This book is designed to serve as a core text for courses in advanced engineering mathematics required by many engineering departments. The style of presentation is such that the student, with a minimum of assistance, can follow the step-by-step derivations. Liberal use of examples and homework problems aid the student in the study of the topics presented.
Ordinary differential equations, including a number of physical applications, are reviewed in Chapter One. The use of series methods are presented in Chapter Two, Subsequent chapters present Laplace transforms, matrix theory and applications, vector analysis, Fourier series and transforms, partial differential equations, numerical methods using finite differences, complex variables, and wavelets. The material is presented so that four or five subjects can be covered in a single course, depending on the topics chosen and the completeness of coverage.
Incorporated in this textbook is the use of certain computer software packages. Short tutorials on Maple, demonstrating how problems in engineering mathematics can be solved with a computer algebra system, are included in most sections of the text. Problems have been identified at the end of sections to be solved specifically with Maple, and there are computer laboratory activities, which are more difficult problems designed for Maple. In addition, MATLAB and Excel have been included in the solution of problems in several of the chapters.
There is a solutions manual available for those who select the text for their course. This text can be used in two semesters of engineering mathematics. The many helpful features make the text relatively easy to use in the classroom.
Chapter 1: Ordinary Differential Equations.
Chapter 2: Series Method.-
Chapter 3: Laplace Transforms.
Chapter 4: The Theory of Matrices.
Chapter
5: Matrix Applications.
Chapter 6: Vector Analysis.
Chapter 7: Fourier
Series.
Chapter 8: Partial Differential Equations.
Chapter 9: Numerical
Methods.
Chapter 10: Complex Variables.
Chapter 11: Wavelets.- For Further
Study.- Appendices.
Merle C. Potter received his Ph.D. from The University of Michigan and is Professor Emeritus of Mechanical Engineering at Michigan State University. He has co-authored textbooks based on teaching Thermodynamics, Fluid Mechanics, Applied Mathematics, and related subjects. Dr. Potters research included the stability of various fluid flows, separated flow around bodies, and energy conservation studies. He has authored and coauthored 34 textbooks and exam review books. Jack L. Lessing received his Ph.D. in mathematics from the University of Illinois and after two years at Bell Laboratories took a position at the University of Michigan. During his long tenure at the University of Michigan he published textbooks, devised new courses, served as thesis advisor for many Ph.D. candidates, published numerous research papers and received the prestigious AMOCO award for his outstanding teaching. Edward F. Aboufadel received his Ph.D. from Rutgers University and is an Assistant Vice President & Professor of Mathematics at Grand Valley State University. He is an applied mathematician and the co-author of a textbook on wavelets. Aboufadels research projects have included automated pothole detection, visualizing water pollution data, and mathematical designs for 3D printing.
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