1 1 Gnuplot gnuplot Windows gnuplot gp443win32.zip gnuplot binary, contrib, demo, docs, license 5 BUGS, Chang
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- しなつ しばもと
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1 Gnuplot で微分積分 2011 年度前期 数学解析 I 講義資料 ( ) 矢崎成俊 ( 宮崎大学 )
2 1 1 Gnuplot gnuplot Windows gnuplot gp443win32.zip gnuplot binary, contrib, demo, docs, license 5 BUGS, ChangeLog, Copyright, INSTALL, NEWS, README, README.1ST, README.Windows, VERSION (1) (4) (1) [ ] [ ] [ ] (2) [ ] (3) [ ] (4) 3 [ ] binary
3 2 1 Gnuplot wgnuplot.exe Windows gnuplot gnuplot.exe hogehoge.exe README.Windows Windows OS Unix Mac 1.1 Gnuplot wgnuplot.exe Enter G N U P L O T Version 4.4 patchlevel 3 last modified March 2011 System: MS-Windows 32 bit Copyright (C) , 1998, 2004, Thomas Williams, Colin Kelley and many others gnuplot home: faq, bugs, etc: immediate help: plot window: type "help seeking-assistance" type "help" hit h Terminal type set to wxt gnuplot> _ gnuplot gnuplot> _ _
4 1.2 3 gnuplot> exit gnuplot> quit gnuplot> q gnuplot 1.2 you gp-files (C:) you gp-files C:Y=UsersY=youY=DocumentsY=gp-files C:Y=UsersY= Y=DocumentsY=gp-files
5 4 1 Gnuplot C:Y=UsersY=youY=DocumentsY= gnuplot change directory gnuplot> cd C:Y=UsersY=shigeY=DocumentsY=gp-files gnuplot 4 ChDir C:Y=UsersY=youY=DocumentsY=gp-files current working directory print working directory gnuplot> pwd C:Y=UsersY=youY=DocumentsY=gp-files gnuplot> OK 1.3 Gnuplot (plot) y = sin x gnuplot> plot sin(x)
![1.3 Gnuplot 5 x [ 10, 10] y [ 1, 1] x [ 2π, 2π], y [ 2, 2] gnuplot> plot [-2*pi:2*pi] [-2:2] sin(x) gnuplot>](/docs-images/93/112116805/images/6-0.jpg "plot [0:4*pi] sin(x) x [0, 4π] y gnuplot> plot [0:2*pi] [0:1.5] sin(x), x, x-x**3/3!, Y= > x-x**3/3!+x**5/5!")
6 1.3 Gnuplot 5 x [ 10, 10] y [ 1, 1] x [ 2π, 2π], y [ 2, 2] gnuplot> plot [-2*pi:2*pi] [-2:2] sin(x) gnuplot> plot [0:4*pi] sin(x) x [0, 4π] y gnuplot> plot [0:2*pi] [0:1.5] sin(x), x, x-x**3/3!, Y= > x-x**3/3!+x**5/5! Y=
7 6 1 Gnuplot Ctrl + P 1 previous Ctrl P P Ctrl + N next 1 Ctrl N N gnuplot> plot sin(x) cos x Ctrl + P Del Back space sin cos (plot... using... with) data.dat
8 1.3 Gnuplot gnuplot> plot data.dat using 1:2 with lines data.dat 1 x 2 y gnuplot> plot data.dat using 1:2 with linespoint, x*x x 2
9 8 1 Gnuplot using 3:1 data.dat 3 x 1 y gnuplot> plot data.dat using 3:1 w lp, x**(1.0/3.0) w lp with linespoint x 1/3 using x:y 1 x 2 y
10 1.3 Gnuplot 9 gnuploty=demo world.dat gp-files 2 gnuplot> plot world.dat gnuplot> plot world.dat w l w l with lines
11 10 1 Gnuplot gnuplot> plot world.dat w lp gnuplot> plot world.dat w filledcurve w with
12 1.3 Gnuplot 11 (+, -, *, /, **, %,!) +, -, *, / **, (mod) %! gnuplot> plot [0.02:0.2] cos(exp(x**x)/x)/x exp(x cos x ) x x [0.02, 0.2] y = x gnuplot> plot [0.02:0.2] cos(exp(x**x)/x)/x w lp
13 12 1 Gnuplot gnuplot> set samples gnuplot> plot [0.02:0.2] cos(exp(x**x)/x)/x w l
14 1.3 Gnuplot 13 Gnuplot (print) gnuplot> print 123.0/5.0 gnuplot> print gnuplot> print 123/5 gnuplot> print 24! gnuplot> print 10! gnuplot> (set term, set output) 3 (1) jpeg
15 14 1 Gnuplot gnuplot> set terminal jpeg gnuplot> set term jpeg (2) gnuplot> set output world.jpeg (3) gnuplot> plot world.dat w filledcurve gp-files world.jpeg 0KB gnuplot> set output dummy world.jpeg 75KB dummy gnuplot Windows gnuplot> set term windows
16 1.3 Gnuplot 15 gnuplot homepage demo Windows 7.hlp WinHlp32.exe Microsoft(R) Download Center Windows 7 Windows Help (WinHlp32.exe) URL gnuplot Help gnuplot> help gnuplot>? with gnuplot> help with
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18 (load) A reset 1 set term set output 2 set term windows color enhanced x^2 x 2 x_2 x 2 reset x^2 x_2 noenhanced set key 8 (1.1a, a) (l, left) l r (right)
19 18 2 c (center) unset key A 1:gnuplot> reset 2:gnuplot> set term windows color enhanced 3:gnuplot> set size square 4:gnuplot> set samples :gnuplot> a = 1.5 6:gnuplot> set xrange [-a:a] ( a x a) 7:gnuplot> set yrange [-a:a] ( a y a) 8:gnuplot> set key at a*1.1, a l 9:gnuplot> set arrow 1 from -a, 0 to a, 0 head 10:gnuplot> set arrow 2 from 0, -a to 0, a head 11:gnuplot> f(x, n) = x**n f(x, n) = x n 12:gnuplot> set title polynomial functions 13:gnuplot> plot f(x, 1) t x, f(x, 2) t x^2, Y= 14:> f(x, 3) t x^3, f(x, 4) t x^4, Y= 15:> f(x, 5) t x^5, f(x, 6) t x^6, Y= 16:> f(x, 7) t x^7, f(x, 8) t x^8 17:gnuplot> pause -1 18:gnuplot> set title odd degree functions 19:gnuplot> plot f(x, 1) t x, f(x, 3) t x^3, Y= 20:> f(x, 5) t x^5, f(x, 7) t x^7 set arrow 9 1 ( a, 0) (0, a) head 10 2 unset arrow 1 1 unset arrow plot f(x, 1) t x,
20 2.1 (load) 19 plot f(x, 1) t x x 1 x t f(x, 1) pause OK pause A 2
21 20 2 a A 5 a a 6 A programa.gnu gnuplot> load programa.gnu programa.gnu
22 programa.gnu reset set term windows color enhanced set size square set samples a = 1.5 set xrange [-a:a] set yrange [-a:a] set key at a*1.1, a l set arrow 1 from -a, 0 to a, 0 head set arrow 2 from 0, -a to 0, a head f(x, n) = x**n set title polynomial functions plot f(x, 1) t x, f(x, 2) t x^2, Y= f(x, 3) t x^3, f(x, 4) t x^4, Y= f(x, 5) t x^5, f(x, 6) t x^6, Y= f(x, 7) t x^7, f(x, 8) t x^8 pause -1 set title odd degree functions plot f(x, 1) t x, f(x, 3) t x^3, Y= f(x, 5) t x^5, f(x, 7) t x^7 2.2 polynomial functions poly.gnu poly.gnu (1) (3) poly.gnu (1) set grid set arrow lt linetype lw linewidth f(x, n) = x**n A (programa.gnu) odd degree even degree pause -1 y
23 22 2 poly.gnu (1) reset set term windows color enhanced set size square set samples a = 1.5 set xrange [-a:a] set yrange [-a:a] set grid set key at a*1.1, a l set arrow 1 from -a, 0 to a, 0 head back filled lt -1 lw 2 set arrow 2 from 0, -a to 0, a head back filled lt -1 lw 2 f(x, n) = x**n set title polynomial functions plot f(x, 1) t x, f(x, 2) t x^2, f(x, 3) t x^3, Y= f(x, 4) t x^4, f(x, 5) t x^5, f(x, 6) t x^6, Y= f(x, 7) t x^7, f(x, 8) t x^8 set title odd degree functions plot f(x, 1) t x, f(x, 3) t x^3, Y= f(x, 5) t x^5, f(x, 7) t x^7 set title even degree functions plot f(x, 2) t x^2, f(x, 4) t x^4, Y= f(x, 6) t x^6, f(x, 8) t x^8 (poly.gnu (2) )
24 2.2 23
25 24 2 poly.gnu (1) poly.gnu (2) poly.gnu (2) unset key set title degree 1: y=x plot f(x, 1) set title degree 2: y=x^2 plot f(x, 2) set title degree 3: y=x(x^2-1) plot x*(x**2-1) set title degree 4: y=5x^2(x^2-1) plot 5*x**2*(x**2-1) (poly.gnu (3) ) y = x y = x 2
26 poly.gnu (2) poly.gnu (3) poly.gnu (3) set title degree 5: y=10x(x^2-1)(x^2-0.25) plot 10*x*(x**2-1)*(x**2-0.25) set title degree 6: y=15x^2(x^2-1)(x^2-0.25) plot 15*x**2*(x**2-1)*(x**2-0.25)
27 trigonometric functions tri.gnu tri.gnu (1) (4) unset boder boder set boder set xtics -a,pi/2,a x -a a π 2 set ytics -floor(a),1,floor(a) y -floor(a) floor(a) 1 floor(a) floor function [a] [a] = a unset key unset xxx xxx set xxx
28 tri.gnu (1) reset set term windows color enhanced set size square set samples a = 2*pi unset border set xrange [-a:a] set yrange [-a:a] set key at a, a l set xtics -a,pi/2,a set ytics -floor(a),1,floor(a) set grid set arrow 1 from -a, 0 to a, 0 head back filled lt -1 lw 2 set arrow 2 from 0, -a to 0, a head back filled lt -1 lw 2 unset key set title y=sin x plot sin(x) set title y=cos x plot cos(x) y = cos x (tri.gnu (2) )
29 28 2 tri.gnu (2) set title y=tan x plot tan(x) set title trigonometric functions set key at a, a r plot sin(x), cos(x), tan(x) (tri.gnu (3) )
30 tri.gnu (3) set title scaling: sin x vs. sin 2x plot sin(x), sin(2*x) set title scaling: sin x, 2sin x, 3sin x, 4sin x plot sin(x), 2*sin(x), 3*sin(x), 4*sin(x) set title scaling: sin x, (sin x)/2, sin(x/2) plot sin(x), sin(x)/2, sin(x/2) set title scaling: sin x, (sin 2x)/2, 2sin(x/2) plot sin(x), sin(2*x)/2, 2*sin(x/2) (tri.gnu (4) ) x y sin
31 30 2
32 set title sin(1/x) plot sin(1/x) tri.gnu (4) x = 0 t = 1 x sin 1 x = sin t x t 2.4 exponential functions exp.gnu
33 32 2 exp.gnu reset set term windows color enhanced set size square set samples a = 6 b = -1 c = b + 2 * a unset border set xrange [-a:a] set yrange [b:c] set xtics -a,1,a set ytics b,1,c set grid set arrow 1 from -a, 0 to a, 0 head back filled lt -1 lw 2 set arrow 2 from 0, b to 0, c head back filled lt -1 lw 2 unset key set title y=e^x plot exp(x) set title y=e^{-x} plot exp(-x) set key at a, c l set title y=e^x and y=e^{-x} plot exp(x), exp(-x) set title y=0.5^x, 0.6^x, 0.7^x, 0.8^x, 0.9^x, 1^x, 1.1^x plot 0.5**x, 0.6**x, 0.7**x, 0.8**x, 0.9**x, 1**x, 1.1**x set title y=1.1^x, 1.2^x, 1.3^x, 1.4^x, 1.5^x, 2^x, e^x plot 1.1**x, 1.2**x, 1.3**x, 1.4**x, 1.5**x, 2**x, exp(x)
34 2.4 33
35 logarithmic functions log.gnu log.gnu (1), (2) log.gnu (1) reset set term windows color enhanced set size square set samples a = 6 unset border set xrange [-a:a] set yrange [-a:a] set xtics -a,1,a set ytics -a,1,a set grid set arrow 1 from -a, 0 to a, 0 head back filled lt -1 lw 2 set arrow 2 from 0, -a to 0, a head back filled lt -1 lw 2 unset key set title y=e^x plot exp(x) set title y=log x=log_e x plot log(x) set key at a, a l set title y=e^x, y=x, y=log x plot exp(x) t e^x, x, log(x) t log x set key at a, a l set title y=2^x, y=x, y=log_2 x plot 2**x t 2^x, x, log(x)/log(2) t log_2 x (log.gnu (2) )
36 log.gnu (2) set key at a, a l set title y=0.5^x, y=x, y=log_{0.5} x plot 0.5**x t 0.5^x, x, log(x)/log(0.5) t log_{0.5} x set key at a, a l set title Y= y=log_{0.5} x, y=log_{0.9} x, y=log_{1.1} x, y=log_2 x plot log(x)/log(0.5) t log_{0.5} x, Y= log(x)/log(0.9) t log_{0.9} x, Y= log(x)/log(1.1) t log_{1.1} x, Y= log(x)/log(2.0) t log_2 x plot sin x lim x 0 x = 1 ( sin x < x < tan x 0 < x < pi ) 2
37 36 2 set key limit1.gnu reset set term windows color enhanced set size square set samples a = pi/2 unset border set xrange [0:a] set yrange [0:1] set xtics 0,0.2,a set ytics 0,0.2,1 set grid set arrow 1 from 0, 0 to a, 0 head back filled lt -1 lw 2 set arrow 2 from 0, 0 to 0, 1 head back filled lt -1 lw 2 set key left box set title sin x < x < tan x plot sin(x), x, tan(x)
38 lim x ( lim n n n) e e = ( 1 + x) 1 x = e (1) x > 1 x n, α x = n + α n = [x], 0 α < 1 [x] x < [x] + 1, n x < n + 1 gnuplot gnuplot> reset; set term windows color enhanced gnuplot> set samples 10000; set key left nobox gnuplot> plot [1:10][1:10] floor(x), x, floor(x)+1 (2) n x < n n + 1 < 1 x 1 n n + 1 < x n
39 38 2 n x < n + 1 ( ) n ( < x ( < 1 + n + 1 x) 1 ) n+1 n f(x) = g(x) = h(x) = ( ( x [x] + 1 ) x (3) lim n + n + ) [x] ( = ) n n + 1 ( ) [x]+1 ( = ) n+1 [x] n f(x) < g(x) < h(x) ( 1 + n) 1 n = e lim n + ( n + 1 ) n+1 = e ( ) n ( = ) n+1 ( ) 1 e n + 1 n + 1 n = e (4) n + lim x + f(x) = e ( 1 + n) 1 n+1 ( = ) n ( ) e(1 + 0) = e n n (5) lim x + f(x) < g(x) = lim x + h(x) = e ( x) x < h(x) (3), (4) lim g(x) = x + ( 1 + x) 1 x = e (3) (5) gnuplot
40 limit2.gnu reset; set term windows color enhanced set size square; set samples unset border set grid f(x) = ( / ( floor(x) ) )**floor(x) g(x) = ( / x )**x h(x) = ( / floor(x) )**( floor(x) ) a = 5 b = (a - 1) / 10.0 set xtics 1,b set ytics 1,0.5 set xrange [1:a] set yrange [1:5] set arrow 1 from 1, exp(1.0) to a, exp(1.0) nohead set label 1 e at 1-b/4, exp(1.01) r set title Y= lim(1+1/n)^n=e ---> lim(1+1/x)^x=e by squeeze theorem plot f(x) t ( / ( n + 1 ) )^n, n = [ x ], Y= g(x) t ( / x )^x, Y= h(x) t ( / n )^{n + 1}, n = [ x ] a = 21; b = (a - 1) / 10.0 set xtics 1,b; set xrange [1:a] set arrow 1 from 1, exp(1.0) to a, exp(1.01) nohead set label 1 e at 1-b/4, exp(1.01) r replot; a = 51; b = (a - 1) / 10.0 set xtics 1,b; set xrange [1:a] set arrow 1 from 1, exp(1.0) to a, exp(1.01) nohead set label 1 e at 1-b/4, exp(1.01) r replot a = 21 a = 51 a = 5 a replot set label e right 1 at
41 40 2
42 ( lim n ( = e lim 1 + n + n) 1 x = e x + x) lim g(n) lim g(x) n + x + lim sin(πn) = 0 lim sin(πx) n + x gnuplot arcsin x, arccos x, arctan x asin(x), acos(x), atan(x) gnuplot> reset; set term windows color enhanced gnuplot> set samples 10000; set key left nobox gnuplot> set xzeroaxis; set yzeroaxis gnuplot> plot [-1:1][-pi/2:pi] asin(x), acos(x) gnuplot> plot [-10:10][-pi/2:pi/2] atan(x) sinh x, cosh x, tanh x sinh(x), cosh(x), tanh(x) atan(x) tanh(x)
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)
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
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y2=x2(x+1)-001.ps
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di-problem.dvi
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no35.dvi
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数学の基礎訓練I
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PowerPoint プレゼンテーション
準備編 CUI とはコマンドの基本知識 * Graphical User Interface マウスで操作 * Command User Interface キーボードによるコマンド入力 CUI の特長 コンピュータはもともとキーボードだけで使える 今でも GUI でなく CUI で使う ( しか使えない ) アプリがある コマンド ( 命令 ) を打ちさえすればやってくれる 明快 コマンドを勉強すればするほど熟練者になれる
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PowerPoint プレゼンテーション
ファイルシステム 各自自分のファイルシステムは 各自しっかり把握し 整備は自分で行う * 自分のファイルシステムで迷子になる (1) どこにどのファイルがあるのか分からなくなる (2) 今自分はどこで作業しているのか ( つまりカレントディレクトリはどこか ) 分からなくなるのが 実習がうまくできない主な原因のひとつです 迷子になったら Finder で自分のファイルシステムを確認するのが良いでしょう
数値計算
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Microsoft PowerPoint - 14Gnuplot.ppt
Gnuplot との連携 Gnuplot による関数の描画 Gnuplot によるデータのプロット Gnuplot による 3-D グラフの描画 Gnuplot による 3-D データのプロット 今日のポイント グラフ描画ソフト gnuplot を体験してみよう Gnuplot とは グラフ描画専用のフリーウェア Windows 版の名称は wgnuplot インストールはフォルダごとコピーするだけ
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dy + P (x)y = Q(x) (1) dx dy dx = P (x)y + Q(x) P (x), Q(x) dy y dx Q(x) 0 homogeneous dy dx = P (x)y 1 y dy = P (x) dx log y = P (x) dx + C y = C exp
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電気電子数学入門 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/073471 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. i 14 (tool) [ ] IT ( ) PC (EXCEL) HP() 1 1 4 15 3 010 9 ii 1... 1 1.1 1 1.
春期講座 ~ 極限 1 1, 1 2, 1 3, 1 4,, 1 n, n n {a n } n a n α {a n } α {a n } α lim n an = α n a n α α {a n } {a n } {a n } 1. a n = 2 n {a n } 2, 4, 8, 16,
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5 partial differentiation (total) differentiation 5. z = f(x, y) (a, b) A = lim h f(a + h, b) f(a, b) h........................................................... ( ) f(x, y) (a, b) x A (a, b) x (a, b)