1 (* ========================================================================= *)
2 (* Theory of multivariate calculus in Euclidean space. *)
3 (* ========================================================================= *)
5 loadt "Library/card.ml";; (* For countable set theorems. *)
6 loadt "Library/permutations.ml";; (* For determinants *)
7 loadt "Library/products.ml";; (* For determinants and integrals *)
8 loadt "Library/floor.ml";; (* Useful here and there *)
9 loadt "Multivariate/misc.ml";; (* Background stuff *)
10 loadt "Library/binomial.ml";; (* For Leibniz deriv formula etc. *)
11 loadt "Library/iter.ml";; (* n-fold iteration of function *)
13 (* ------------------------------------------------------------------------- *)
14 (* The main core theory. *)
15 (* ------------------------------------------------------------------------- *)
17 loadt "Multivariate/vectors.ml";; (* Basic vectors, linear algebra *)
18 loadt "Multivariate/determinants.ml";; (* Determinant and trace *)
19 loadt "Multivariate/topology.ml";; (* Basic topological notions *)
20 loadt "Multivariate/convex.ml";; (* Convex sets and functions *)
21 loadt "Multivariate/paths.ml";; (* Paths, simple connectedness etc. *)
22 loadt "Multivariate/polytope.ml";; (* Faces, polytopes, polyhedra etc. *)
23 loadt "Multivariate/dimension.ml";; (* Dimensional theorems *)
24 loadt "Multivariate/derivatives.ml";; (* Derivatives *)
26 (* ------------------------------------------------------------------------- *)
27 (* Work in progress. *)
28 (* ------------------------------------------------------------------------- *)
30 loadt "Multivariate/clifford.ml";; (* Geometric (Clifford) algebra *)
31 loadt "Multivariate/integration.ml";; (* Integration *)
32 loadt "Multivariate/measure.ml";; (* Lebesgue measure *)
34 (* ------------------------------------------------------------------------- *)
35 (* Complex numbers (as R^2) and complex analysis. *)
36 (* ------------------------------------------------------------------------- *)
38 loadt "Multivariate/complexes.ml";; (* Complex numbers *)
39 loadt "Multivariate/canal.ml";; (* Complex analysis *)
40 loadt "Multivariate/transcendentals.ml";; (* Real & complex transcendentals *)
41 loadt "Multivariate/realanalysis.ml";; (* Some analytical stuff on R *)
42 loadt "Multivariate/moretop.ml";; (* Further topological results *)
43 loadt "Multivariate/cauchy.ml";; (* Complex line integrals *)
45 (* ------------------------------------------------------------------------- *)
46 (* Updated database, for convenience where dynamic updating doesn't work. *)
47 (* ------------------------------------------------------------------------- *)
49 loadt "Multivariate/complex_database.ml";;