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El objetivo de este libro es presentar el modo de trabajo con el software MAPLE para las versiones recientes del programa bajo entorno Microsoft Windows y otros sistemas operativos profundizando especialmente sus aplicaciones en el terreno del Cálculo y el Análisis Matemático con aplicaciones en la Ingeniería y las Ciencias. La mayoría de las especialidades de Ciencias e Ingeniería presentan en sus currículum materias de Cálculo y Análisis Matemático. Las nuevas orientaciones de los grados universitarios hacia las materias prácticas hace necesario desarrollar las programaciones de las asignaturas basadas en el cálculo con ayuda de herramientas informáticas. El software MAPLE adquiere una gran importancia desde esta ópticaAsimismo, en el terreno profesional. MAPLE es una herramienta muy importante para realizar cálculo simbólico y numérico. Por otro lado, en la investigación también es esencial el manejo de herramientas de computación matemática que faciliten la ardua tarea del descubrimiento y el desarrollo de la ingeniería del conocimiento. En lo que se refiere al cálculo numérico, las nuevas versiones de este software son más rápidas en la solución de los algoritmos asociados a las técnicas. Lo mismo ocurre en el campo del cálculo simbólico, en el que MAPLE es software pionero.El libro presenta al final en cada capítulo gran variedad de ejemplos y ejercicios resueltos con MAPLE con la finalidad de ilustrar adecuadamente los conceptos teóricos.
In the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. Let us look at some examples, the history of computing the number ? began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated ? (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). The ?rst formula for computing decimal digits of ? was disc- ered by J. Machin (in 1706), who was the ?rst to correctly compute 100 digits of ?. Then many people used his method, e. g. , W. Shanks calculated ? with 707 digits (within 15 years), although due to mistakes only the ?rst 527 were correct. For the next examples, we can mention the history of computing the ?ne-structure constant ? (that was ?rst discovered by A. Sommerfeld), and the mathematical tables, exact - lutions, and formulas, published in many mathematical textbooks, were not veri?ed rigorously [25]. These errors could have a large e?ect on results obtained by engineers. But sometimes, the solution of such problems required such techn- ogy that was not available at that time. In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - provetheresultsthatahumancanobtainwithoutanytechnology. With respectto our example of computing?, we can mention that recently (in 2002) Y. Kanada, Y. Ushiro, H. Kuroda, and M.
This book is intended for use as a supplemental tool for courses in engineering mathematics, applied ordinary and partial differential equations, vector analysis, applied complex analysis, and other advanced courses in which MAPLE is used. Each chapter has been written so that the material it contains may be covered in a typical laboratory session of about 1-1/2 to 2 hours. The goals for every laboratory are stated at the beginning of the chapter. Mathematical concepts are then discussed within a framework of abundant engineering applications and problem-solving techniques using MAPLE. Each chapter is also followed by a set of exploratory exercises that are intended to serve as a starting point for a student's mathematical experimentation. Since most of the exercises can be solved in more than one way, there is no answer key for either students or professors.
How to Use This Handbook The Maple Handbook is a complete reference tool for the Maple language, and is written for all Maple users, regardless of their dis cipline or field(s) of interest. All the built-in mathematical, graphic, and system-based commands available in Maple V Release 2 are detailed herein. Please note that The Maple Handbook does not teach about the mathematics behind Maple commands. If you do not know the meaning of such concepts as definite integral, identity matrix, or prime integer, do not expect to learn them here. As well, while the introductory sections to each chapter taken together do provide a basic overview of the capabilities of Maple, it is highly recom mended that you also read a more thorough tutorial such as In troduction to Maple by Andre Heck or First Leaves: A Tutorial Introduction to Maple. Overall Organization One of the main premises of The Maple Handbook is that most Maple users approach the system to solve a particular problem (or set of problems) in a specific subject area. Therefore, all commands are organized in logical subsets that reflect these different cate gories (e.g., calculus, algebra, data manipulation, etc.) and the com mands within a subset are explained in a similar language, creating a tool that allows you quick and confident access to the information necessary to complete the problem you have brought to the system.
Fast becoming the first choice in computer algebra systems (CAS) among engineers and scientists, Maple is easy-to-use software that performs numerical and symbolic analysis to solve complex mathematical problems. This book shows you how to tap the full power of Maple's latest version in solving real-world quantitative problems in circuit theory, control theory, curve-fitting, mechanics, and digital signal processing.
This unique book provides a streamlined, self-contained and modern text for a one-semester mathematical methods course with an emphasis on concepts important from the application point of view. Part I of this book follows the ?paper and pencil? presentation of mathematical methods that emphasizes fundamental understanding and geometrical intuition. In addition to a complete list of standard subjects, it introduces important, contemporary topics like nonlinear differential equations, chaos and solitons. Part II employs the Maple software to cover the same topics as in Part I in a computer oriented approach to instruction. Using Maple liberates students from laborious tasks while helping them to concentrate entirely on concepts and on better visualizing the mathematical content. The focus of the text is on key ideas and basic technical and geometric insights presented in a way that closely reflects how physicists and engineers actually think about mathematics.
Este libro sigue el esquema básico de la asignatura troncal Matemáticas 2 (capítulos 1, 2, 3, 4 y 5) y parte del temario de las asignaturas Matemáticas 1 (capítulo 1) y Matemáticas 3 (capítulos 6 y 7), que los autores imparten en la EUETIB. No obstante, su contenido es perfectamente adaptable a cursos de álgebra lineal, cálculo en varias variables y ecuaciones diferenciales de cualquier ingeniería. El texto tiene como objetivo principal iniciar al estudiante en los conceptos básicos del álgebra lineal, el cálculo de funciones de varias variables, el análisis vectorial, las ecuaciones diferenciales y la teoría de las transformadas. Los contenidos se estructuran en tres partes. La primera parte trata del álgebra lineal e introduce los conceptos de valores y vectores propios. La segunda parte está dedicada a las funciones de varias variables: nociones básicas de límite, continuidad y derivación; cálculo de extremos libres y condicionados; integración múltiple y análisis vectorial. La tercera parte trata de las ecuaciones diferenciales de primer orden y de orden superior, la transformada de Laplace y la transformada de Fourier. Al final de cada capítulo, se incluye una recopilación de problemas resueltos y propuestos, junto con su resolución utilizando el programa de cálculo simbólico Maple.