Advanced Engineering Mathematics
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Through previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Now, ADVANCED ENGINEERING MATHEMATICS features revised examples and problems as well as newly added content that has been fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and problem sets. In this new edition, computational assistance in the form of a self contained Maple Primer has been included to encourage students to make use of such computational tools. The content has been reorganized into six parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, and much more. Booknews This revised textbook (second edition, 1987) introduces students of engineering, science, and applied mathematics to some of the mathematics and mathematical modeling employed by these disciplines. The prerequisite is a standard course in calculus, including partial derivatives, multiple integrals, improper integrals, and infinite series. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Pt. 1Ordinary Differential Equations1Ch. 1First-Order Differential Equations3Ch. 2Second-Order Differential Equations65Ch. 3The Laplace Transform113Ch. 4Series Solutions163Pt. 2Vectors and Linear Algebra199Ch. 5Vectors and Vector Spaces201Ch. 6Matrices and Systems of Linear Equations241Ch. 7Determinants311Ch. 8Eigenvalues, Diagonalization, and Special Matrices337Pt. 3Systems of Differential Equations and Qualitative Methods375Ch. 9Systems of Linear Differential Equations377Ch. 10Qualitative Methods and Systems of Nonlinear Differential Equations425Pt. 4Vector Analysis509Ch. 11Vector Differential Calculus511Ch. 12Vector Integral Calculus553Pt. 5Fourier Analysis, Orthogonal Expansions, and Wavelets623Ch. 13Fourier Series625Ch. 14The Fourier Integral and Fourier Transforms681Ch. 15Special Functions, Orthogonal Expansions, and Wavelets765Pt. 6Partial Differential Equations855Ch. 16The Wave Equation857Ch. 17The Heat Equation915Ch. 18The Potential Equation955Ch. 19Canonical Forms, Existence and Uniqueness of Solutions, and Well-Posed Problems987Pt. 7Complex Analysis1001Ch. 20Geometry and Arithmetic of Complex Numbers1003Ch. 21Complex Functions1027Ch. 22Complex Integration1065Ch. 23Series Representations of Functions1101Ch. 24Singularities and the Residue Theorem1121Ch. 25Conformal Mappings1163Pt. 8Historical Notes1211Ch. 26Development of Areas of Mathematics1213Ch. 27Biographical Sketches1225Answers and Solutions to Selected Odd-Numbered ProblemsIndex
