Advanced engineering mathematics / Dennis G. Zill, Loyola Marymount University
- Author:
- Zill, Dennis G., 1940-
- Published:
- Burlington, MA : Jones & Bartlett Learning, [2016]
- Copyright Date:
- ©2018
- Edition:
- Sixth edition.
- Physical Description:
- xvi, 943 pages, 78 variously numbered pages ; 29 cm
- Contents:
- Machine generated contents note: 2.Introduction to Differential Equations -- 2.1.Definitions and Terminology -- 2.2.Initial-Value Problems -- 2.3.Differential Equations as Mathematical Models -- Review -- 2.First-Order Differential Equations -- 2.1.Solution Curves Without a Solution -- 2.1.1.Direction Fields -- 2.1.2.Autonomous First-Order DEs -- 2.2.Separable Equations -- 2.3.Linear Equations -- 2.4.Exact Equations -- 2.5.Solutions by Substitutions -- 2.6.A Numerical Method -- 2.7.Linear Models -- 2.8.Nonlinear Models -- 2.9.Modeling with Systems of First-Order DEs -- Review -- 3.Higher-Order Differential Equations -- 3.1.Theory of Linear Equations -- 3.1.1.Initial-Value and Boundary-Value Problems -- 3.1.2.Homogeneous Equations -- 3.1.3.Nonhomogeneous Equations -- 3.2.Reduction of Order -- 3.3.Homogeneous Linear Equations with Constant Coefficients -- 3.4.Undetermined Coefficients -- 3.5.Variation of Parameters -- 3.6.Cauchy-Euler Equations -- 3.7.Nonlinear Equations -- 3.8.Linear Models: Initial-Value Problems -- 3.8.1.Spring/Mass Systems: Free Undamped Motion -- 3.8.2.Spring/Mass Systems: Free Damped Motion -- 3.8.3.Spring/Mass Systems: Driven Motion -- 3.8.4.Series Circuit Analogue -- 3.9.Linear Models: Boundary-Value Problems -- 3.10.Green's Functions -- 3.10.1.Initial-Value Problems -- 3.10.2.Boundary-Value Problems -- 3.11.Nonlinear Models -- 3.12.Solving Systems of Linear Equations -- Review -- 4.The Laplace Transform -- 4.1.Definition of the Laplace Transform -- 4.2.The Inverse Transform and Transforms of Derivatives -- 4.2.1.Inverse Transforms -- 4.2.2.Transforms of Derivatives -- 4.3.Translation Theorems -- 4.3.1.Translation on the s-axis -- 4.3.2.Translation on the t-axis -- 4.4.Additional Operational Properties -- 4.4.1.Derivatives of Transforms -- 4.4.2.Transforms of Integrals -- 4.4.3.Transform of a Periodic Function -- 4.5.The Dirac Delta Function -- 4.6.Systems of Linear Differential Equations -- Review -- 5.Series Solutions of Linear Differential Equations -- 5.1.Solutions about Ordinary Points -- 5.1.1.Review of Power Series -- 5.1.2.Power Series Solutions -- 5.2.Solutions about Singular Points -- 5.3.Special Functions -- 5.3.1.Bessel Functions -- 5.3.2.Legendre Functions -- Review -- 6.Numerical Solutions of Ordinary Differential Equations -- 6.1.Euler Methods and Error Analysis -- 6.2.Runge-Kutta Methods -- 6.3.Multistep Methods -- 6.4.Higher-Order Equations and Systems -- 6.5.Second-Order Boundary-Value Problems -- Review -- 7.Vectors -- 7.1.Vectors in 2-Space -- 7.2.Vectors in 3-Space -- 7.3.Dot Product -- 7.4.Cross Product -- 7.5.Lines and Planes in 3-Space -- 7.6.Vector Spaces -- 7.7.Gram-Schmidt Orthogonalization Process -- Review -- 8.Matrices -- 8.1.Matrix Algebra -- 8.2.Systems of Linear Algebraic Equations -- 8.3.Rank of a Matrix -- 8.4.Determinants -- 8.5.Properties of Determinants -- 8.6.Inverse of a Matrix -- 8.6.1.Finding the Inverse -- 8.6.2.Using the Inverse to Solve Systems -- 8.7.Cramer's Rule -- 8.8.The Eigenvalue Problem -- 8.9.Powers of Matrices -- 8.10.Orthogonal Matrices -- 8.11.Approximation of Eigenvalues -- 8.12.Diagonalization -- 8.13.LU-Factorization -- 8.14.Cryptography -- 8.15.An Error-Correcting Code -- 8.16.Method of Least Squares -- 8.17.Discrete Compartmental Models -- Review -- 9.Vector Calculus -- 9.1.Vector Functions -- 9.2.Motion on a Curve -- 9.3.Curvature and Components of Acceleration -- 9.4.Partial Derivatives -- 9.5.Directional Derivative -- 9.6.Tangent Planes and Normal Lines -- 9.7.Curl and Divergence -- 9.8.Line Integrals -- 9.9.Independence of the Path -- 9.10.Double Integrals -- 9.11.Double Integrals in Polar Coordinates -- 9.12.Green's Theorem -- 9.13.Surface Integrals -- 9.14.Stokes' Theorem -- 9.15.Triple Integrals -- 9.16.Divergence Theorem -- 9.17.Change of Variables in Multiple Integrals -- Review -- 10.Systems of Linear Differential Equations -- 10.1.Theory of Linear Systems -- 10.2.Homogeneous Linear Systems -- 10.2.1.Distinct Real Eigenvalues -- 10.2.2.Repeated Eigenvalues -- 10.2.3.Complex Eigenvalues -- 10.3.Solution by Diagonalization -- 10.4.Nonhomogeneous Linear Systems -- 10.4.1.Undetermined Coefficients -- 10.4.2.Variation of Parameters -- 10.4.3.Diagonalization -- 10.5.Matrix Exponential -- Review -- 11.Systems of Nonlinear Differential Equations -- 11.1.Autonomous Systems -- 11.2.Stability of Linear Systems -- 11.3.Linearization and Local Stability -- 11.4.Autonomous Systems as Mathematical Models -- 11.5.Periodic Solutions, Limit Cycles, and Global Stability -- Review -- 12.Orthogonal Functions and Fourier Series -- 12.1.Orthogonal Functions -- 12.2.Fourier Series -- 12.3.Fourier Cosine and Sine Series -- 12.4.Complex Fourier Series -- 12.5.Sturm-Liouville Problem -- 12.6.Bessel and Legendre Series -- 12.6.1.Fourier-Bessel Series -- 12.6.2.Fourier-Legendre Series -- Review -- 13.Boundary-Value Problems in Rectangular Coordinates -- 13.1.Separable Partial Differential Equations -- 13.2.Classical PDEs and Boundary-Value Problems -- 13.3.Heat Equation -- 13.4.Wave Equation -- 13.5.Laplace's Equation -- 13.6.Nonhomogeneous Boundary-Value Problems -- 13.7.Orthogonal Series Expansions -- 13.8.Fourier Series in Two Variables -- Review -- 14.Boundary-Value Problems in Other Coordinate Systems -- 14.1.Polar Coordinates -- 14.2.Cylindrical Coordinates -- 14.3.Spherical Coordinates -- Review -- 15.Integral Transform Method -- 15.1.Error Function -- 15.2.Applications of the Laplace Transform -- 15.3.Fourier Integral -- 15.4.Fourier Transforms -- 15.5.Fast Fourier Transform -- Review -- 16.Numerical Solutions of Partial Differential Equations -- 16.1.Laplace's Equation -- 16.2.Heat Equation -- 16.3.Wave Equation -- Review -- 17.Functions of a Complex Variable -- 17.1.Complex Numbers -- 17.2.Powers and Roots -- 17.3.Sets in the Complex Plane -- 17.4.Functions of a Complex Variable -- 17.5.Cauchy-Riemann Equations -- 17.6.Exponential and Logarithmic Functions -- 17.7.Trigonometric and Hyperbolic Functions -- 17.8.Inverse Trigonometric and Hyperbolic Functions -- Review -- 18.Integration in the Complex Plane -- 18.1.Contour Integrals -- 18.2.Cauchy-Goursat Theorem -- 18.3.Independence of the Path -- 18.4.Cauchy's Integral Formulas -- Review -- 19.Series and Residues -- 19.1.Sequences and Series -- 19.2.Taylor Series -- 19.3.Laurent Series -- 19.4.Zeros and Poles -- 19.5.Residues and Residue Theorem -- 19.6.Evaluation of Real Integrals -- Review -- 20.Conformal Mappings -- 20.1.Complex Functions as Mappings -- 20.2.Conformal Mappings -- 20.3.Linear Fractional Transformations -- 20.4.Schwarz-Christoffel Transformations -- 20.5.Poisson Integral Formulas -- 20.6.Applications -- Review -- I.Derivative and Integral Formulas -- II.Gamma Function -- III.Table of Laplace Transforms -- IV.Conformal Mappings.
- Subject(s):
- ISBN:
- 9781284105902 hardcover text with access code
1284105903 hardcover text with access code - Note:
- Includes index.
- Source of Acquisition:
- Purchased with funds from the Paterno Libraries Endowment; 2016
- Endowment Note:
- Paterno Libraries Endowment
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