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Mathieu functions are employed in solving a variety of problems in mathematic (al?) physics. In many cases the configuration involves elliptical coordinates. Of course, the circular geometry is the degenerate case of the elliptical cross section. This volume contains values for, and curves of the angular and radial Mathieu functions and their first derivatives. The latter are often needed in the solution of problems, in particular in solving electromagnetic wave propagation problems. Also included are data on zero crossings of the radial Mathieu functions. These are often needed for determining the cut-off frequencies for propagating modes. Other tables are available for the Mathieu functions, but there is very little data available for derivatives or zero crossings. It is felt that the principal value of this volume is in the multitude of curves included. The analyst dealing with elliptical cases can, by inspection of the curves, find values of the functions and derivatives at the origin, maxima and minima, zero crossings, and qualitative behavior of the plots as a function of several parameters. To the authors knowledge, this is the most extensive presentation of plotted information. It is hoped that the information will be helpful in the solution of practical problems. This book is divided into two sections. Section I deals only with the functions themselves, defining the equations and terminology used and presenting the tabular data and curves. Section II treats the derivatives and the zeros. Again the terminology and equations for the first derivatives are given. The Mathieu functions are named after Emile L. Mathieu (1835-1890), a French mathematician, who in 1868 published an article dealing with vibratory movement of the elliptic membrane. The asteroid 27947 Emilemathieu is named in his honor.
This text aims to provide students in engineering with a sound presentation of post-calculus mathematics. It features numerous examples, many involving engineering applications, and contains all mathematical techniques for engineering degrees. The book also contains over 5000 exercises, which range from routine practice problems to more difficult applications. In addition, theoretical discussions illuminate principles, indicate generalizations and establish limits within which a given technique may or may not be safely used.
Includes Part 1A: Books and Part 1B: Pamphlets, Serials and Contributions to Periodicals
Learn to fully harness the power of Microsoft Excel(r) to perform scientific and engineering calculations With this text as your guide, you can significantly enhance Microsoft Excel's(r) capabilities to execute the calculations needed to solve a variety of chemical, biochemical, physical, engineering, biological, and medicinal problems. The text begins with two chapters that introduce you to Excel's Visual Basic for Applications (VBA) programming language, which allows you to expand Excel's(r) capabilities, although you can still use the text without learning VBA. Following the author's step-by-step instructions, here are just a few of the calculations you learn to perform: * Use worksheet functions to work with matrices * Find roots of equations and solve systems of simultaneous equations * Solve ordinary differential equations and partial differential equations * Perform linear and non-linear regression * Use random numbers and the Monte Carlo method This text is loaded with examples ranging from very basic to highly sophisticated solutions. More than 100 end-of-chapter problems help you test and put your knowledge to practice solving real-world problems. Answers and explanatory notes for most of the problems are provided in an appendix. The CD-ROM that accompanies this text provides several useful features: * All the spreadsheets, charts, and VBA code needed to perform the examples from the text * Solutions to most of the end-of-chapter problems * An add-in workbook with more than twenty custom functions This text does not require any background in programming, so it is suitable for both undergraduate and graduate courses. Moreover, practitioners in science and engineering will find that this guide saves hours of time by enabling them to perform most of their calculations with one familiar spreadsheet package.
Originally published in 1946, this book contains a series of tables with data relating to the Airy function.