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Full Description
Beginning with linear algebra and later expanding into calculus of variations, Advanced Engineering Mathematics provides accessible and comprehensive mathematical preparation for advanced undergraduate and beginning graduate students taking engineering courses. This book offers a review of standard mathematics coursework while effectively integrating science and engineering throughout the text. It explores the use of engineering applications, carefully explains links to engineering practice, and introduces the mathematical tools required for understanding and utilizing software packages.
Provides comprehensive coverage of mathematics used by engineering students
Combines stimulating examples with formal exposition and provides context for the mathematics presented
Contains a wide variety of applications and homework problems
Includes over 300 figures, more than 40 tables, and over 1500 equations
Introduces useful Mathematica™ and MATLAB® procedures
Presents faculty and student ancillaries, including an online student solutions manual, full solutions manual for instructors, and full-color figure sides for classroom presentations
Advanced Engineering Mathematics
covers ordinary and partial differential equations, matrix/linear algebra, Fourier series and transforms, and numerical methods. Examples include the singular value decomposition for matrices, least squares solutions, difference equations, the z-transform, Rayleigh methods for matrices and boundary value problems, the Galerkin method, numerical stability, splines, numerical linear algebra, curvilinear coordinates, calculus of variations, Liapunov functions, controllability, and conformal mapping.This text also serves as a good reference book for students seeking additional information. It incorporates Short Takes sections, describing more advanced topics to readers, and Learn More about It sections with direct references for readers wanting more in-depth information.
Contents
Linear Algebraic Equations, Matrices, and Eigenvalues. Matrix Theory. Scalar ODEs I: Homogeneous Problems. Scalar ODEs II: Nonhomogeneous Problems. Linear Systems of ODEs. Geometry, Calculus, and Other Tools. Integral Theorems, Multiple Integrals, and Applications. Numerical Methods I. Fourier Series. Partial Differential Equations Models. Separation of Variables for PDEs. Numerical Methods II. Optimization. Calculus of Variations. Functions of a Complex Variable. Conformal Mappings and the Laplace Equation. Integral Transform Methods. Nonlinear Ordinary Differential Equations. Key Terms. Reference. Appendices. Index.
