Название: Mathematical Methods for Engineering and Science, 2nd Edition
Автор: Merle C. Potter, Brian F. Feeny
Издательство: Springer
Год: 2023
Страниц: 512
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

This book introduces undergraduate students of engineering and science to applied mathematics essential to the study of many problems. Topics are differential equations, power series, Laplace transforms, matrices and determinants, vector analysis, partial differential equations, complex variables, and numerical methods. Approximately, 160 examples and 1000 homework problems aid students in their study. This book presents mathematical topics using derivations rather than theorems and proofs. This textbook is uniquely qualified to apply mathematics to physical applications (spring-mass systems, electrical circuits, conduction, diffusion, etc.), in a manner that is efficient and understandable.

Ordinary differential equations, including several physical applications, are reviewed in Chapter 1. Fourier series are also presented in this chapter so that differential equations describing the behavior of systems with periodic input functions can be solved. The solution of ordinary differential equations using power series is the subject of Chapter 2. Subsequent chapters introduce Laplace Transforms, Matrices and Determinants, Vector Analysis, Partial Differential Equations, Numerical Methods and Complex Variables. The material is presented so that any subset of these topics may be included in a three- or four-credit course. The actual instructional pace may vary with the topics chosen and the completeness of coverage. The style of presentation is such that the step-by-step derivations may be followed by the reader with a minimum of assistance from the instructor. Liberal use of examples and homework problems should aid the student in the study of the mathematical methods presented.

There are several additions to this edition of the text. Additional applications of separable, first-order linear, and exact ordinary differential equations are included. Applications of matrix methods have been added, including eigenvalue problems and least-squares fitting of data. Problems have also been added to help students exercise these topics. MATLAB, as a common and useful software tool, has been integrated into the text primarily in matrix computations and numerical solution of differential equations. An Introduction to MATLAB has been added as a section in the Appendix and should help students who lack experience with the package.

MATLAB is one of the most widely used computational packages. Its potential depth of computation and the sophistication of graphical display can be extensive. This appendix provides a very brief introduction, just meant to get the reader started. This introduction might best be reviewed while MATLAB is running on the reader’s computer, so that the reader can actively follow along, as probably the best way to learn the commands and coding is actually do them. There are examples in the book that use MATLAB, and these will introduce more details as needed. As the reader faces further needs, the abundant MATLAB documentation can be accessed using an internet search engine.