[...]... 2nd ed., Boston: Butterworth-Heinemann, 1996 Physics with Maple Frank Y Wang Copyright â 2006 WILEY-VCH Verlag GmbH & Co 1 Introduction In this chapter we offer a brief introduction to Maple and its application to physics We demonstrate Maples capabilities in algebraic manipulations, graphs and calculus Applying basic principles in mechanics to set equations, we employ Maple to solve physical problems;... them from experimenting with the worksheets to discover how they work, and in this process one begins building up the foundation for their advancement of knowledge in later years The most important aspect for every topic is to discern the central physical ideas Physics with Maple: The Computer Algebra Resource for Mathematical Methods in Physics Frank Y Wang Copyright â 2006 WILEY-VCH Verlag GmbH & Co... attack research problems Using a computer with a projector, the author has demonstrated the use of Maple during lectures in a classroom; we perform calculations using Maple, and defer or skip lengthy algebraic manipulation so that we maintain the focus of students on underlying physical principles By introducing a topic with results generated almost instantly with Maple, we provide a preview of what a... between intermediate and advanced undergraduate level, for a student who has completed general physics and calculus courses By solving problems with Maple, one strengthens their physics knowledge, and acquires computer skills A trend in recent years for many physics textbooks is the inclusion of computer-related topics For instance, the third edition of Classical Electrodynamics by Jackson, published... physical problems; our approach is to learn Maple commands directly from working examples 1.1 Overview Maple is software for symbolic computation With conventional software, calculations are restricted to numerical values, but Maple can manipulate symbolic expressions For the most basic usage, Maple serves as a numeric calculator, as in the following examples Using Maple to do numerical computations is straightforward:... 1267650600228229401496703205376 ẳà 13.37908816 > > ằ ã ằẵ é à 4 3 1.333333333 Physics with Maple: The Computer Algebra Resource for Mathematical Methods in Physics Frank Y Wang Copyright â 2006 WILEY-VCH Verlag GmbH & Co KGaA, Weinheim ISBN: 3-5 2 7-4 064 0-9 2 1 Introduction > ìếệỉạ à 2I > ẩ é ẩ á ắẳà > 3.1415926535897932385 ĩễẩ à > e é à > 23.14069264 > ẩ ĩễẵà (e) > é à 22.45915771 The rst calculation... dimension shown in Figure 1.3: particle 1 with mass m1 moves with initial velocity v1i , and particle 2 with mass m2 moves with initial velocity v2i Because v1i > v2i , particle 1 will catch up with particle 2 Find the nal velocities of particles 1 and 2 after the collision 1.2 Basic Algebra and Solving Equations ẹẵ ẵ ẹắ ắ 13 ẹẵ ẵ before ẹắ ắ after Figure 1.3: One-dimensional collision problem Solution... precise input to produce the correct results In this process we are compelled to examine the underlying physics in every layer We believe that, through consideration of signicant physical problems with computer software such as Maple, a students understanding of physics is greatly strengthened Frank Y Wang New York City, August 2005 Guide for Users The objective of this book is to enable a student to... Weinheim ISBN: 3-5 2 7-4 064 0-9 XVIII Guide for Users Many exercises at the end of a chapter are sophisticated: they serve to provide additional information to the main text and to whet a students appetite for advanced topics One is not expected to be able to solve all of them, but nonetheless one should grasp the central ideas Furthermore, identifying a problem for which solution with Maple is suitable... that problem; for all chapters, an open-ended question is provided for the reader to discover problems from physics textbooks, and to create their own exercises by developing Maple worksheets to illustrate the advantage of an approach with computer algebra Such an exercise provides research projects of innite variety The reader is strongly encouraged to export a Maple worksheet as ỉẹé text, and to establish . 1.1 > 8 > 4 > 1267650600228229401496703205376 > 13.37908816 > 4 3 > 1.333333333 Physics with Maple : The Computer Algebra Resource for Mathematical Methods in Physics. Frank Y. Wang Copyright © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-5 2 7-4 064 0-9 Physics. ideas. Physics with Maple : The Computer Algebra Resource for Mathematical Methods in Physics. Frank Y. Wang Copyright © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-5 2 7-4 064 0-9 XVIII. SystemswithManyDegreesofFreedom 86 3.6 ForceofConstraint 89 Physics with Maple : The Computer Algebra Resource for Mathematical Methods in Physics. Frank Y. Wang Copyright © 2006 WILEY-VCH Verlag