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999			_c48363 _d48363
001			19363166
003			OSt
005			20230220125306.0
008			161103s2017 ohu 000 0 eng
010			_a 2016958774
020			_a9781337274524
040			_aDLC _beng _erda _cDLC
041			_aeng
042			_apcc
082			_a620.00151
100	1		_aO'Neil, Peter V. _eauthor.
245	1	0	_aAdvanced engineering mathematics, SI / _cPeter V. O'Neil, University of Alabama at Birmingham
250			_a8th edition
263			_a1701
264		1	_aBoston, MA _bCengage, _c[2017]
264		4	_cc2017
300			_axvii, 839 pages ; _c 26 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
500			_aDr. Peter O?Neil has been a professor of mathematics at the University of Alabama at Birmingham since 1978. At the University of Alabama at Birmingham, he has served as chairman of mathematics, dean of natural sciences and mathematics, and university provost. Dr. Peter O?Neil has also served on the faculty at the University of Minnesota and the College of William and Mary in Virginia, where he was chairman of mathematics. He has been awarded the Lester R. Ford Award from the Mathematical Association of America. He received both his M.S and Ph.D. in mathematics from Rensselaer Polytechnic Institute. His primary research interests are in graph theory and combinatorial analysis.
505			_aPART I: ORDINARY DIFFERENTIAL EQUATIONS.1. First-Order Differential Equations.Terminology and Separable Equations. Singular Solutions, Linear Equations. Exact Equations. Homogeneous, Bernoulli and Riccati Equations.2. Second-Order Differential Equations.The Linear Second-Order Equation. The Constant Coefficient Homogeneous Equation. Particular Solutions of the Nonhomogeneous Equation. The Euler Differential Equation, Series Solutions. Frobenius Series Solutions.3. The Laplace Transform.Definition and Notation. Solution of Initial Value Problems. The Heaviside Function and Shifting Theorems. Convolution. Impulses and the Dirac Delta Function. Systems of Linear Differential Equations.4. Eigenfunction Expansions.Eigenvalues, Eigenfunctions, and Sturm-Liouville Problems. Eigenfunction Expansions, Fourier Series.Part II: PARTIAL DIFFERENTIAL EQUATIONS.5. The Heat Equation.Diffusion Problems in a Bounded Medium. The Heat Equation with a Forcing Term F(x,t). The Heat Equation on the Real Line. A Reformulation of the Solution on the Real Line. The Heat Equation on a Half-Line, The Two-Dimensional Heat Equation.6. The Wave Equation.Wave Motion on a Bounded Interval. The Effect of c on the Motion. Wave Motion with a Forcing Term F(x). Wave Motion in an Unbounded Medium. The Wave Equation on the Real Line. d'Alembert's Solution and Characteristics. The Wave Equation with a Forcing Term K(x,t). The Wave Equation in Higher Dimensions.7. Laplace's Equation.The Dirichlet Problem for a Rectangle. Dirichlet Problem for a Disk. The Poisson Integral Formula. The Dirichlet Problem for Unbounded Regions. A Dirichlet Problem in 3 Dimensions. The Neumann Problem. Poisson's Equation.8. Special Functions and Applications.Legendre Polynomials. Bessel Functions. Some Applications of Bessel Functions.9. Transform Methods of Solution.Laplace Transform Methods. Fourier Transform Methods. Fourier Sine and Cosine Transforms.Part III: MATRICES AND LINEAR ALGEBRA.10. Vectors and the Vector Space Rn.Vectors in the Plane and 3 - Space. The Dot Product. The Cross Product. n-Vectors and the Algebraic Structure of Rn. Orthogonal Sets and Orthogonalization. Orthogonal Complements and Projections.11. Matrices, Determinants and Linear Systems.Matrices and Matrix Algebra. Row Operations and Reduced Matrices. Solution of Homogeneous Linear Systems. Solution of Nonhomogeneous Linear Systems. Matrix Inverses. Determinants, Cramer's Rule. The Matrix Tree Theorem.12. Eigenvalues, Diagonalization and Special Matrices.Eigenvalues and Eigenvectors. Diagonalization. Special Matrices and Their Eigenvalues and Eigenvectors. Quadratic Forms.PART IV: SYSTEMS OF DIFFERENTIAL EQUATIONS.13. Systems of Linear Differential Equations.Linear Systems. Solution of X' = AX When A Is Constant. Exponential Matrix Solutions. Solution of X' = AX + G for Constant A.14. Nonlinear Systems and Qualitative Analysis.Nonlinear Systems and Phase Portraits. Critical Points and Stability. Almost Linear Systems, Linearization.Part V: VECTOR ANALYSIS. 15. Vector Differential Calculus.Vector Functions of One Variable. Velocity, Acceleration, and Curvature. The Gradient Field. Divergence and Curl. Streamlines of a Vector Field.16. Vector Integral Calculus.Line Integrals. Green's Theorem. Independence of Path and Potential Theory. Surface Integrals. Applications of Surface Integrals. Gauss's Divergence Theorem. Stokes's Theorem.PART VI: FOURIER ANALYSIS.17. Fourier Series.Fourier Series On [-L, L]. Fourier Sine and Cosine Series. Integration and Differentiation of Fourier Series. Properties of Fourier Coefficients. Phase Angle Form. Complex Fourier Series, Filtering of Signals.18. Fourier Transforms.The Fourier Transform. Fourier Sine and Cosine Transforms.PART VII: COMPLEX FUNCTIONS.19. Complex Numbers and Functions.Geometry and Arithmetic of Complex Numbers. Complex Functions, Limits. The Exponential and Trigonometric Functions. The Complex Logarithm. Powers.20. Integration.The Integral of a Complex Function. Cauchy's Theorem. Consequences of Cauchy's Theorem.21. Series Representations of Functions.Power Series. The Laurent Expansion.22. Singularities and the Residue Theorem.Classification of Singularities. The Residue Theorem. Evaluation of Real Integrals.23. Conformal Mappings.The Idea of a Conformal Mapping. Construction of Conformal Mappings.Notation.ANSWERS TO SELECTED PROBLEMS.
520			_aSPECIALIZED AND ADVANCED TOPICS ADDED AS WEB MODULES. In order to broaden coverage while keeping the length and cost of the book down, certain topics have been added as convenient web modules rather than appearing in the printed text. These modules include applications of complex analysis to the Dirichlet problem and to inverses of Laplace transforms, Lyapunov functions, the discrete Fourier transform, Maxwell?s equations, numerical methods for solving differential equations, LU factoring of matrices, limit cycles for systems of differential equations, and models of plane fluid flow. NEW ?MATH IN CONTEXT? FEATURES CONNECT THE MATHEMATICAL APPLICATIONS TO CURRENT ENGINEERING PROBLEMS. These special features specifically relate mathematical concepts and methods to real world problems that students will find in the workplace. THIS EDITION PRESENTS THE SOLUTION OF INITIAL VALUE PROBLEMS FOR WAVE MOTION AND DIFFUSION PHENOMENA UNDER A VARIETY OF CONDITIONS. This edition considers nonhomogeneous conditions, forcing terms, convection and insulation effects, and other conditions encountered in applications. COVERAGE INCLUDES EXPANDED TREATMENT OF SPECIAL FUNCTIONS. This edition includes even more material about both special functions and their applications to help you better prepare your students. THE BOOK OFFERS A GENERAL APPROACH TO THE SOLUTION OF PROBLEMS USING EIGENFUNCTION EXPANSIONS. NEW ORGANIZATION CLARIFIES AND CLEARLY DIFFERENTIATES TOPICS. This edition?s refined organization allows your students to focus on a particular idea and its applications before progressing to new topics. NEW EXAMPLES AND APPLICATIONS CLARIFY HOW TO SOLVE SPECIFIC TYPES OF PROBLEMS. These new examples apply the mathematical techniques that students are learning to real-world settings, such as the analysis of wave motion and diffusion processes.
650		0	_a Engineering mathematics.
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942			_2ddc _cBK _02