Advanced Engineering Mathematics

商家名称	信用等级	购买信息	订购本书
		Advanced Engineering Mathematics
		Advanced Engineering Mathematics

基本信息·出版社：CL-Engineering
·页码：1194 页
·出版日期：2002年07月
·ISBN：0534400779
·International Standard Book Number：0534400779
·条形码：9780534400774
·EAN：9780534400774
·版本：5
·装帧：精装
·正文语种：英语

内容简介 Through four editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models.ADVANCED ENGINEERING MATHEMATICS featuries a greater number of examples and problems and is 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 incorporate the use of such leading software packages as MAPLE. Computational assistance, exercises and projects have been included to encourage students to make use of these computational tools.The content is organized into eight-parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, Special Functions, Partial Differential Equations, Complex Analysis, and Historical Notes.
作者简介 Served on the faculty at the University of Minnesota, The College of William and Mary in Virginia, where he was chairman of mathematics, and the University of Alabama at Birmingham, where he was chairman of mathematics, dean of natural sciences and mathematics, and university provost. Primary research interests are in graph theory, combinatorial analysis and applications of mathematics to problems in the physical and biological sciences and engineering
媒体推荐 "I found the diagrams and graphs to be particularly good for a book of this nature. I feel that the strength of the book is its breadth and clear organization. It is an excellent reference also."

"There are more than enough problems. This is the best part of the book."

"The independence of the various chapters is a great strength of the book."

"The ordinary differential equations/Laplace/systems material is very well-written and the students are very happy with it."
目录
Part I: ORDINARY DIFFERENTIAL EQUATIONS. 1. First Order Differential Equations. Preliminary Concepts. General and Particular Solutions. Implicitly Defined Solutions. Integral Curves. The Initial Value Problem. Direction Fields. Separable Equations. Some Applications of Separable Differential Equations. Linear Differential Equations. Exact Differential Equations. Integrating Factors. Separable Equations and Integrating Factors. Linear Equations and Integrating Factors. Homogeneous, Bernoulli and Riccati Equations. Homogeneous Differential Equations. The Bernoulli Equation. The Riccati Equation. Applications to Mechanics, Electrical Circuits and Orthogonal Trajectories. Mechanics. Electrical Circuits. Orthogonal Trajectories. Existence and Uniqueness for Solutions of Initial Value Problems. 2. Second Order Differential Equations. Preliminary Concepts. Theory of Solutions of y" + p(x)y'' + q(x)y = f(x). The Homogeneous Equation y" + p(x)y'' + q(x) = 0. The Nonhomogeneous Equation y" + p(x)y'' + q(x)y = f(x). Reduction of Order. The Constant Coefficient Homogeneous Linear Equation. Case 1 A2 - 4B > 0. Case 2 A2 - 4B = 0. Case 3 A2 - 4B < 0. An Alternative General Solution In the Complex Root Case. Euler''s Equation. The Nonhomogeneous Equation y" + p(x)y'' + q(x)y = f(x). The Method of Variation of Parameters. The Method of Undetermined Coefficients. The Principle of Superposition. Higher Order Differential Equations. Application of Second Order Differential Equations to a Mechanical System. Unforced Motion. Forced Motion. Resonance. Beats. Analogy With An Electrical Circuit. 3. The Laplace Transform. Definition and Basic Properties. Solution of Initial Value Problems Using the Laplace Transform. Shifting Theorems and the Heaviside Function. The First Shifting Theorem. The Heaviside Function and Pulses. The Second Shifting Theorem. Analysis of Electrical Circuits. Convolution. Unit Impulses and the Dirac Delta Function. Laplace Transform Solution of Systems. Differential Equations With Polynomial Coefficients. 4. Series Solutions. Power Series Solutions of Initial Value Problems. Power Series Solutions Using Recurrence Relations. Singular Points and the Method of Frobenius. Second Solutions and Logarithm Factors. Appendix on Power Series. Convergence of Power Series. Algebra and Calculus of Power Series. Taylor and Maclaurin Expansions. Shifting Indices. Part II: VECTORS AND LINEAR ALGEBRA. 5. Vectors and Vector Spaces. The Algebra and Geometry of Vectors. The Dot Product. The Cross Product. The Vector Space Rn. Linear Independence, Spanning Sets and Dimension in Rn. Abstract Vector Spaces. 6. Matrices and Systems of Linear Equations. Matrices. Matrix Algebra. Matrix Notation for Systems of Linear Equations. Some Special Matrices. Another Rationale for the Definition of Matrix Multiplication. Random Walks in Crystals. Elementary Row Operations and Elementary Matrices. The Row Echelon Form of a Matrix. The Row and Column Spaces of a Matrix and Rank of a Matrix. Solution of Homogeneous Systems of Linear Equations. The Solution Space of AX = O. Nonhomogeneous Systems of Linear Equations. The Structure of Solutions of AX = B. Existence and Uniqueness of Solutions of AX = B. Summary for Linear Systems. Matrix Inverses. A Method for Finding A-1. 7. Determinants. Permutations. Definition of the Determinant. Properties of Determinants. Evaluation of Determinants by Elementary Row and Column Operations. Cofactor Expansions. Determinants of Triangular Matrices. A Determinant Formula for a Matrix Inverse. Cramer''s Rule. The Matrix Tree Theorem. 8. Eigenvalues, Diagonalization, and Special Matrices. Eigenvalues and Eigenvectors. Gerschgorin''s Theorem. Diagonalization of Matrices. Orthogonal and Symmetric Matrices. Quadratic Forms. Unitary, Hermitian and Skew Hermitian Matrices. Part III: SYSTEMS OF DIFFERENTIAL EQUATIONS AND QUALITATIVE METHODS. 9. Systems of Linear Differential Equations. Theory of the Homogeneous System X'' = AX. General Solution of the Nonhomogeneous System X'' = AX + G. Solution of X'' = AX When A Is Constant. Solution of X'' = AX When A Has Complex Eigenvalues. Solution of X'' = AX When A Does Not Have n Linearly Independent Eigenvectors. Solution of X'' = AX By Diagonalizing A. Exponential Matrix Solutions of X'' = AX. Solution of X'' = AX + G. Variation of Parameters. Solution of X'' = AX + G By Diagonalizing A. 10. Qualitative Methods and Systems of Nonlinear Differential Equations. Nonlinear Systems and Existence of Solutions. The Phase Plane, Phase Portraits and Direction Fields. Phase Portraits of Linear Systems. Critical Points and Stability. Almost Linear Systems. Predator/Prey Population Models. A Simple Predator/Prey Model. An Extended Predator/Prey Model. Competing Species Models. A Simple Competing Species Model. An Extended Competing Species Model. Lyapunov''s Stability Criteria. Limit Cycles and Periodic Solutions. Part IV: VECTOR ANALYSIS. 11. Vector Differential Calculus. Vector Functions of One Variable. Velocity, Acceleration, Curvature and Torsion. Tangential and Normal Components of Acceleration. Curvature As a Function of t. The Frenet Formulas. Vector Fields and Streamlines. The Gradient Field and Directional Derivatives. Level Surfaces, Tangent Planes and Normal Lines. Divergence and Curl. A Physical Interpretation of Divergence. A Physical Interpretation of Curl. 12. Vector Integral Calculus. Line Integrals. Line Integral With Respect to Arc Length. Green''s Theorem. An Extension of Green''s Theorem. Independence of Path and Potential Theory In the Plane. A More Critical Look at Theorem 12.5. Surfaces in 3- Space and Surface Integrals. Normal Vector to a Surface. The Tangent Plane to a Surface. Smooth and Piecewise Smooth Surfaces. Surface Integrals. Applications of Surface Integrals. Surface Area. Mass and Center of Mass of a Shell. Flux of a Vector Field Across a Surface. Preparation for the Integral Theorems of Gauss and Stokes. The Divergence Theorem of Gauss. Archimedes''s Principle. The Heat Equation. The Divergence Theorem As A Conservation of Mass Principle. Green''s Identities. The Integral Theorem of Stokes. An Interpretation of Curl. Potential Theory in 3- Space. Part V: FOURIER ANALYSIS, ORTHOGONAL EXPANSIONS AND WAVELETS. 13. Fourier Series. Why Fourier Series? The Fourier Series of a Function. Even and Odd Functions. Convergence of Fourier Series. Convergence at the End Points. A Second Convergence Theorem. Partial Sums of Fourier Series. The Gibbs Phenomenon. Fourier Cosine and Sine Series. The Fourier Cosine Series of a Function. The Fourier Sine Series of a Function. Integration and Differentiation of Fourier Series. The Phase Angle Form of a Fourier Series. Complex Fourier Series and the Frequency Spectrum. Review of Complex Numbers. Complex Fourier Series. 14. The Fourier Integral and Fourier Transforms. The Fourier Integral. Fourier Cosine and Sine Integrals. The Complex Fourier Integral and the Fourier Transform. Additional Properties and Applications of the Fourier Transform. The Fourier Transform of a Derivative. Frequency Differentiation. The Fourier Transform of an Integral. Convolution. Filtering and the Dirac Delta Function. The Windowed Fourier Transform. The Shannon Sampling Theorem. Lowpass and Bandpass Filters. The Fourier Cosine and Sine Transforms. The Discrete Fourier Transform. Linearity and Periodicity. The Inverse N - Point DFT. DFT Approximation of Fourier Coefficients. Sampled Fourier Series. Approximation of a Fourier Transform by an N - Point DFT. Filtering. The Fast Fourier Transform. Computational Efficiency of the FFT. Use of the FFT in Analyzing Power Spectral Densities of Signals. Filtering Noise From a Signal. Analysis of the Tides in Morro Bay. 15. Special Functions, Orthogonal Expansions and Wavelets. Legendre Polynomials. A Generating Function for the Legendre Polynomials. A Recurrence Relation for the Legendre Polynomials. Orthogonality of the Legendre Polynomials. Fourier-Legendre Series. Computation of Fourier-Legendre Coefficients. Zeros of the Legendre Polynomials. Derivative and Integral Formulas for Pn(x). Bessel Functions. The Gamma Function. Bessel Functions of the First Kind and Solutions of Bessel''s Equation. Bessel Functions of the Second Kind. Modified Bessel Functions. Some Applications of Bessel Functions. A Generating Function for Jn(x). An Integral Formula for Jn(x). A Recurrence Relation for Jv(x). Zeros of Jv(x). Fourier-Bessel Expansions. Fourier-Bessel Coefficients. Sturm-Liouville Theory and Eigenfunction Expansions. The Sturm-Liouville Problem. The Sturm-Liouville Theorem. Eigenfunction Expansions. Approximation In the Mean and Bessel''s Inequality. Convergence in the Mean and Parseval''s Theorem. Completeness of the Eigenfunctions. Orthogonal Polynomials. Chebyshev Polynomials. Laguerre Polynomials. Hermite Polynomials. Wavelets. The Idea Behind Wavelets. The Haar Wavelets. A Wavelet Expansion. Multiresolution Analysis With Haar Wavelets. General Construction of Wavelets and Multiresolution Analysis. Shannon Wavelets. Part VI: PARTIAL DIFFERENTIAL EQUATIONS. 16. The Wave Equation. The Wave Equation and Initial and Boundary Condition. Fourier Series Solutions of the Wave Equation. Vibrating String with Given Initial Velocity and Zero Initial Displacement. Vibrating String With Initial Displacement and Velocity. Verification of Solutions. Transformation of Boundary Value Problems Involving the Wave Equation. Effects of Initial Condition and Constants on the Motion. Wave Motion Along Infinite and Semi-Infinite String. Fourier Transform Solution of Problems on Unbounded Domains. Characteristics and d''Alembert''s Solution. A Nonhomogeneous Wave Equation. Forward and Backward Waves. Normal Modes of Vibration of a Circular Elastic Membrane. Vibrations of a Circular Elastic Membrane, Revisited. Vibrations of a Rectangular Membrane. 17. The Heat Equation. The Heat Equation and Initial and Boundary Conditions. Fourier Series Solutions of the Heat Equation. Ends of the Bar Kept at Temperature Zero. Temperature in a Bar With Insulated Ends. Temperature Distribution in a Bar With Radiating End. Transformations of Boundary Value Problems Involving ...
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