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.
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Table of Contents
1. Computers, Science, and Engineering 2. Infinite Series 3. Complex Numbers and Functions 4. Vectors and Matrices 5. Matrix Transformations 6. Multidimensional Problems 7. Vector Analysis 8. Tensor Analysis 9. Gamma Function 10. Ordinary Differential Equations 11. General Vector Spaces 12. Fourier Series 13. Integral Transforms 14. Series Solutions: Important ODEs 14. General Vector Spaces 15. Partial Differential Equations 16. Calculus of Variations 17. Complex Variable Theory 18. Probability and Statistics Appendix A Methods for Making Plots Appendix B Printing Tables of Function Values Appendix C Data Structures for Symbolic Computing Appendix D Symbolic Computing of Recurrences Formulas Appendix E Partial Fractions Appendix F Mathematical Induction Appendix G Constrained Extrema Appendix H Symbolic Computing for Vector Analysis Appendix I Maple Tensor Utilities Appendix J Wronskians in ODE Theory Appendix K Maple Code for Associated Legendre Functions and Spherical Harmonics Index
