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Mathematics for Physical Science and Engineering
Symbolic Computing Applications in Maple and Mathematica
A complete textbook for graduate physicists, engineers and related specialties seeking to address practical problems in physical science, featuring extensive use of symbolic computation from Maple and Mathematica
Frank E. Harris (Author)
9780128010006
Hardback, published 30 June 2014
944 pages
27.6 x 21.5 x 4.5 cm, 1.98 kg
"...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
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.
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
