About the GuideBooks. The Mathematica GuideBooks by Michael Trott form a four-volume set that has been in development for over a decade. The GuideBooks provide an exploration of the various facets of Mathematica as a tool for solving scientific problems. Each Mathematica GuideBook is available separately and covers one of the key features of Mathematica: programming, visualization, numerics, an...

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The diameter of a graph G is the maximal distance between two vertices of G. A graph G is said to be diameter-edge-invariant, if d(G−e) = d(G) for all its edges, diametervertex-invariant, if d(G − v) = d(G) for all its vertices and diameter-adding-invariant if d(G+ e) = d(e) for all edges of the complement of the edge set of G. This paper describes some properties of such graphs and gives sever...

An overview of the solution methods for ordinary differential equations in the Mathematica function DSolve is presented. Key WordsDifferential Equation, Mathematica, Computer Algebra

Heat kernel coefficients encode the short distance behavior of propagators in the presence of background fields, and are thus useful in quantum field theory. We present a Mathematica program for computing these coefficients and their derivatives, based on an algorithm by Avramidi.[1] ∗Electronic Address: [email protected] 0 I. PROGRAM SUMMARY Title of program: HeatK Version number: 1.0 Ava...