Advanced Engineering Mathematics

0.0

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. Key Features New Maple Primer - An Appendix on the use of Maple for computations encountered throughout the book (real and complex calculus operations, graphs, matrix and vector operations, calculations with special functions, etc). Expanded treatment of the construction and solution of mathematical models of important phenomena, such as mechanical systems, electrical circuits, planetary motion, and oscillation and diffusion processes. Amplified discussion of properties and applications of Legendre polynomials and Bessel functions, including a model for alternating current flow and a solution of Kepler's problem. The book is divided into 7 parts for ease of use. Includes a "Guide to Notation" in the front inside cover showing the symbols and notation used throughout the text paired with the section in which it is defined or used. Presents the correct development of concepts such as Fourier series and integrals, conformal mappings, and special functions, at the beginning of the text followed by applications and models of important phenomena, such as wave and heat propagation and filtering of signals. Includes numerous fully solved example problems as well as review problems following each section of the text. New and revised content including: An application of Laplace transform convolution to a replacement scheduling problem; Solution of Bessel's equation using the Laplace transform; Gram-Schmidt orthogonalization and production and production of orthogonal bases; Orthogonal projection of a vector onto a given subspace; The function space C[a;b]; Least squares and data fitting; Linear transformations and their matrix representations. Additional new material including: Application of vector integral theorems to the development of Maxwell's equations; Orthogonal curvilinear coordinates and vector operations in these coordinates; Use of the Laplace transform to solve partial differential equations involving wave and diffusion phenomena; A complex integral formula for the inverse Laplace transform of a function; LU factorization of matrices into products of lower and upper triangular matrices with an application to the efficient solution of systems of linear equations; Heaviside's formula for the computation of the inverse Laplace transform of a function. Table of Contents Part I: Ordinary Differential Equations 1. First-Order Differential Equations. 2. Linear Second-Order Equations. 3. The Laplace Transform 4. Series Solutions. 5. Approximation Of Solutions Part II: Vectors, Linear Algebra, And Systems Of Linear Differential Equations 6. Vectors And Vector Spaces. 7. Matrices And Linear Systems. 8. Determinants. 9. Eigenvalues, Diagonalization And Special Matrices 10. Systems Of Linear Differential Equations Part III: Vector Analysis 11. Vector Differential Calculus. 12. Vector Integral Calculus. Part IV: Fourier Analysis, Special Functions, And Eigenfunction Expansions 13. Fourier Series. 14. The Fourier Integral And Transforms. 15. Special Functions And Eigenfunction Expansions. Part V: Partial Differential Equations 16. The Wave Equation 17. The Heat Equation. 18. The Potential Equation. Part VI: Complex Functions 19. Complex Numbers And Functions. 20. Complex Integration. 21. Series Representations Of Functions. 22. Singularities And The Residue Theorem. 23. Conformal Mappings And Applications. Part VII: Probability And Statistics 24. Probability. 25. Statistics. Appendix A: Maple Primer. Answers To Selected Problems.