In the four previous editions the author presented a text firmly grounded in the mathematics that engineers and scientists must understand and know how to use. Tapping into decades of teaching at the US Navy Academy and the US Military Academy and serving for twenty-five years at (NASA) Goddard Space Flight, he combines a teaching and practical experience that is rare among authors of advanced engineering mathematics books.
This edition offers a smaller, easier to read, and useful version of this classic textbook. While competing textbooks continue to grow, the book presents a slimmer, more concise option. Instructors and students alike are rejecting the encyclopedic tome with its higher and higher price aimed at undergraduates.
To assist in the choice of topics included in this new edition, the author reviewed the syllabi of various engineering mathematics courses that are taught at a wide variety of schools. Due to time constraints an instructor can select perhaps three to four topics from the book, the most likely being ordinary differential equations, Laplace transforms, Fourier series and separation of variables to solve the wave, heat, or Laplace's equation. Laplace transforms are occasionally replaced by linear algebra or vector calculus.
Sturm-Liouville problem and special functions (Legendre and Bessel functions) are included for completeness. Topics such as z-transforms and complex variables are now offered in a companion book, Advanced Engineering Mathematics: A Second Course by the same author.
MATLAB is still employed to reinforce the concepts that are taught. Of course, this Edition continues to offer a wealth of examples and applications from the scientific and engineering literature, a highlight of previous editions. Worked solutions are given in the back of the book.
List of Definitions
Chapter 1: First-Order Ordinary Differential Equations 1
Chapter 2: Higher-Order Ordinary Differential Equations
Chapter 3: Linear Algebra
Chapter 4: Vector Calculus
Chapter 5: Fourier Series
Chapter 6: The Fourier Transform
Chapter 7: The Laplace Transform
Chapter 8: The Wave Equation
Chapter 9: The Heat Equation
Chapter 10: Laplace’s Equation
Chapter 11: The Sturm-Liouville Problem
Chapter 12: Special Functions
Appendix A: Derivation of the Laplacian in Polar Coordinates 565
Appendix B: Derivation of the Laplacian in Spherical Polar Coordinates 566
Answers
Index
Biography
Dean G. Duffy is a former mathematics instructor at the US Naval Academy and US Military Academy. He spent 25 years working on numerical weather prediction, oceanic wave modeling, and dynamical meteorology at NASA’s Goddard Space Flight Center. Prior to this, he was a numerical weather prediction officer in the US Air Force. He earned his Ph.D. in meteorology from MIT. Dr. Duffy has written several books on transform methods, engineering mathematics, and mixed boundary value problems including Green’s Functions with Applications, Second Edition, published by CRC Press.
