##### PREFACE OF ADVANCED ENGINEERING MATHEMATICS

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. GRAPH THEORY

• Orthogonal projections and least squares approximations of vectors and functions. This provides 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. MATERIALS SCIENCE AND ENGINEERING SEMICONDUCTOR

• Heaviside’s formula for the computation of inverse Laplace transforms.

• A complex integral formula for the inverse Laplace transform, including an application to heat diffusion in a slab. ROBOT DYNAMICS AND CONTROL

• Vector operations in orthogonal curvilinear coordinates.

• Application of vector integral theorems to the development of Maxwell’s equations.ADVANCED ENGINEERING MATHEMATICS

• An application of the Laplace transform convolution to a replacement scheduling problem.ADVANCED ENGINEERING MATHEMATICS

The second new feature of this edition is the interaction of the text with MapleTM. An appendix (called A Maple Primer) is included on the use of MapleTM and references to the use of MapleTM are made throughout the text.ADVANCED ENGINEERING MATHEMATICS

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.ELECTRIC POWER GENERATION

Finally, the answer section in the back of the book has been expanded to provide more information to the student. ELECTRONIC CIRCUIT ANALYSIS

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. FLUID DYNAMICS

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