
Advanced Engineering Mathematics, 2/e
Michael Greenberg, University of Delaware
Published January, 1998 by Prentice Hall Engineering/Science/Mathematics
Copyright 1998, 1324 pp.
Cloth
ISBN 0133214311

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This clear, pedagogically rich book develops a strong understanding
of the mathematical principles and practices that today's engineers
and scientists need to know. Equally effective as either a textbook
or reference manual, it approaches mathematical concepts from a practicaluse
perspective making physical applications more vivid and substantial.
Its comprehensive instructional framework supports a conversational,
downtoearth narrative style offering easy accessibility and frequent
opportunities for application and reinforcement.
Develops a deep understanding of essential principles
as well as handson/howto knowledge of actual practices.
Serves as an excellent reference tool for both students
and practitioners with coverage reaching well beyond Ordinary Differential
Equations.
Reflects the author's vast engineering background, making
mathematical principles and applications more relevant to future engineers.
Physical applications integrated throughout the text include...
 Harmonic oscillator systems.<%16>
 Discussion of beats.
 Application of rank to stoichiometry and dimensional
analysis.
Designs pedagogy with the needs of both instructors and
students in mind, combining technical rigor with clarity and accessibility.
Features a wealth of diverse exercise and problem sets
to both challenge and reinforce students' understanding.
Provides unique Closure features at the end
of each section and chapter reviews at the end of each chapter
to review and summarize main points.
Includes useful and unique topics often ignored by other
texts, including...
 Dimensional analysis to minimize parameters and guide
plots and experiments.
 Introduction to singular integrals.
 Application of the mathematical concept of nonlinearity
to nerve impulse and visual perception.
 An “omega method” for the derivation of the various
space derivatives of base vectors in nonCartesian coordinate systems.
NEW—Updates and improves coverage throughout the
text to reflect the latest trends in the field and make the learning
process more effective and efficient.
NEW—Opens coverage with seven chapters on Ordinary
Differential Equations offering flexibility for use in either ODE
dedicated courses or combined ODE/Linear Algebra courses.
NEW—Incorporates the Maple Computer Algebra
System in the form of optional specialinterest sections and exercises.
I. ORDINARY DIFFERENTIAL EQUATIONS.
1. Introduction to Differential Equations.
2. Equations of First Order.
3. Linear Differential Equations of Second Order and Higher.
4. Power Series Solutions.
5. Laplace Transform.
6. Quantitative Methods: Numerical Solution of Differential
Equations.
7. Qualitative Methods: Phase Plane and Nonlinear Differential
Equations.
II. LINEAR ALGEBRA.
8. Systems of Linear Algebraic Equations; Gauss Elimination.
9. Vector Space.
10. Matrices and Linear Equations.
11. The Eigenvalue Problem.
12. Extension to Complex Case (Optional).
III. SCALAR and VECTOR FIELD THEORY.
13. Differential Calculus of Functions of Several Variables.
14. Vectors in 3Space.
15.Curves, Surfaces, and Volumes.
16. Scalar and Vector Field Theory.
IV. FOURIER SERIES AND PARTIAL DIFFERENTIAL EQUATIONS.
17. Fourier Series, Fourier Integral, Fourier Transform.
18. Diffusion Equation.
19. Wave Equation.
20. Laplace Equation.
V. COMPLEX VARIABLE THEORY.
21. Functions of a Complex Variable.
22. Conformal Mapping.
23. The Complex Integral Calculus.
24. Taylor Series, Laurent Series, and the Residue Theorem.
Appendix A: Review of Partial Fraction Expansions.
Appendix B: Existence and Uniqueness of Solutions of Systems
of Linear Algebraic Equations.
Appendix C: Table of Laplace Transforms.
Appendix D: Table of Fourier Transforms.
Appendix E: Table of Fourier Cosine and Sine Transforms.
Appendix F: Table of Conformal Maps.
