Complex functions with Geogebra

Complex functions, generally feature some interesting peculiarities, seen as extensions real functions, complementing the study of real analysis. However, the visualization of some complex functions properties requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the study of the functions defined from ℂ to ℂ through traditional techniques and by the use of Domain Colouring. Here, we will show how we can use GeoGebra for the study of complex functions, using several representations and creating tools which complement the tools already provided by the software. Our proposals designed for students of the first year of engineering and science courses can and should be used as an educational tool in collaborative learning environments. The main advantage in its use in individual terms is the promotion of the deductive reasoning (conjecture / proof). In performed the literature review few references were found involving this educational topic and by the use of a single software.

The young woman's companion, or, Frugal housewife : containing the most approved methods of pickling, preserving, potting, collaring, confectionary, managing and colouring foreign wines and spirits, making English wines, compounds, &c., &c. : also, the art of cookery containing directions for dressing all kinds of butchers' meat, poultry, game, fish, &c., &c. : with the complete art of carving, illustrated and made plain by engravings : likewise instructions for marketing : with the theory of brewing malt liquor : to which are added directions for letter writing, drawing, painting, &c., and several valuable miscellaneous pieces.

Includes index

Lucas' progressive drawing book, in three parts: : Part I--The principles of drawing in pencil, Part II--Colouring and shading in india ink, Part III--A treatise on perspective; : consisting chiefly of original views of American scenery, and embracing the latest and best improvements in the mode of instruction.

Poem "The colours" by E. Van Blon, part 2, p. [65]-66.

Colouring matters for dyeing textiles; with numerous engravings and diagrams,

"The matter has been revised and brought up to date by Mr. A. R. Foster."--Pref.

Metal-colouring and bronzing,

Mode of access: Internet.

The principles of beauty in colouring systematized /

Illustrations consist of color chips.

A practical treatise on painting : in three parts : consisting of hints on composition, chiaroscuro, and colouring : the whole illustrated by examples from the Italian, Venetian, Flemish, and Dutch schools /

Pagination, part 1: 31 pages, 9 leaves of plates; part 2: vi, 45 pages, 8 leaves of plates; part 3: ix, 64 pages, 8 leaves of plates.

The artist's assistant; or School of science; forming a practical introduction to the polite arts: in painting, drawing, designing, perspective, engraving, colouring, &c., with ample directions for japanning, enamelling, gilding, silvering, lacquering, &c. and a valuable selection of miscellaneous secrets.

Bookplate of Howard C. Levis.

A practical treatise on painting : in three parts : consisting of hints on composition, chiaroscuro, and colouring : the whole illustrated by examples from the Italian, Venetian, Flemish, and Dutch schools.

Each part has also been published separately, and has special t. p. and pagination.

Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.