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Preface

This seventh edition of Advanced Engineering Mathematics differs from the sixth in four ways.
First, based on reviews and user comments, new material has been added, including the
following.

• Orthogonal projections and least squares approximations of vectors and functions. This pro-
vides a unifying theme in recognizing partial sums of eigenfunction expansions as projections
onto subspaces, as well as understanding lines of best fit to data points.
• Orthogonalization and the production of orthogonal bases.
• LU factorization of matrices.
• Linear transformations and matrix representations.
• Application of the Laplace transform to the solution of Bessel’s equation and to problems
involving wave motion and diffusion.
• Expanded treatment of properties and applications of Legendre polynomials and Bessel
functions, including a solution of Kepler’s problem and a model of alternating current flow.
• Heaviside’s formula for the computation of inverse Laplace transforms.
• A complex integral formula for the inverse Laplace transform, including an application to heat
diffusioninaslab.
• Vector operations in orthogonal curvilinear coordinates.
• Application of vector integral theorems to the development of Maxwell’s equations.
• An application of the Laplace transform convolution to a replacement scheduling problem.

TM
The second new feature of this edition is the interaction of the text with Maple .An
appendix (called A Maple Primer) is included on the use of Maple TM and references to the use of
Maple TM are made throughout the text.
Third, there is an added emphasis on constructing and analyzing models, using ordinary and
partial differential equations, integral transforms, special functions, eigenfunction expansions,
and matrix and complex function methods.
Finally, the answer section in the back of the book has been expanded to provide more
information to the student.
This edition is also shorter and more convenient to use than preceding editions. The chapters
comprising Part 8 of the Sixth Edition, Counting and Probability, and Statistics, are now available
on the 7e book website for instructors and students.

Supplements for Instructors:

• A detailed and completely revised Instructor’s Solutions Manual and
• PowerPoint Slides

are available through the Instructor’s Resource site at login.cengage.com.

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Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

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