctan 1 (6) Arctan ( 3 ) 3 2. n (1) ta
009 IA 5 I, 3, 4, 5, 6, 7 6 3. () Arcsin ( (4) Arccos ) 3 () Arcsin( ) (3) Arccos (5) Arctan (6) Arctan ( 3 ) 3. n () tan x (nπ π/, nπ + π/) f n (x) f n (x) fn (x) Arctan x () sin x [nπ π/, nπ +π/] g n
untitled
COM 6 20040920 (Mathematica-1) iijima COM 6 Mathematica (iijima@ae.keio.ac.jp) 1 COM 6 20040920 (Mathematica-1) iijima 1. Mathematica 1.1 1.2 1.3 1.4 2 COM 6 20040920 (Mathematica-1) iijima 1.1 3 COM 6
1 8, : 8.1 1, 2 z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = n i=1 a ii x 2 i + i<j 2a ij x i x j = ( x, A x), f =
1 8, : 8.1 1, z = ax + by + c ax by + z c = a b +1 x y z c = 0, (0, 0, c), n = ( a, b, 1). f = a ii x i + i
Excel ではじめる数値解析 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
Excel ではじめる数値解析 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009631 このサンプルページの内容は, 初版 1 刷発行時のものです. Excel URL http://www.morikita.co.jp/books/mid/009631 i Microsoft Windows
/02/18
3 09/0/8 i III,,,, III,?,,,,,,,,,,,,,,,,,,,,?,?,,,,,,,,,,,,,,!!!,? 3,,,, ii,,,!,,,, OK! :!,,,, :!,,,,,, 3:!,, 4:!,,,, 5:!,,! 7:!,,,,, 8:!,! 9:!,,,,,,,,, ( ),, :, ( ), ( ), 6:!,,, :... : 3 ( )... iii,,
1 1 3 ABCD ABD AC BD E E BD 1 : 2 (1) AB = AD =, AB AD = (2) AE = AB + (3) A F AD AE 2 = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD 1 1
ABCD ABD AC BD E E BD : () AB = AD =, AB AD = () AE = AB + () A F AD AE = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD AB + AD AB + 7 9 AD AB + AD AB + 9 7 4 9 AD () AB sin π = AB = ABD AD
*3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i i r 3r + 4i 1 i 1 i *4 1 i 9 i 1 1 i i 3 9 +
1 2 IT 1 *1 1 2 3 π i 1i 2i 3i πi i 2 1 *2 2 + 3 + 4i π ei 3 4 4 2 2 *1 *2 x 2 + 1 = x 2 + x + 1 = 2 3 1 2 2 2 2 *3 i 9 (1,) i (i,) (1,) 9 (i,) i i 2 1 ( 1, ) (1,) 18 2 i, 2 i 1 2 1 2 2 1 i r 3r + 4i 1
4 4 4 a b c d a b A c d A a da ad bce O E O n A n O ad bc a d n A n O 5 {a n } S n a k n a n + k S n a a n+ S n n S n n log x x {xy } x, y x + y 7 fx
4 4 5 4 I II III A B C, 5 7 I II A B,, 8, 9 I II A B O A,, Bb, b, Cc, c, c b c b b c c c OA BC P BC OP BC P AP BC n f n x xn e x! e n! n f n x f n x f n x f k x k 4 e > f n x dx k k! fx sin x cos x tan
num2.dvi
kanenko@mbk.nifty.com http://kanenko.a.la9.jp/ 16 32...... h 0 h = ε () 0 ( ) 0 1 IEEE754 (ieee754.c Kerosoft Ltd.!) 1 2 : OS! : WindowsXP ( ) : X Window xcalc.. (,.) C double 10,??? 3 :, ( ) : BASIC,
高等学校学習指導要領解説 数学編
5 10 15 20 25 30 35 5 1 1 10 1 1 2 4 16 15 18 18 18 19 19 20 19 19 20 1 20 2 22 25 3 23 4 24 5 26 28 28 30 28 28 1 28 2 30 3 31 35 4 33 5 34 36 36 36 40 36 1 36 2 39 3 41 4 42 45 45 45 46 5 1 46 2 48 3
I A A441 : April 21, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka ) Google
I4 - : April, 4 Version :. Kwhir, Tomoki TA (Kondo, Hirotk) Google http://www.mth.ngoy-u.c.jp/~kwhir/courses/4s-biseki.html pdf 4 4 4 4 8 e 5 5 9 etc. 5 6 6 6 9 n etc. 6 6 6 3 6 3 7 7 etc 7 4 7 7 8 5 59
No2 4 y =sinx (5) y = p sin(2x +3) (6) y = 1 tan(3x 2) (7) y =cos 2 (4x +5) (8) y = cos x 1+sinx 5 (1) y =sinx cos x 6 f(x) = sin(sin x) f 0 (π) (2) y
No1 1 (1) 2 f(x) =1+x + x 2 + + x n, g(x) = 1 (n +1)xn + nx n+1 (1 x) 2 x 6= 1 f 0 (x) =g(x) y = f(x)g(x) y 0 = f 0 (x)g(x)+f(x)g 0 (x) 3 (1) y = x2 x +1 x (2) y = 1 g(x) y0 = g0 (x) {g(x)} 2 (2) y = µ
1 B64653 1 1 3.1....................................... 3.......................... 3..1.............................. 4................................ 4..3.............................. 5..4..............................
2009 I 2 II III 14, 15, α β α β l 0 l l l l γ (1) γ = αβ (2) α β n n cos 2k n n π sin 2k n π k=1 k=1 3. a 0, a 1,..., a n α a
009 I II III 4, 5, 6 4 30. 0 α β α β l 0 l l l l γ ) γ αβ ) α β. n n cos k n n π sin k n π k k 3. a 0, a,..., a n α a 0 + a x + a x + + a n x n 0 ᾱ 4. [a, b] f y fx) y x 5. ) Arcsin 4) Arccos ) ) Arcsin
S I. dy fx x fx y fx + C 3 C dy fx 4 x, y dy v C xt y C v e kt k > xt yt gt [ v dt dt v e kt xt v e kt + C k x v + C C k xt v k 3 r r + dr e kt S dt d
S I.. http://ayapin.film.s.dendai.ac.jp/~matuda /TeX/lecture.html PDF PS.................................... 3.3.................... 9.4................5.............. 3 5. Laplace................. 5....
入試の軌跡
4 y O x 4 Typed by L A TEX ε ) ) ) 6 4 ) 4 75 ) http://kumamoto.s.xrea.com/plan/.. PDF) Ctrl +L) Ctrl +) Ctrl + Ctrl + ) ) Alt + ) Alt + ) ESC. http://kumamoto.s.xrea.com/nyusi/kumadai kiseki ri i.pdf
(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y
[ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)
( ) kadai4, kadai4.zip.,. 3 cos x [ π, π] Python. ( 100 ), x cos x ( ). (, ). def print cos(): print cos()
![( ) kadai4, kadai4.zip.,. 3 cos x [ π, π] Python. ( 100 ), x cos x ( ). (, ). def print cos(): print cos()](/thumbs/91/105030926.jpg "( ) kadai4, kadai4.zip.,. 3 cos x [ π, π] Python. ( 100 ), x cos x ( ). (, ). def print cos(): print cos()")
4 2010.6 1 :, HP.. HP 4 (, PGM/PPM )., python,,, 2, kadai4,.,,, ( )., ( ) N, exn.py ( 3 ex3.py ). N 3.., ( )., ( ) N, (exn.txt).. 1 ( ) kadai4, kadai4.zip.,. 3 cos x [ π, π] Python. ( 100 ), x cos x (
I, II 1, A = A 4 : 6 = max{ A, } A A 10 10%
1 2006.4.17. A 3-312 tel: 092-726-4774, e-mail: hara@math.kyushu-u.ac.jp, http://www.math.kyushu-u.ac.jp/ hara/lectures/lectures-j.html Office hours: B A I ɛ-δ ɛ-δ 1. 2. A 1. 1. 2. 3. 4. 5. 2. ɛ-δ 1. ɛ-n
I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin. sin. sin + π si
I 8 No. : No. : No. : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No. : I No. sin cos sine, cosine : trigonometric function π : π =.4 : n =, ±, ±, sin + nπ = sin cos + nπ = cos sin = sin : cos = cos :. sin.
ｽﾗｲﾄﾞ ﾀｲﾄﾙなし
AHP Analytic Hierarchy Process X4 X X4 X4 X4 a b c d AHP 00 ad4 6 2 a b c a b c a b c d 5.5 2 d d a b 5 a c.5 ad 2 6 3 a b a b c d 5.5 2 0.25 c.5 d a a b c d 5.5 2 a a b c d 5.5 2 b c 0.25.5 b c 0.2 2/3
chap1.dvi
1 1 007 1 e iθ = cos θ + isin θ 1) θ = π e iπ + 1 = 0 1 ) 3 11 f 0 r 1 1 ) k f k = 1 + r) k f 0 f k k = 01) f k+1 = 1 + r)f k ) f k+1 f k = rf k 3) 1 ) ) ) 1+r/)f 0 1 1 + r/) f 0 = 1 + r + r /4)f 0 1 f
all.dvi
fortran 1996 4 18 2007 6 11 2012 11 12 1 3 1.1..................................... 3 1.2.............................. 3 2 fortran I 5 2.1 write................................ 5 2.2.................................
I 1
I 1 1 1.1 1. 3 m = 3 1 7 µm. cm = 1 4 km 3. 1 m = 1 1 5 cm 4. 5 cm 3 = 5 1 15 km 3 5. 1 = 36 6. 1 = 8.64 1 4 7. 1 = 3.15 1 7 1 =3 1 7 1 3 π 1. 1. 1 m + 1 cm = 1.1 m. 1 hr + 64 sec = 1 4 sec 3. 3. 1 5 kg
さくらの個別指導 ( さくら教育研究所 ) A a 1 a 2 a 3 a n {a n } a 1 a n n n 1 n n 0 a n = 1 n 1 n n O n {a n } n a n α {a n } α {a
... A a a a 3 a n {a n } a a n n 3 n n n 0 a n = n n n O 3 4 5 6 n {a n } n a n α {a n } α {a n } α α {a n } a n n a n α a n = α n n 0 n = 0 3 4. ()..0.00 + (0.) n () 0. 0.0 0.00 ( 0.) n 0 0 c c c c c
1/1 lim f(x, y) (x,y) (a,b) ( ) ( ) lim limf(x, y) lim lim f(x, y) x a y b y b x a ( ) ( ) xy x lim lim lim lim x y x y x + y y x x + y x x lim x x 1
1/5 ( ) Taylor ( 7.1) (x, y) f(x, y) f(x, y) x + y, xy, e x y,... 1 R {(x, y) x, y R} f(x, y) x y,xy e y log x,... R {(x, y, z) (x, y),z f(x, y)} R 3 z 1 (x + y ) z ax + by + c x 1 z ax + by + c y x +
(2000 )
(000) < > = = = (BC 67» BC 1) 3.14 10 (= ) 18 ( 00 ) ( ¼"½ '"½ &) ¼ 18 ¼ 0 ¼ =3:141596535897933846 ¼ 1 5cm ` ¼ = ` 5 = ` 10 () ` =10¼ (cm) (1) 3cm () r () () (1) r () r 1 4 (3) r, 60 ± 1 < > µ AB ` µ ±
sin cos No. sine, cosine : trigonometric function π : π = 3.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin : odd cos = cos : even.
08 No. : No. : No.3 : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No.0 : No. : sin cos No. sine, cosine : trigonometric function π : π = 3.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin
1 MS-Windows Maxima. MS-Windows UNIX MacOS X.,MS-Windows2000. MS-Windows XP Vista., Maxima CD-ROM,MS-Windows Maxima,,,. 2 Maxima Maxima,,Maxima. URI h
1 MS-Windows Maxima. MS-Windows UNIX MacOS X.,MS-Windows2000. MS-Windows XP Vista., Maxima CD-ROM,MS-Windows Maxima,,,. 2 Maxima Maxima,,Maxima. URI http://sourceforge.net/project/maxima/. 1 Firefox. Internet
13 Student Software TI-Nspire CX CAS TI Web TI-Nspire CX CAS Student Software ( ) 1 Student Software 37 Student Software Nspire Nspire Nspir
13 Student Software TI-Nspire CX CAS TI Web TI-Nspire CX CAS Student Software ( ) 1 Student Software 37 Student Software 37.1 37.1 Nspire Nspire Nspire 37.1: Student Software 13 2 13 Student Software esc
I No. sin cos sine, cosine : trigonometric function π : π =.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin : odd cos = cos : even.
I 0 No. : No. : No. : No.4 : No.5 : No.6 : No.7 : No.8 : No.9 : No.0 : I No. sin cos sine, cosine : trigonometric function π : π =.4 : n = 0, ±, ±, sin + nπ = sin cos + nπ = cos : parity sin = sin : odd
No δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i x j δx j (5) δs 2
No.2 1 2 2 δs δs = r + δr r = δr (3) δs δs = r r = δr + u(r + δr, t) u(r, t) (4) δr = (δx, δy, δz) u i (r + δr, t) u i (r, t) = u i δx j (5) δs 2 = δx i δx i + 2 u i δx i δx j = δs 2 + 2s ij δx i δx j
数学の基礎訓練I
I 9 6 13 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 3 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............
II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )
II 214-1 : October 2, 214 Version : 1.1 Kawahira, Tomoki TA (Kondo, Hirotaka ) http://www.math.nagoya-u.ac.jp/~kawahira/courses/14w-biseki.html pdf 1 2 1 9 1 16 1 23 1 3 11 6 11 13 11 2 11 27 12 4 12 11
vol.31_H1-H4.ai
http://www.jmdp.or.jp/ http://www.donorsnet.jp/ CONTENTS 29 8,715 Vol. 31 2 3 ac ad bc bd ab cd 4 Point! Point! Point! 5 Point! Point! 6 7 314 611 122 4 125 2 72 2 102 3 2 260 312 0 3 14 3 14 18 14 60
W u = u(x, t) u tt = a 2 u xx, a > 0 (1) D := {(x, t) : 0 x l, t 0} u (0, t) = 0, u (l, t) = 0, t 0 (2)
3 215 4 27 1 1 u u(x, t) u tt a 2 u xx, a > (1) D : {(x, t) : x, t } u (, t), u (, t), t (2) u(x, ) f(x), u(x, ) t 2, x (3) u(x, t) X(x)T (t) u (1) 1 T (t) a 2 T (t) X (x) X(x) α (2) T (t) αa 2 T (t) (4)
.....................................................................
............ / /.......................................... ..................................................................... CADSUPER FX FX FX FX FX FX DWG/DXF FX FX FX FX 1-1 CADSUPER FX CADSUPER
I
I 6 4 10 1 1 1.1............... 1 1................ 1 1.3.................... 1.4............... 1.4.1.............. 1.4................. 1.4.3........... 3 1.4.4.. 3 1.5.......... 3 1.5.1..............
０４年度LS民法Ⅰ教材改訂版.PDF
?? A AB A B C AB A B A B A B A A B A 98 A B A B A B A B B A A B AB AB A B A BB A B A B A B A B A B A AB A B B A B AB A A C AB A C A A B A B B A B A B B A B A B B A B A B A B A B A B A B A B
fx-3650P_fx-3950P_J
SA1109-E J fx-3650p fx-3950p http://edu.casio.jp RCA500002-001V04 AB2 Mode
combine: combine(exp1 ) collect: collect(exp1,x) convert: convert(exp1,opt ) > convert(sin(x),exp); > convert(sinh(x),exp); > convert(exp(i*x),trig);
1 Maple exp Maple 1.1 1.1.1 solve( ), diff( ), int( ), 1: simplify: lhs, rhs: subs: expand: numer, denom: assume: factor: coeff: assuming: normal: nops, op assign: combine: about: collect: anames( user
. sinh x sinh x) = e x e x = ex e x = sinh x 3) y = cosh x, y = sinh x y = e x, y = e x 6 sinhx) coshx) 4 y-axis x-axis : y = cosh x, y = s
. 00 3 9 [] sinh x = ex e x, cosh x = ex + e x ) sinh cosh 4 hyperbolic) hyperbola) = 3 cosh x cosh x) = e x + e x = cosh x ) . sinh x sinh x) = e x e x = ex e x = sinh x 3) y = cosh x, y = sinh x y =
2 (1) a = ( 2, 2), b = (1, 2), c = (4, 4) c = l a + k b l, k (2) a = (3, 5) (1) (4, 4) = l( 2, 2) + k(1, 2), (4, 4) = ( 2l + k, 2l 2k) 2l + k = 4, 2l
ABCDEF a = AB, b = a b (1) AC (3) CD (2) AD (4) CE AF B C a A D b F E (1) AC = AB + BC = AB + AO = AB + ( AB + AF) = a + ( a + b) = 2 a + b (2) AD = 2 AO = 2( AB + AF) = 2( a + b) (3) CD = AF = b (4) CE
[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s
![[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s](/thumbs/94/118579915.jpg "[ ] 0.1 lim x 0 e 3x 1 x IC ( 11) ( s114901) 0.2 (1) y = e 2x (x 2 + 1) (2) y = x/(x 2 + 1) 0.3 dx (1) 1 4x 2 (2) e x sin 2xdx (3) sin 2 xdx ( 11) ( s")
[ ]. lim e 3 IC ) s49). y = e + ) ) y = / + ).3 d 4 ) e sin d 3) sin d ) s49) s493).4 z = y z z y s494).5 + y = 4 =.6 s495) dy = 3e ) d dy d = y s496).7 lim ) lim e s49).8 y = e sin ) y = sin e 3) y =
ORIGINAL TEXT I II A B 1 4 13 21 27 44 54 64 84 98 113 126 138 146 165 175 181 188 198 213 225 234 244 261 268 273 2 281 I II A B 292 3 I II A B c 1 1 (1) x 2 + 4xy + 4y 2 x 2y 2 (2) 8x 2 + 16xy + 6y 2
1 6 2011 3 2011 3 7 1 2 1.1....................................... 2 1.2................................. 3 1.3............................................. 4 6 2.1................................................