Finding the roots of an equation F(x)=0 when F(x) involves transcendental functions and x is complex usually involves some kind of search method. The efficiency of a search method depends to a certain extent on knowledge of the roots--where they are likely to occur in the x plane, and how many there are. If a root is known to lie in a given region in the x plane, then a search routine can quickly find the root to the desired accuracy. But if no information about the location of the roots is available, a search over a wide area must be conducted, and this can be time consuming and expensive. Consequently, a method for locating the general area of the roots and determining the pattern of the roots is very valuable. The report describes a simple method for graphically displaying the pattern of roots in the complex plane. (Modified author abstract).

Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute?not always needed, but indispensable when it is. The author?s goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations. Solving Transcendental Equations is unique in that it is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval, and the very reliable spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding, and it includes three chapters on analytical methods?explicit solutions, regular pertubation expansions, and singular perturbation series (including hyperasymptotics)?unlike other books that give only numerical algorithms for solving algebraic and transcendental equations. This book is written for specialists in numerical analysis and will also appeal to mathematicians in general. It can be used for introductory and advanced numerical analysis classes, and as a reference for engineers and others working with difficult equations.

Taking a novel, more appealing approach than current texts, An Integrated Introduction to Computer Graphics and Geometric Modeling focuses on graphics, modeling, and mathematical methods, including ray tracing, polygon shading, radiosity, fractals, freeform curves and surfaces, vector methods, and transformation techniques. The author begins with f

Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute--not always needed, but indispensible when it is. The author's goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations.

This book constitutes the refereed proceedings of the International Conference, VISIGRAPP 2011, the Joint Conference on Computer Vision, Theory and Applications (VISAPP), on Imaging Theory and Applications (IMAGAPP), on Computer Graphics Theory and Applications (GRAPP), and on Information Visualization Theory and Applications (IVAPP), held in Vilamoura, Portugal, in March 2011. The 15 revised full papers presented together with one invited paper were carefully reviewed and selected. The papers are organized in topical sections on computer graphics theory and applications; imaging theory and applications; information visualization theory and applications; and computer vision theory and applications.