Calculus

Calculus

Base.diff — Method.
diff(f, x, n) where T

Take the nth order derivative of $f$ with respect to $x$.

\[\frac{\partial^n f(x,...)}{\partial x^n}\]
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Base.diff — Method.
diff(f, x) where T

Take the derivative of $f$ with respect to $x$

\[\frac{\partial f(x, ...)}{\partial x}\]
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Base.sum — Method.
sum(f::T, k, start, finish) where T

Compute the sum,

\[ \sum_{k=start}^{finish} f(k),\]

simplifying the sum if possible.

Examples

julia> sum(m"1/n^2", :n, 1, "inf")

                                        2
                                     %pi
                                     ----
                                      6
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Maxima.ilt — Method.
ilt(f::T, s, t) where T

Compute the inverse Laplace transform of $f(s)$.

$t$ is the new variable and $s$ is the old variable.

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Maxima.integrate — Method.
integrate(f::T, x, a, b) where T

Evaluate the definite integral of $f$ with respect to $x$ from $a$ to $b$.

\[ \int_a^b f(x) dx\]
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Maxima.integrate — Method.
integrate(f::T, x) where T

Evaluate the indefinite integral

\[\int f(x) dx\]

Examples

julia> integrate(:(sin(x)), :x)
:(-cos(x))

See also

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Maxima.laplace — Method.
laplace(f::T, t, s) where T

Compute the Laplace transform of $f(t)$ where $s$ is the new variable.

\[\mathcal{L}\lbrace f \rbrace (s) = \int_0^\infty f(t) e^{-st} dt\]
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Maxima.limit — Method.
limit(f, x, a, side) where T

Take the left or right sided limit as $x$ approaches $a$ of $f(x)$.

side may be either "plus" or "minus" denoting the right and left sided limit respectively

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Maxima.limit — Method.
limit(f, x, a) where T

Take the limit as $x$ approaches $a$ of $f(x)$

\[lim_{x \rightarrow a} f(x)\]
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Maxima.product — Method.
product(f::T, k, start, finish) where T

Compute the product,

\[ \prod_{k=start}^{finish} f(k),\]

simplifying the product if possible.

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Maxima.risch — Method.
risch(f::T, x) where T

Compute the indefinite integral of $f$ with respect to $x$ using the Risch algorithm

See also

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Maxima.taylor — Method.
taylor(f::T, x, x0, n) where T

Taylor expand $f(x)$ around $x_0$ to nth order

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