矢吹太朗『コンピュータでとく数学』（オーム社, 2024）
- 2 * (-3)
- 2 (-3)
- (1 + 2) * 3
- 2^10
- 2**10
- -2 < -1
- 2 + 2 == 5
- x<1
- not(0<1)
- (0<1)or(2>3)
- (0 < 1) & (2 > 3)
- Not[10<x]
- x==5 where x=5
- a (b+1) where a=1+2,b=9
- a = 1 + 2; b = 9; a * (b + 1)
- x1 = 2; x2 = 3; x1 + x2
- f(5) where f(x)=2x+3
- f(2,3) where f(x,y)=x+y
- g(x) where x={2,3},g(x)=x[[1]]+x[[2]]
- Expand[(x+1)^2]
- N[Sqrt[2],30]
- 0.1 + 0.2 == 0.3
- 1/10+2/10==3/10
- simplify sin(x)^2+cos(x)^2
- simplify sqrt(5+2sqrt(6))
- simplify sqrt((x-1)^2) where x-1>=0
- plot x^2+2x-4,x=-5..3
- plot x^2+y^2,x=-1..1,y=-1..1
- x^2+y^2=1
- x^2+y^2<=1
- 2x+3y=8,5x-7y=-9
- y<=x and y>=x^2
- x2+2x-4=0
- 2x+3y=8,5x-7y=-9
- 2^x+sin x=0
- x^2+2x-4<0
- histogram {36,43,53,55,56,56,57,60,61,73}
- mean {36,43,53,55,56,56,57,60,61,73}
- var {36,43,53,55,56,56,57,60,61,73}
- standardize {36,43,53,55,56,56,57,60,61,73}
- {35,114},{45,124},{55,143},{65,158},{75,166}
- covariance {35,45,55,65,75},{114,124,143,158,166}
- correlation {35,45,55,65,75},{114,124,143,158,166}
- linear fit {35,114},{45,124},{55,143},{65,158},{75,166}
- P(X=2),discrete uniform distribution min=1,max=6
- P(X=3),distributed binomial distribution n=10,p=3/10
- binomial distribution
- P(X<=3),distributed binomial distribution n=10,p=3/10
- P(150<=X<=200),uniform distribution min=0,max=360
- integral 1/360 150 to 200
- int 1/360 0 to x
- d/dx x/360
- P(6-3*2<=X<=6+3*2),normal distribution mu=6,sigma=2
- P(mu-3sigma<=X<=mu+3sigma),normal distribution
- normal distribution
- test for binomial parameter p0=4/10,p-hat=2/15,n=15
- X~normal distribution(15*4/10,sqrt(15*4/10(1-4/10))),P(X<=2)*2
- t-test mu0=25,xbar=25.21429,s=0.7151423,n=7
- t-interval xbar=25.21429,s=0.7151423,n=7
- linear fit {1,2,3},{1,3,6},{2,5,3},{3,7,6}
- PseudoInverse[{{1,1,2},{1,1,3},{1,2,5},{1,3,7}}].{3,6,3,6}
- lim f(x) as x->1 where f(x)=2x-3
- lim 2x-3 as x->1
- lim g(x) as x->sqrt(2) where g(x)=(x^2-2)/(x-sqrt(2))
- limit (1+1/x)^x as x->infinity
- limit 1/x^2 as x->0
- lim |x|/x as x->0
- f(x)=x^3,f'(1)
- lim_(h->0) (f(a+h)-f(a))/h where f(x)=x^3,a=1
- f(x)=x^3,f'(x)
- d^2/dx^2 x^3
- series sin(x) at x=0 to order 5
- series sqrt(1+x) to order 7
- local extrema of x^3-12x
- int_1^4 (-x^2+4x+1)dx
- simplify int_a^x (-t^2+4t+1)dt
- int -x^2+4x+1 dx
- y'(x)=-x^2+4x+1
- y'(x)=-x^2+4x+1,y(0)=1
- y'(x)=-x y(x)
- d/dx(int_a^x f(t)dt)
- int_0^(pi/2) log(sin(x)) dx
- int (p x+q)^100 dx
- int 1/x^a x=0..1
- int 1/x^a x=1..infinity
- int exp(-x^2) x=-infinity..infinity
- lim f(x1,x2) as (x1,x2)->(0,0) where f(x1,x2)=x1 x2^2/(x1^2+x2^2)
- lim f(x,y) as (x,y)->(0,0) where f(x,y)=x^2 y/(x^4+y^2)
- d/dx 2-x^2-y^2,d/dy 2-x^2-y^2
- grad(2-x^2-y^2)
- hessian matrix of 2x^3+5xy+2y^2
- local extrema of 2x1^3+x1 x2^2+5x1^2+x2^2
- int f(x,y) dy dx y=0..x,x=0..1 where f(x,y)=x^2+y^2
- int f(x,y) dx dy x=y..1,y=0..1 where f(x,y)=x^2+y^2
- {1/10+2/10,1/10+2/10-3/10}=={3/10,0}
- 100{1,2}+10{3,1}
- norm {3,4}
- sqrt({x,y}.{x,y})
- normalize {3,4}
- arccos(a.b/norm(a)/norm(b)) where a={1,0},b={1,1}
- vector angle {1,0},{1,1}
- {{1,2,0},{0,3,4}}
- DiagonalMatrix[{5,7}]
- symmetric matrix {{1,2},{2,3}}
- 10{{2,3},{5,7}}
- {{10,20},{30,40}}+{{2,3},{4,5}}
- {{2,3},{5,7}}.{{1,2},{3,4}}
- det {{3,2},{1,2}}
- inverse {{2,3},{5,7}}
- (inverse {{3,2},{1,2}}).{8,4}
- rref {{4,2,8},{2,1,4}}
- rank {{2,0,2},{0,2,-2},{2,2,0}}
- linear independence {3,1},{2,2}
- c1{3,1}+c2{2,2}={0,0}
- row space {{1,2}}
- row space {{1,1,0},{0,1,1}}
- column space {{1,0,1},{1,1,0},{0,1,-1}}
- QR decomposition {{1,2},{1,2},{0,0}}
- null space of transpose {{1,0},{1,1},{0,1}}