/usr/lib/open-axiom/input/calculus2.input is in open-axiom-test 1.4.1+svn~2626-2ubuntu2.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 | -- Input for page FormalDerivativePage
)clear all
differentiate(f, x)
f := operator f
x := operator x
y := operator y
a := f(x z, y z, z**2) + x y(z+1)
dadz := differentiate(a, z)
eval(eval(dadz, 'x, z +-> exp z), 'y, z +-> log(z+1))
eval(eval(a, 'x, z +-> exp z), 'y, z +-> log(z+1))
differentiate(%, z)
-- Input for page SeriesArithmeticPage
)clear all
x := series x
num := 3 + x
den := 1 + 7 * x
num / den
base := 1 / (1 - x)
expon := x * base
base ** expon
-- Input for page SeriesConversionPage
)clear all
f := sin(a*x)
series(f,x = 0)
g := y / (exp(y) - 1)
series(g)
h := sin(3*x)
series(h,x,x = %pi/12)
series(sqrt(tan(a*x)),x = 0)
series(sec(x) ** 2,x = %pi/2)
bern := t * exp(t*x) / (exp(t) - 1)
series(bern,t = 0)
-- Input for page SeriesDifferentialEquationPage
)clear all
)set streams calculate 7
y := operator 'y
eq := differentiate(y(x), x, 3) - sin(differentiate(y(x), x, 2)) * exp(y(x)) = cos(x)
seriesSolve(eq, y, x = 0, [1, 0, 0])
x := operator 'x
eq1 := differentiate(x(t), t) = 1 + x(t)**2
eq2 := differentiate(y(t), t) = x(t) * y(t)
seriesSolve([eq2, eq1], [x, y], t = 0, [y(0) = 1, x(0) = 0])
-- Input for page LaplacePage
)clear all
sin(a*t) * cosh(a*t) - cos(a*t) * sinh(a*t)
laplace(%, t, s)
laplace((exp(a*t) - exp(b*t))/t, t, s)
laplace(2/t * (1 - cos(a*t)), t, s)
laplace(exp(-a*t) * sin(b*t) / b**2, t, s)
laplace((cos(a*t) - cos(b*t))/t, t, s)
laplace(exp(a*t+b)*Ei(c*t), t, s)
laplace(a*Ci(b*t) + c*Si(d*t), t, s)
laplace(sin(a*t) - a*t*cos(a*t) + exp(t**2), t, s)
-- Input for page SeriesCoefficientPage
)clear all
x := series(x)
y := exp(x) * sin(x)
coefficient(y,6)
coefficient(y,15)
y
-- Input for page SymbolicIntegrationPage
)clear all
f := (x**2+2*x+1) / (x**6+6*x**5+15*x**4+20*x**3+15*x**2+6*x+2)
integrate(f, x)
g := log(1 + sqrt(a * x + b)) / x
integrate(g, x)
integrate(1/(x**2 - 2),x)
integrate(1/(x**2 + 2),x)
h := x**2 / (x**4 - a**2)
integrate(h, x)
complexIntegrate(h, x)
expandLog %
rootSimp %
ratForm %
-- Input for page DerivativePage
)clear all
f := exp exp x
differentiate(f, x)
differentiate(f, x, 4)
g := sin(x**2 + y)
differentiate(g, y)
differentiate(g, [y, y, x, x])
-- Input for page SeriesFormulaPage
)clear all
taylor(n +-> 1/factorial(n),x = 0)
taylor(n +-> (-1)**(n-1)/n,x = 1,1..)
taylor(n +-> (-1)**(n-1)/n,x = 1,1..7)
laurent(n +-> (-1)**(n-1)/(n + 2),x = 1,-1..)
puiseux(i +-> (-1)**((i-1)/2)/factorial(i),x = 0,1..,2)
puiseux(j +-> j**2,x = 8,-4/3..,1/2)
series(n +-> 1/factorial(n),x = 0)
series(n +-> (-1)**(n - 1)/(n + 2),x = 1,-1..)
series(i +-> (-1)**((i - 1)/2)/factorial(i),x = 0,1..,2)
-- Input for page SeriesCreationPage
)clear all
x := series x
1/(1 - x - x**2)
sin(x)
sin(1 + x)
sin(a * x)
series(1/log(y),y = 1)
f : UTS(FLOAT,z,0) := exp(z)
series(1/factorial(n),n,w = 0)
-- Input for page SeriesFunctionPage
)clear all
x := series x
rat := x**2 / (1 - 6*x + x**2)
sin(rat)
y : UTS(FRAC INT,y,0) := y
exp(y)
tan(y**2)
cos(y + y**5)
log(1 + sin(y))
z : UTS(EXPR INT,z,0) := z
exp(2 + tan(z))
w := taylor w
exp(2 + tan(w))
-- Input for page LimitPage
)clear all
f := sin(a*x) / tan(b*x)
limit(f,x=0)
g := csc(a*x) / csch(b*x)
limit(g,x=0)
h := (1 + k/x)**x
limit(h,x=%plusInfinity)
-- Input for page SeriesBernoulliPage
)clear all
reduce(+,[m**4 for m in 1..10])
sum4 := sum(m**4, m = 1..k)
eval(sum4, k = 10)
f := t*exp(x*t) / (exp(t) - 1)
)set streams calculate 5
ff := taylor(f,t = 0)
factorial(6) * coefficient(ff,6)
g := eval(f, x = x + 1) - f
normalize(g)
taylor(g,t = 0)
B5 := factorial(5) * coefficient(ff,5)
1/5 * (eval(B5, x = k + 1) - eval(B5, x = 1))
sum4
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