Mathematics for Physical Science and Engineering: Symbolic Computing Applications in Maple and Mathematica

ISBN-13: 9780128010006 / Angielski / Twarda / 2014 / 768 str.

Frank Harris

Opis

Mathematics for Physical Science and Engineering is a complete text in mathematics for physical science that includes the use of symbolic computation to illustrate the mathematical concepts and enable the solution of a broader range of practical problems. This book enables professionals to connect their knowledge of mathematics to either or both of the symbolic languages Maple and Mathematica. The book begins by introducing the reader to symbolic computation and how it can be applied to solve a broad range of practical problems. Chapters cover topics that include: infinite series; complex numbers and functions; vectors and matrices; vector analysis; tensor analysis; ordinary differential equations; general vector spaces; Fourier series; partial differential equations; complex variable theory; and probability and statistics. Each important concept is clarified to students through the use of a simple example and often an illustration. This book is an ideal reference for upper level undergraduates in physical chemistry, physics, engineering, and advanced/applied mathematics courses. It will also appeal to graduate physicists, engineers and related specialties seeking to address practical problems in physical science.

• Clarifies each important concept to students through the use of a simple example and often an illustration
• Provides quick-reference for students through multiple appendices, including an overview of terms in most commonly used applications (Mathematica, Maple)
• Shows how symbolic computing enables solving a broad range of practical problems

Recenzje

"...a remarkably clear and impressively well-balanced introduction to mathematical methods for physicists and engineers.it does a very good job of picking the most important techniques." --MAA.org, Aug 2015

"...designed to clarify and optimize the efficiency of the student's acquisition of mathematical understanding and skill and...provide students with a mathematical toolbox that will rapidly become of routine use in a scientific or engineering career." --Zentralblatt MATH, Sep 2014

Spis treści

1. Computers, Science, and Engineering 2. Infinite Series 3. Complex Numbers and Functions 4. Vectors and Matrices 5. Matrix Transformations 6. Multidimensional Problems7. Vector Analysis8. Tensor Analysis9. Gamma Function10. Ordinary Differential Equations11. General Vector Spaces12. Fourier Series13. Integral Transforms 14. Series Solutions: Important ODEs14. General Vector Spaces 15. Partial Differential Equations16. Calculus of Variations17. Complex Variable Theory18. Probability and StatisticsAppendix A Methods for Making PlotsAppendix B Printing Tables of Function ValuesAppendix C Data Structures for Symbolic ComputingAppendix D Symbolic Computing of Recurrences FormulasAppendix E Partial FractionsAppendix F Mathematical InductionAppendix G Constrained ExtremaAppendix H Symbolic Computing for Vector AnalysisAppendix I Maple Tensor UtilitiesAppendix J Wronskians in ODE TheoryAppendix K Maple Code for Associated Legendre Functions and Spherical HarmonicsIndex

O autorze

Frank E. Harris was awarded his A. B. (Chemistry) from Harvard University in 1951 and his Ph.D. (Physical Chemistry) from University of California in 1954. The author of 244 research publications and multiple books, Dr. Harris has been a Professor of Physics and Chemistry, University of Utah and Resident Adjunct Professor of Chemistry, Quantum Theory Project, University of Florida. He served on the Editorial Board of the International Journal of Quantum Chemistry, and has been named a Fellow for both the American Institute of Chemists and the American Physical Society.