sicmutils.calculus.derivative — net.littleredcomputer/sicmutils 0.12.1

canonicalize-differential clj

(canonicalize-differential dx)

D clj

Derivative operator. Produces a function whose value at some point can multiply an increment in the arguments, to produce the best linear estimate of the increment in the function value.

derivative clj

(derivative f)

differential-of clj

(differential-of dx)

The differential of a quantity is, if we're a differential, the differential of the coefficient of the highest-order term part, or else the input itself.

differential? clj

(differential? x)

dx*dy clj

(dx*dy dx dy)

Form the product of the differentials dx and dy.

dx+dy clj

(dx+dy dx dy)

Adds two objects differentially. (One of the objects might not be differential; in which case we lift it into a trivial differential before the addition.)

make-differential clj

(make-differential tags->coefs)

The input here is a mapping (loosely defined) between sets of differential tags and coefficients. The mapping can be an actual map, or just a sequence of pairs. The differential tag sets are sequences of integer tags, which should be sorted.

max-order-tag clj

(max-order-tag ds)

From each of the differentials in the sequence ds, find the highest order term; then return the greatest tag found in any of these terms; i.e., the highest-numbered tag of the highest-order term.

taylor-series-terms clj

(taylor-series-terms f x dx)

The (infinite) sequence of terms of the taylor series of the function f evaluated at x, with incremental quantity dx.

with-and-without-tag clj

(with-and-without-tag tag dx)

Split the differential into the parts with and without tag and return the pair

with-tag clj

(with-tag tag dx)

The differential containing only those terms with the given tag

without-tag clj

(without-tag tag dx)

The differential containing only those terms without the given tag

∂ clj

(∂ & selectors)

Partial differentiation of a function at the (zero-based) slot index provided.