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| LastUpdate 6/22/2024 |
| My first encounter with computers was during a university lecture. It
was a lecture on how to write a programing language called "Fortran".
I remember punching holes in a peace of paper tape and letting a big computer
read the program I created. In my first year as a teacher , I encountered a computer called "NEC-PC9801" at the school where I worked. As a strage medium , I inserted a 5-inch floppy disk , which I think is quite large , into the main unit. By the way , the strage medium of the personal computer I purchased for home use was a casstte tape. It wasn't just for personal computers. It was for cassette tape recorders that are still around today for listening to and memorizing music. The boot program is also included in this cassette tape , and it takes about 5 minutes for the computer to start up. At that time , computers were machines for numerical processing and could not process mathematical formulas. However , computers now calculate not only numbers , but also formulas. If you use formula manipulation software , "organize formulas" , "expand" , "factorize" , "solve linear equation" , "solve quadratic equations" , "solve cubic equations" , "solve quartic equations" , " differentiate" , and "Integration" is easy for you to do. Three-dimensional graphs can be easily drawn using Maxima. By dragging the graph , you can freely change the viewing direction of the graph. Typical formula manipulation software includes (1) "Mathematica" , (2) "Maple" , and (3) "Maxima". While (1) , (2) are expensive , ranging from 200,000 yen to 300,000 yen , (3) "Maxima" is free software, so it is free. In addition , the source code of "Maxima "is open to the public (open source) , and all kinds of people around the world volunteer to participate in its development. "Maxima" is written in a programming language called "LISP". In addition , "wxMaxima 0.8.7"was used for the following examples. |
| 【Example 1】 Draw a graph of a 3D explicit function. ［Mexican hat］ |
［１］Function expression  （－３π≦ｘ≦３π）（－３π≦ｙ≦３π）［２］Input formula plot3d(sin(sqrt(x^2+y^2))/sqrt(x^2+y^2),[x,-3*%pi,3*%pi],[y,-3*%pi,3*%pi],[plot_format,gnuplot],[grid,50,50]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 2】 Draw a graph of a 3D explicit function. ［Caldera shape］ |
［１］Function expression  （－２≦ｘ≦２）（－２≦ｙ≦２）［２］Input formula plot3d(exp(-(x^2+y^2)/2)*(x^2+y^2)/(2*%pi),[x,-2,2],[y,-2,2],[plot_format,gnuplot],[grid,50,50]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 3】 Draw a graph of a 3D explicit function. ［A slightly sunken saddle shape］ |
［１］Function expression  （－２≦ｘ≦２）（－２≦ｙ≦２）［２］Input formula plot3d(3*exp(-(x^2+y^2))*(2*x^2+y^2),[x,-2,2],[y,-2,2],[plot_format,gnuplot],[grid,50,50]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 4】 Draw a wireframe graph of a 3D implicit function. ［Sphere］ |
［１］Function expression  （－１≦ｘ≦１）（－１≦ｙ≦１）（－１≦ｚ≦１）［２］Input formula draw3d(implicit(x^2+y^2+z^2=1,x,-1,1,y,-1,1,z,-1,1)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 5】 Draw a graph of a 3D implicit function with hidden surface processing. ［Sphere］ |
［１］Function expression （－１≦ｘ≦１）（－１≦ｙ≦１）（－１≦ｚ≦１）［２］Input formula draw3d(enhanced3d=true,implicit(x^2+y^2+z^2=1,x,-1,1,y,-1,1,z,-1,1)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 6】 Draw a graph of a 3D implicit function with hidden surface processing. ［Hollow drum］ |
［１］Function expression  （－２≦ｘ≦２）（－２≦ｙ≦２）（－２≦ｚ≦２）［２］Input formula draw3d(enhanced3d=true,implicit(x^2+y^2-z^2=1,x,-2,2,y,-2,2,z,-2,2)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 7】 Draw a graph of a 3D implicit function with hidden surface processing. ［Sewer pipe joint］ |
［１］Function expression  （－１≦ｘ≦１）（－１≦ｙ≦１）（－１≦ｚ≦１）［２］Input formula draw3d(enhanced3d=true,implicit((x^2-1)^2+(y^2-1)^2+(z^2-1)^2=1.5, x,-1,1,y,-1,1,z,-1,1)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 8】 Draw a graph of a 3D implicit function with hidden surface processing. ［a cell with nucleus in the center］ |
［１］Function expression ｃｏｓ(ｘ＋φｙ)＋ｃｏｓ(ｘ－φｙ) ＋ｃｏｓ(ｙ＋φｚ)＋ｃｏｓ(ｙ－φｚ)＋ｃｏｓ(ｚ＋φｘ)＋ｃｏｓ(ｚ－φｘ)＝２ （However , φ represents the golden ratio.） ［２］Input formula draw3d(enhanced3d=true,implicit(cos(x+%phi*y)+cos(x-%phi*y)+cos(y+%phi*z) +cos(y-%phi*z)+cos(z+%phi*x)+cos(z-%phi*x)=2,x,-4,4,y,-4,4,z,-4,4)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 9】 Draw a graph of a 3D parameter. ［Sphere］ |
［１］Function expression ｘ＝ｃｏｓｓ・ｃｏｓｔ ｙ＝ｃｏｓｓ・ｓｉｎｔ ｚ＝ｓｉｎｓ （０≦ｓ≦２π） （０≦ｔ≦π） ［２］Input formula plot3d([cos(s)*cos(t),cos(s)*sin(t),sin(s)],[s,0,2*%pi],[t,0,%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 10】 Draw a graph of a 3D parameter. ［Donut shape（torus）］ |
［１］Function expression ｘ＝(５＋２ｃｏｓｓ)ｃｏｓｔ ｙ＝(５＋２ｃｏｓｓ)ｓｉｎｔ ｚ＝２ｓｉｎｓ （０≦ｓ≦２π） （０≦ｔ≦２π） ［２］Input formula plot3d([(5+2*cos(s))*cos(t),(5+2*cos(s))*sin(t),2*sin(s)],[s,0,2*%pi],[t,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 11】 Draw a graph of a 3D parameter ［Spring type］ |
［１］Function expression ｘ＝(５＋ｃｏｓｓ)ｃｏｓｔ ｙ＝(５＋ｃｏｓｓ)ｓｉｎｔ ｚ＝ｓｉｎｓ＋０．６ｔ （０≦ｓ≦２π） （０≦ｔ≦７π） ［２］Input formula plot3d([(5+cos(s))*cos(t),(5+cos(s))*sin(t),sin(s)+0.6*t],[s,0,2*%pi],[t,0,7*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 12】 Draw a graph of a 3D parameter. ［Mobius strip］ |
［１］Function expression    （－π≦ｓ≦π） （－１≦ｔ≦１）［２］Input formula plot3d([cos(s)*(3+t*cos(s/2)),sin(s)*(3+t*cos(s/2)),t*sin(s/2)],[s,0-%pi,%pi],[t,-1,1]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 13】 Draw a graph of a 3D parameter. ［Klein's jar］ |
［１］Function expression    （－π≦ｓ≦π） （－π≦ｔ≦π） ［２］Input formula plot3d([5*cos(s)*(cos(s/2)*cos(t)+sin(s/2)*sin(2*t)+3)-10, -5*sin(s)*(cos(s/2)*cos(t)+sin(s/2)*sin(2*t)+3.0),5*(-sin(s/2)*cos(t)+cos(s/2)*sin(2*t))], [s,-%pi,%pi],[t,-%pi,%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example14】 Draw a graph of a 2D explicit function. ［Quadratic function］ |
［１］Function expression  （－２≦ｘ≦２）［２］Input formula plot2d(3*x^2-1,[x,-2,2]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 15】 Draw a graph of a 2D explicit function. ［Expotential・Trigonometric function］ |
［１］Function expression  （０≦ｘ≦２０）［２］Input formula plot2d(exp(x)*sin(7*x),[x,0,20]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 16】 Draw a graph of a 2D explicit function. ［Draw multiple graphs simultaneously］ |
［１］Function expression ｙ＝ｓｉｎｘ、ｙ＝ｓｉｎ２ｘ、ｙ＝ｓｉｎ３ｘ （０≦ｘ≦２π） ［２］Input formula plot2d([sin(x),sin(2*x),sin(3*x)],[x,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 17】 Draw a graph of a 2D implicit function. ［Circle］ |
［１］Function expression  ［２］Input formula implicit_plot(x^2+y^2=1,[x,-2,2],[y,-2,2]); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(implicitplot)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 18】 Draw a graph of a 2D implicit function. ［Four leaf clover］ |
［１］Function expression  ［２］Input formula implicit_plot((x^2+y^2)^4-(x^2-y^2)^2=0,[x,-2,2],[y,-2,2]); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(implicitplot)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 19】 Draw a graph of a 2D implicit function. ［Circle and Four leaf clover］ |
［１］Function expression ［２］Input formula plot2d([x^2+y^2=1,(x^2+y^2)^4-(x^2-y^2)^2=0],[x,-2,2],[y,-2,2]); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(implicitplot)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 20】 Draw a graph of a 2D parameter. ［∞ shape］ |
［１］Function expression ｘ＝ｃｏｓｔ ｙ＝ｓｉｎ２ｔ （０≦ｔ≦２π） １００ divisions ［２］Input formula plot2d([parametric,cos(t),sin(2*t)],[t,0,2*%pi],[nticks,100]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 21】 Draw a graph of a 2D parameter. ［Chrysanthemum petal shape］ |
［１］Function expression ｘ＝４ｓｉｎ４ｔｃｏｓｔ ｙ＝４ｓｉｎ４ｔｓｉｎｔ （０≦ｔ≦２π） ４００ divisions ［２］Input formula plot2d([parametric,4*sin(4*t)*cos(t),4*sin(4*t)*sin(t)],[t,0,2*%pi],[nticks,400]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 22】 Draw a graph of a 2D parameter. ［Swirl shape］ |
［１］Function expression ｘ＝ｔｃｏｓｔ  (500 divisions)ｙ＝ｔｓｉｎｔ ［２］Input formula plot2d([parametric,t*cos(t),t*sin(t)],[t,0,35*%pi/2],[nticks,500]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 23】 Draw a graph of a 2D parameter. ［Heart shape］ |
［１］Function expression ｘ＝(１＋ｃｏｓｔ)ｃｏｓｔ ｙ＝(１＋ｃｏｓｔ)ｓｉｎｔ （０≦ｔ≦２π） １００ divisions ［２］Input formula plot2d([parametric,(1+cos(t))*cos(t),(1+cos(t))*sin(t)],[t,0,2*%pi],[nticks,100]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 24】 Draw a wireframe graph of a 3D implicit function. ［ellipsoid］ |
［１］Function expression  ［２］Input formula draw3d(implicit(x^2/1^2+y^2/2^2+z^2/3^2=1,x,-1,1,y,-2,2,z,-3,3)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 25】 Draw a wireframe graph of a 3D implicit function. ［Single leaf hyperbola］ |
［１］Function expression  ［２］Input formula draw3d(implicit(x^2/1^2+y^2/2^2-z^2/3^2=1,x,-7,7,y,-7,7,z,-7,7)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 26】 Draw a wireframe graph of a 3D implicit function. ［Bilobal hyperbola］ |
［１］Function expression  ［２］Input formula draw3d(implicit(x^2/1^2-y^2/2^2-z^2/3^2=1,x,-2,2,y,-4,4,z,-8,8)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 27】 Draw a wireframe graph of a 3D implicit function. ［Elliptical paraboloid］ |
［１］Function expression  ［２］Input formula draw3d(implicit(x^2/1^2+y^2/2^2=1/20*z,x,-1,1,y,-2,2,z,0,20)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 28】 Draw a wireframe graph of a 3D implicit function. ［Hyperbolic paraboloid］ |
［１］Function expression  ［２］Input formula draw3d(implicit(x^2/1^2-y^2/2^2=1/2*z,x,-2,2,y,-3,3,z,-4,4)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 29】 Draw a wireframe graph of a 3D implicit function. ［Elliptical cylinder］ |
［１］Function expression  ［２］Input formula draw3d(implicit(x^2/1^2+y^2/2^2=1,x,-2,2,y,-2,2,z,-10,10)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 30】 Draw a wireframe graph of a 3D implicit function. ［Hyperbolic column］ |
［１］Function expression  ［２］Input formula draw3d(implicit(x^2/2^2-y^2/3^2=1,x,-10,10,y,-10,10,z,-20,20)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 31】 Draw a wireframe graph of a 3D implicit function. ［Parabolic column］ |
［１］Function expression  ［２］Input formula draw3d(implicit(x^2=y,x,-5,5,y,0,25,z,-20,20)); ［３］Drawing result  ＜How to draw a graph＞ First , input "load(draw)" and press the Shift key and Enter key at the same time to load the package. Next , as in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 32】 Draw a graph of a 2D explicit function. ［Make it easier to see by specifying the range of y values］ |
［１］Function expression  ［２］Input formula plot2d((x^3+2*x^2-4*x-3)/(x+1),[x,-3,3],[y,-10,10]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 33】 Draw a graph of a 2D explicit function. ［Display multiple graphs simultaneously］ |
［１］Function expression  ［２］Input formula plot2d([exp(-2*x),exp(x),1],[x,-2,2],[y,0,10]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 34】 Draw a graph of a 2D explicit function. ［Find the number of real solutions to an equation］ |
［１］Equation  ［２］Input formula plot2d([x/8,cos(x)],[x,-15,15],[y,-2,2]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. Since there are 5 intersections , we know that the equation has 5 real solutions. |
| 【Example 35】 Draw a graph of a 2D parameter. ［Specify the number of divisions］ |
［１］Function expression  ０≦ｔ≦２π［２］Input formula plot2d([parametric,3*cos(t)+cos(13*t),3*sin(t)+sin(13*t)],[t,0,2*%pi],[nticks,300]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 36】 Draw a graph of a 2D parameter. ［Lissajous curve］ |
［１］Function expression  ［２］Input formula plot2d([parametric,cos(7*t),sin(4*t)],[t,0,2*%pi],[nticks,300]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 37】 Draw a graph of a 2D parameter. ［Bernoulli's lemniscate curve］ |
［１］Function expression  ［２］Input formula plot2d([parametric,cos(t)/(1+sin(t)^2),sin(t)*cos(t)/(1+sin(t)^2)],[t,0,2*%pi],[nticks,300]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 38】 Draw a graph of a 3D explicit function. ［Do not specify the number of devisions］ |
［１］Function expression  ［２］Input formula plot3d(exp(-sqrt(x^2+y^2)/2)*cos(%pi*sqrt(x^2+y^2)),[x,-4,4],[y,-4,4]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 39】 Draw a graph of a 3D explicit function. ［Shark minimal surface］ |
［１］Function expression  ［２］Input formula plot3d(log(cos(x)/cos(y)),[x,-%pi/2,%pi/2],[y,-%pi/2,%pi/2]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 40】 Draw a graph of a 3D explicit function. ［Define and draw a function］ |
［１］Function expression  （０＜ｘ≦２，０＜ｙ≦２）［２］Input formula u(a,x,y,p,q,r):=a*(p*x^(-r)+q*y^(-r))^(-1/r); plot3d(u(2,x,y,2,3,2),[x,0.01,2],[y,0.01,2]); ［３］Drawing result  ＜How to draw a graph＞ First , enter the first line of the above input express in half-width , and press the Shift key and Enter key at the same time. Next , enter the second line in half-width and press the Shift key and Enter key at the same time. |
| 【Example 41】 Draw a graph of a 3D parameter. ［Torus］ |
［１］Function expression  ０≦ｓ≦２π、０≦ｔ≦２π ［２］Input formula plot3d([cos(s)*(3+cos(t)),sin(s)*(3+cos(t)),sin(t)],[s,0,2*%pi],[t,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 42】 Draw a graph of a 3D parameter. ［Asteroidal sphere］ |
［１］Function expression  ０≦ｓ≦２π、０≦ｔ≦２π ［２］Input formula plot3d([cos(s)^3*cos(t)^3,sin(s)^3*cos(t)^3,sin(t)^3],[s,0,2*%pi],[t,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 43】 Draw a graph of a 3D parameter. ［Henneberg Minimal Surface］ |
［１］Function expression    ０．３≦ｓ≦０．９ 、 ０≦ｔ≦２π ［２］Input formula plot3d([2*sinh(s)*cos(t)-(2/3)*sinh(3*s)*cos(3*t),2*sinh(s)*sin(t)-(2/3)*sinh(3*s) *sin(3*t),2*cosh(2*s)*cos(2*t)],[s,0.3,0.9],[t,0,2*%pi],[grid,4,72]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 44】 Draw a graph of a 2D explicit function. ［Make it easier to see by specifying the range of y-axis values］ |
［１］Function expression  ［２］Input formula plot2d(1/(x-1)+1,[x,-5,5],[y,-5,5]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 45】 Draw a graph of a 2D explicit function. ［Compare with the Taylor expansion graph of the approximation formula］ |
［１］Function expression  ［２］Input formula plot2d([cos(x),1-x^2/2+x^4/24-x^6/720,1-x^2/2+x^4/24-x^6/720+x^8/40320, 1-x^2/2+x^4/24-x^6/720+x^8/40320-x^10/3628800],[x,-2*%pi,2*%pi],[y,-5,5]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 46】 Draw a graph of a 2D explicit function. ［Find a number of real solutions to an equation］ |
［１］Equation  ［２］Input formula plot2d([exp(x),3-x^2],[x,-2,2],[y,-1,4]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. Since there are two points of intersection , we know that the equation has two real solutions. |
| 【Example 47】 Draw a graph of a 2D parameter. ［Circle：Don't specify the number of divisions］ |
［１］Function expression  ０≦ｔ≦２π［２］Input formula plot2d([parametric,cos(t),sin(t)],[t,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 48】 Draw a graph of a 2D parameter. ［Circle：specify 15 divisions］ |
［１］Function expression ０≦ｔ≦２π［２］Input formula plot2d([parametric,cos(t),sin(t)],[t,0,2*%pi],[nticks,15]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 49】 Draw a graph of a 2D parameter. ［Circle：specify 100 divisions］ |
［１］Function expression ０≦ｔ≦２π［２］Input formula plot2d([parametric,cos(t),sin(t)],[t,0,2*%pi],[nticks,100]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 50】 Draw a graph of a 3D explicit function. ［Do not specify the number of divisions］ |
［１］Function expression  ［２］Input formula plot3d(x^3-3*x*y^2,[x,-1,1],[y,-1,1]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 51】 Draw a graph of a 3D explicit function. ［Don't specify the number of divisions］ |
［１］Function expression  －１≦ｘ≦１、－１≦ｙ≦１［２］Input formula plot3d((x^2*y)/(x^4+y^2),[x,-1,1],[y,-1,1]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 52】 Draw a graph of a 3D explicit function. ［Specify the number of divisions］ |
［１］Function expression  －１≦ｘ≦１、－１≦ｙ≦１［２］Input formula plot3d((x^2*y)/(x^4+y^2),[x,-1,1],[y,-1,1],[grid,100,100]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 53】 Draw a graph of a 3D parameter. ［Spherical surface：Specify the number of division］ |
［１］Function expression  ０≦ｓ≦２π、０≦ｔ≦２π ［２］Input formula plot3d([cos(s)*cos(t),cos(s)*sin(t),sin(s)],[s,0,2*%pi],[t,0,2*%pi],[grid,50,50]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 54】 Draw a graph of a 3D parameter. ［Amazing shapes and equations］ |
［１］Function expression      ０≦ｕ≦２π、０≦ｖ≦２π ［２］Input formula plot3d([3*cos(u)+5*cos(3*u)+(3*(cos(u)+5*cos(3*u))*cos(v))/(2*sqrt(234+90*cos(2*u))) -(3*cos(6*u)*(sin(u)+5*sin(3*u))*sin(v))/(2*sqrt(13+5*cos(2*u))*sqrt(22+5*cos(2*u) +9*cos(12*u))),3*sin(u)+5*sin(3*u)+(3*cos(v)*(sin(u)+5*sin(3*u)))/(2*sqrt(234+90*cos (2*u)))+(3*(5*cos(3*u)+cos(5*u)+cos(7*u)+5*cos(9*u))*sin(v))/(4*sqrt(13+5*cos(2*u)) *sqrt(22+5*cos(2*u)+9*cos(12*u))),3*sin(6*u)-(sqrt(13+5*cos(2*u))*sin(v))/(2*sqrt (22+5*cos(2*u)+9*cos(12*u)))],[u,0,2*%pi],[v,0,2*%pi],[grid,80,8]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 55】 Draw a graph of a 3D parameter. ［Rotating body 1］ |
［１］Rotating body A solid created by rotating the part enclosed by parabola y=x^2 , x=-3 , x=3 , the x-axis around the x-axis. ［２］Input formula plot3d([t,t^2*cos(s),t^2*sin(s)],[t,-3,3],[s,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 56】 Draw a graph of a 3D parameter. ［Rotating body 2］ |
［１］Rotating body A solid created by rotating the part enclosed by parabola x=√ｙ , y=0 , y=9 , the y-axis around the y-axis. ［２］Input formula plot3d([sqrt(t)*cos(s),t,sqrt(t)*sin(s)],[t,0,9],[s,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 57】 Draw a graph of a 3D parameter. ［Rotating body 3］ |
［１］Rotating body A solid created by rotating the part enclosed by parabola y=x^2-2 , x=-3 , x=3 , the x-axis around the x-axis. ［２］Input formula plot3d([t,(t^2-2)*cos(s),(t^2-2)*sin(s)],[t,-3,3],[s,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 58】 Draw a graph of a 3D parameter. ［Rotating body 4］ |
［１］Rotating body A solid created by rotating the part enclosed by parabola y=x^2+2 , x=-3 , x=3 , the x-axis around the x-axis. ［２］Input formula plot3d([t,(t^2+2)*cos(s),(t^2+2)*sin(s)],[t,-2,2],[s,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 59】 Draw a graph of a 3D parameter. ［Rotating body 5］ |
［１］Rotating body A solid created by rotating circle: x^2+y^2=4 around the x-axis. ［２］Input formula plot3d([t,sqrt(4-t^2)*cos(s),sqrt(4-t^2)*sin(s)],[t,-2,2],[s,0,2*%pi]); ［３］Drawing result  ＜How to draw a graph＞ As in the above input formula , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 60】 Approximation of expressions by Taylor Expansion ［ｙ＝ｓｉｎｘ］ |
［１］Input expression for Taylor Expansion of sinx taylor(sin(x),x,0,12); ［２］Deployment result  ［３］An input expression that draws the graph of ｙ＝ｓｉｎｘ and its approximation plot2d([sin(x),x-x^3/6+x^5/120-x^7/5040+x^9/362880-x^11/39916800],[x,-10,10],[y,-1.2,1.2]); ［４］Drawing result  ＜How to draw a graph＞ As in the input formula in [3] above , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Example 61】 Approximation of expressions by Taylor Expansion ［ｙ＝ｃｏｓｘ］ |
［１］Input expression for Taylor Expansion of cosx taylor(cos(x),x,0,12); ［２］Deployment result  ［３］An input expression that draws the graph of ｙ＝ｃｏｓｘ and its aaproximation plot2d([cos(x),1-x^2/2+x^4/24-x^6/720+x^8/40320-x^10/3628800+x^12/479001600] ,[x,-10,10],[y,-1.2,1.2]); ［４］Drawing result  ＜How to draw a graph＞ As in the input formula in [3] above , enter all in half-width and press the Shift key and Enter key at the same time. |
【Example 62】 Approximation of expressions by Taylor Expansion  |
［１］Inut expression for Taylor Expansion of e^x taylor(exp(x),x,0,6); ［２］Deployment result 1+x+x^2/2+x^3/6+x^4/24+x^5/120+... ［３］ An input expression that draws the graph of  and its approximationplot2d([exp(x),1+x+x^2/2+x^3/6+x^4/24+x^5/120],[x,-3,3],[y,0,5]); ［４］Drawing result  ＜How to draw a graph＞ As in the input formula in [3] above , enter all in half-width and press the Shift key and Enter key at the same time. |
【Example 63】 Prove Euler's formula |
［１］Input expression for Taylor Expansion of ｓｉｎｘ taylor(ｓｉｎ(x),x,0,12); ［２］Taylor Expansion result of ｓｉｎｘ  －－－①［３］Input expression for Taylor Expansion of cosｘ taylor(cos(x),x,0,12); ［４］Taylor Expansion result of cosｘ  －－－②［５］Input expression for Taylor Expansion of  taylor(exp(%i*x),x,0,12); ［６］Taylor Expansion result of  －－－③ Above , from ① , ② , ③   ＝ ｃｏｓｘ ＋ ｉｓｉｎｘ Therefore , ＝ ｃｏｓｘ ＋ ｉｓｉｎｘ ＜How to display the expansion formula＞ As in the input formulas in [1] , [3] , [5] above , enter all in half-width and press the Shift key and Enter key at the same time. |
| 【Problem 1】 How many digits is 2^30 in integer ? However , ｌｏｇ(10，2)＝0.3010. |
| This problem always comes up in common logarithms. If you teach in the order of ①→②→③→④ below , you can make the number of digits more specific. ①Display 2^30 , 2^50 , 2^100 , 3^30 , 3^50 , and 3^100 computed by Ｍａｘｉｍａ and count the number of digits. ②Teach how to find the number of digits by using common rogarithms. ③Find the number of digits in 2^30 , 2^50 , 2^100 , 3^30 , 3^50 , and 3^100 using common logarithms and comfirm that it matches the number of digits you just counted. ④Touching on how to count large numbers. Below are the results caluculated by Maxima. 2^30＝1073741824 2^50＝1125899906842624 2^100＝1267650600228229401496703205376 3^30＝205891132094649 3^50＝717897987691852588770249 3^100＝515377520732011331036461129765621272702107522001 ＜How to use "Ｍａｘｉｍａ"＞ For example , to calculate 2^30 Enter 2^30 in half-width , and press the Shift key and Enter key at the same time. |
| 【Problem 2】 Expand （ａ＋ｂ）^3 and （ａ＋ｂ＋ｃ）^2 |
| Expanding （ａ＋ｂ）^3 or （ａ＋ｂ＋ｃ）^2 doesn't surprise you much. I wondered if it would be possible to have a class that surprises and impresses students by having Maxima calculate and display the expansion of （ａ＋ｂ）^50 and （ａ＋ｂ＋ｃ）^20 in the introduction of the expansion of equations. Below is the result of expansion by Maxima （ａ＋ｂ）^50 ＝b^50+50*a*b^49+1225*a^2*b^48+19600*a^3*b^47+230300*a^4*b^46+2118760*a^5*b^45 +15890700*a^6*b^44+99884400*a^7*b^43+536878650*a^8*b^42+2505433700*a^9*b^41 +10272278170*a^10*b^40+37353738800*a^11*b^39+121399651100*a^12*b^38 +354860518600*a^13*b^37+937845656300*a^14*b^36+2250829575120*a^15*b^35 +4923689695575*a^16*b^34+9847379391150*a^17*b^33+18053528883775*a^18*b^32 +30405943383200*a^19*b^31+47129212243960*a^20*b^30+67327446062800*a^21*b^29 +88749815264600*a^22*b^28+108043253365600*a^23*b^27+121548660036300*a^24*b^26 +126410606437752*a^25*b^25+121548660036300*a^26*b^24+108043253365600*a^27*b^23 +88749815264600*a^28*b^22+67327446062800*a^29*b^21+47129212243960*a^30*b^20 +30405943383200*a^31*b^19+18053528883775*a^32*b^18+9847379391150*a^33*b^17 +4923689695575*a^34*b^16+2250829575120*a^35*b^15+937845656300*a^36*b^14 +354860518600*a^37*b^13+121399651100*a^38*b^12+37353738800*a^39*b^11 +10272278170*a^40*b^10+2505433700*a^41*b^9+536878650*a^42*b^8+99884400*a^43*b^7 +15890700*a^44*b^6+2118760*a^45*b^5+230300*a^46*b^4+19600*a^47*b^3+1225*a^48*b^2 +50*a^49*b+a^50 （ａ＋ｂ＋ｃ）^20 ＝c^20+20*b*c^19+20*a*c^19+190*b^2*c^18+380*a*b*c^18+190*a^2*c^18+1140*b^3*c^17 +3420*a*b^2*c^17+3420*a^2*b*c^17+1140*a^3*c^17+4845*b^4*c^16+19380*a*b^3*c^16 +29070*a^2*b^2*c^16+19380*a^3*b*c^16+4845*a^4*c^16+15504*b^5*c^15+77520*a*b^4*c^15 +155040*a^2*b^3*c^15+155040*a^3*b^2*c^15+77520*a^4*b*c^15+15504*a^5*c^15 +38760*b^6*c^14+232560*a*b^5*c^14+581400*a^2*b^4*c^14+775200*a^3*b^3*c^14 +581400*a^4*b^2*c^14+232560*a^5*b*c^14+38760*a^6*c^14+77520*b^7*c^13 +542640*a*b^6*c^13+1627920*a^2*b^5*c^13+2713200*a^3*b^4*c^13+2713200*a^4*b^3*c^13 +1627920*a^5*b^2*c^13+542640*a^6*b*c^13+77520*a^7*c^13+125970*b^8*c^12 +1007760*a*b^7*c^12+3527160*a^2*b^6*c^12+7054320*a^3*b^5*c^12 +8817900*a^4*b^4*c^12+7054320*a^5*b^3*c^12+3527160*a^6*b^2*c^12 +1007760*a^7*b*c^12+125970*a^8*c^12+167960*b^9*c^11+1511640*a*b^8*c^11 +6046560*a^2*b^7*c^11+14108640*a^3*b^6*c^11+21162960*a^4*b^5*c^11 +21162960*a^5*b^4*c^11+14108640*a^6*b^3*c^11+6046560*a^7*b^2*c^11 +1511640*a^8*b*c^11+167960*a^9*c^11+184756*b^10*c^10+1847560*a*b^9*c^10 +8314020*a^2*b^8*c^10+22170720*a^3*b^7*c^10+38798760*a^4*b^6*c^10 +46558512*a^5*b^5*c^10+38798760*a^6*b^4*c^10+22170720*a^7*b^3*c^10 +8314020*a^8*b^2*c^10+1847560*a^9*b*c^10+184756*a^10*c^10+167960*b^11*c^9 +1847560*a*b^10*c^9+9237800*a^2*b^9*c^9+27713400*a^3*b^8*c^9 +55426800*a^4*b^7*c^9+77597520*a^5*b^6*c^9+77597520*a^6*b^5*c^9 +55426800*a^7*b^4*c^9+27713400*a^8*b^3*c^9+9237800*a^9*b^2*c^9 +1847560*a^10*b*c^9+167960*a^11*c^9+125970*b^12*c^8+1511640*a*b^11*c^8 +8314020*a^2*b^10*c^8+27713400*a^3*b^9*c^8+62355150*a^4*b^8*c^8 +99768240*a^5*b^7*c^8+116396280*a^6*b^6*c^8+99768240*a^7*b^5*c^8 +62355150*a^8*b^4*c^8+27713400*a^9*b^3*c^8+8314020*a^10*b^2*c^8 +1511640*a^11*b*c^8+125970*a^12*c^8+77520*b^13*c^7+1007760*a*b^12*c^7 +6046560*a^2*b^11*c^7+22170720*a^3*b^10*c^7+55426800*a^4*b^9*c^7 +99768240*a^5*b^8*c^7+133024320*a^6*b^7*c^7+133024320*a^7*b^6*c^7 +99768240*a^8*b^5*c^7+55426800*a^9*b^4*c^7+22170720*a^10*b^3*c^7 +6046560*a^11*b^2*c^7+1007760*a^12*b*c^7+77520*a^13*c^7+38760*b^14*c^6 +542640*a*b^13*c^6+3527160*a^2*b^12*c^6+14108640*a^3*b^11*c^6 +38798760*a^4*b^10*c^6+77597520*a^5*b^9*c^6+116396280*a^6*b^8*c^6 +133024320*a^7*b^7*c^6+116396280*a^8*b^6*c^6+77597520*a^9*b^5*c^6 +38798760*a^10*b^4*c^6+14108640*a^11*b^3*c^6+3527160*a^12*b^2*c^6 +542640*a^13*b*c^6+38760*a^14*c^6+15504*b^15*c^5+232560*a*b^14*c^5 +1627920*a^2*b^13*c^5+7054320*a^3*b^12*c^5+21162960*a^4*b^11*c^5 +46558512*a^5*b^10*c^5+77597520*a^6*b^9*c^5+99768240*a^7*b^8*c^5 +99768240*a^8*b^7*c^5+77597520*a^9*b^6*c^5+46558512*a^10*b^5*c^5 +21162960*a^11*b^4*c^5+7054320*a^12*b^3*c^5+1627920*a^13*b^2*c^5 +232560*a^14*b*c^5+15504*a^15*c^5+4845*b^16*c^4+77520*a*b^15*c^4 +581400*a^2*b^14*c^4+2713200*a^3*b^13*c^4+8817900*a^4*b^12*c^4 +21162960*a^5*b^11*c^4+38798760*a^6*b^10*c^4+55426800*a^7*b^9*c^4 +62355150*a^8*b^8*c^4+55426800*a^9*b^7*c^4+38798760*a^10*b^6*c^4 +21162960*a^11*b^5*c^4+8817900*a^12*b^4*c^4+2713200*a^13*b^3*c^4 +581400*a^14*b^2*c^4+77520*a^15*b*c^4+4845*a^16*c^4+1140*b^17*c^3 +19380*a*b^16*c^3+155040*a^2*b^15*c^3+775200*a^3*b^14*c^3 +2713200*a^4*b^13*c^3+7054320*a^5*b^12*c^3+14108640*a^6*b^11*c^3 +22170720*a^7*b^10*c^3+27713400*a^8*b^9*c^3+27713400*a^9*b^8*c^3 +22170720*a^10*b^7*c^3+14108640*a^11*b^6*c^3+7054320*a^12*b^5*c^3 +2713200*a^13*b^4*c^3+775200*a^14*b^3*c^3+155040*a^15*b^2*c^3 +19380*a^16*b*c^3+1140*a^17*c^3+190*b^18*c^2+3420*a*b^17*c^2 +29070*a^2*b^16*c^2+155040*a^3*b^15*c^2+581400*a^4*b^14*c^2 +1627920*a^5*b^13*c^2+3527160*a^6*b^12*c^2+6046560*a^7*b^11*c^2 +8314020*a^8*b^10*c^2+9237800*a^9*b^9*c^2+8314020*a^10*b^8*c^2 +6046560*a^11*b^7*c^2+3527160*a^12*b^6*c^2+1627920*a^13*b^5*c^2 +581400*a^14*b^4*c^2+155040*a^15*b^3*c^2+29070*a^16*b^2*c^2 +3420*a^17*b*c^2+190*a^18*c^2+20*b^19*c+380*a*b^18*c+3420*a^2*b^17*c +19380*a^3*b^16*c+77520*a^4*b^15*c+232560*a^5*b^14*c+542640*a^6*b^13*c +1007760*a^7*b^12*c+1511640*a^8*b^11*c+1847560*a^9*b^10*c +1847560*a^10*b^9*c+1511640*a^11*b^8*c+1007760*a^12*b^7*c +542640*a^13*b^6*c+232560*a^14*b^5*c+77520*a^15*b^4*c+19380*a^16*b^3*c +3420*a^17*b^2*c+380*a^18*b*c+20*a^19*c+b^20+20*a*b^19+190*a^2*b^18 +1140*a^3*b^17+4845*a^4*b^16+15504*a^5*b^15+38760*a^6*b^14 +77520*a^7*b^13+125970*a^8*b^12+167960*a^9*b^11+184756*a^10*b^10 +167960*a^11*b^9+125970*a^12*b^8+77520*a^13*b^7+38760*a^14*b^6 +15504*a^15*b^5+4845*a^16*b^4+1140*a^17*b^3+190*a^18*b^2+20*a^19*b+a^20 ＜How to use "Maxima"＞ For example , when expanding (a+b)^50 Enter expand((a+b)^50) in half-width , and press the Shift key and Enter key at the same time. |
| 【Problem 3】 Solve the higher equation ｘ^3＋２ｘ^2＋２ｘ＋１＝０. |
| The high-level equation handled in high school is a form that can be solved
by using factor decomposition or the like , or can be solved as x^2=t or
the like. Solve the cubic equation ax^3+bx^2+cx+d=0 in "Maxima". Then the formula of the cubic equation is displayed. Will the students be surprised and impressed ? Also , if you solve the cubic equation ｘ^3－６ｘ－１０＝０ , and the quartic equation ｘ^4＋３ｘ^3－１８ｘ^2＋６ｘ－５＝０ using Maxima and display them , the complexity of the solution should surprise the students. ＜How to use "Ｍａｘｉｍａ"＞ For example , when solving ax^3+bx^2+cx+d=0 Enter solve(ａ*ｘ^3＋ｂ*ｘ^2＋ｃ*ｘ＋ｄ＝０,x) in half-width , press the Shift key and Enter key at the same time. |
| The result of letting "Maxima" solve a cubic equation ａｘ^3＋ｂｘ^2＋ｃｘ＋ｄ＝０ |
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| The result of letting "Maxima" solve a cubic equation ｘ^3－６ｘ－１０＝０ |
 |
| 【Problem 4】 Factor ａｂ－ａ＋ｂ－１ |
| This is a problem of cleaning up and factoring for one character. If we let Maxima solve more complex factorizations and display them , I wondered if it would be possible to create a class that surprises and impresses the students. Students would be surprised if (ａ＋ｂ＋ｃ)(ｂｃ＋ｃａ＋ａｂ)－ａｂｃ , (ｂ－ｃ)^3＋(ｃ－ａ)^3＋(ａ－ｂ)^3 , ａ^3＋ｂ^3＋ｃ^3－３ａｂｃ , and (ｂ＋ｃ)(ｃ＋ａ)(ａ＋ｂ)＋ａｂｃ were factored instantly , using Maxima displayed. Below is the result of following with "Maxima" (a+b+c)(bc+ca+ab)-abc = (b+a)(c+a)(c+b) (b-c)^3+(c-a)^3+(a-b)^3 = 3(b-a)(c-a)(c-b) a^3+b^3+c^3-3*a*b*c = (c+b+a)(c^2-b*c-a*c+b^2-a*b+a^2) (b+c)(c+a)(a+b)+abc = (c+b+a)(bc+ac+ab) ＜How to use "Maxima"＞ For example , when factoring (a+b+c)(bc+ca+ab)-abc Enter factor((a+b+c)*(b*c+c*a+a*b)-a*b*c) in half-width , and press the Shift key and Enter key at the same time. |
| 【Problem 5】 Differentiate (ｘ＋７ｘ^2)^(1/3). |
| I wonder if I could create a class that surprise and impress students
by searching for more complex expressions in workbooks and using "Maxima"
to differentiate them and display them. Below is the result of differentiating with "Maxima" {(ｘ＋７ｘ^2)^(1/3)}’ = (14*x+1)/(3*(7*x^2+x)^(2/3)) ＜How to use "Ｍａｘｉｍａ"＞ For example , when differentiating (ｘ＋７ｘ^2)^(1/3) Enter diff((x+7*x^2)^(1/3), x) in half-width , and press the Shift key and Enter key at the same time. |
| 【Problem 6】 Integrate √(１＋５ｘ) |
| I wonder if I could create a class that surprises and impresses by searching
for more complex expressions in workbooks and using "Maxima"
to integrate them and display them. Below is the result of integrating with "Maxima". ∫√(１＋５ｘ)ｄｘ = (2*(5*x+1)^(3/2))/15 ＜How to use "Ｍａｘｉｍａ"＞ For example , when integrating √(１＋５ｘ) Enter integrate(sqrt(1+5*x) , x) in half-width , and press the Shift key and Enter key at the same time. |
| Formula manipulation software "Maxima" | Formula manipulation software "wxＭａｘｉｍａ" |
| Click on the formula manipulation software "ｗｘＭａｘｉｍａ" above to open Maxima's official website. Click Download on the left menue of this wxMaxima official site. Next , click Sourceforge download page. And , click Maxima Windows. Furthermore , click 5.26.0-Windows. Then , ckick maxima-5.26.0.exe to download "maxima 5.26.0.exe". Double-click "maxima-5.26.0.exe" downloaded to launch the Maxima installer. After that , follow the instructions on the screen to install. However , 5.26.0 in "maxima-5.26.0.exe" represents the version. (2/12/2012) |
| Since the icon of "wxMaxima" is created on the desktop , double-click it to start "Maxima". |
| You can download a Maxima data file "MSample.wxm" containing
all the sample programs shown on this website. Click the data file "MSamp.lzh" and save it to your desktop or other location. Unzip the downloaded file "MSamp.lzh" , put the cursor on the input expression you want to excute , and press the Shift key and Enter key at the same time to excute it. Of course , "Maxima" must be installed before that. |
| Data file "MSamp.wxm" |