Notation for differentiation

Abstract: 1. Suffix notation and tensor algebra 2. Special functions 3. Non-linear ordinary differential equations 4. Approximate solutions of ordinary differential equations 5. Contour integration 6. Applications of contour integration 7. Laplace and Fourier transforms 8. Partial differential equations 9. Calculus of variations.

Abstract: A set of symbols based on the minimum subset of Seitz matrices required to generate the complete symmetry may be derived for each of the three-dimensional crystallographic space groups. This has a number of desirable properties including explicit information on the choice of origin. It also leads to a simple and general algorithmic procedure for generating equivalent positions.

Abstract: Two simple linear notation systems are suggested to encode molecular structure including stereochemical elements Both systems give rise to a unique numbering of the molecular graph, and thus also lead to a unique linear notation Both linear notation systems are extremely compact and require only standard chemical symbols A string comparison technique is developed to measure the similarity of two molecular linear notations This procedure allows one to define a molecular similarity index with values that range from zero to unity, the zero value characterizing complete dissimilarity and the value of unity denoting identity The notation and similarity index procedures are applied to several small molecular structures

Abstract: This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships, which are necessary for vector differential calculus. Then differentiation by vectors is introduced and a host of major vector differential and vector derivative relationships is proven explicitly in a very elementary step by step approach. The paper is thus intended to serve as reference material, giving details, which are usually skipped in more advanced discussions of the subject matter.