book

Advanced Engineering Mathematics, 6th Edition

by Dennis G. Zill

August 2016

Intermediate to advanced

1024 pages

50h 1m

English

Jones & Bartlett Learning

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1.1 Definitions and Terminology1.2 Initial-Value Problems1.3 Differential Equations as Mathematical ModelsChapter 1 in Review
2.1 Solution Curves Without a Solution2.1.1 Direction Fields2.1.2 Autonomous First-Order DEs2.2 Separable Equations2.3 Linear Equations2.4 Exact Equations2.5 Solutions by Substitutions2.6 A Numerical Method2.7 Linear Models2.8 Nonlinear Models2.9 Modeling with Systems of First-Order DEsChapter 2 in Review
3.1 Theory of Linear Equations3.1.1 Initial-Value and Boundary-Value Problems3.1.2 Homogeneous Equations3.1.3 Nonhomogeneous Equations3.2 Reduction of Order3.3 Homogeneous Linear Equations with Constant Coefficients3.4 Undetermined Coefficients3.5 Variation of Parameters3.6 Cauchy–Euler Equations3.7 Nonlinear Equations3.8 Linear Models: Initial-Value Problems3.8.1 Spring/Mass Systems: Free Undamped Motion3.8.2 Spring/Mass Systems: Free Damped Motion3.8.3 Spring/Mass Systems: Driven Motion3.8.4 Series Circuit Analogue3.9 Linear Models: Boundary-Value Problems3.10 Green’s Functions3.10.1 Initial-Value Problems3.10.2 Boundary-Value Problems3.11 Nonlinear Models3.12 Solving Systems of Linear EquationsChapter 3 in Review
4.1 Definition of the Laplace Transform4.2 The Inverse Transform and Transforms of Derivatives4.2.1 Inverse Transforms4.2.2 Transforms of Derivatives4.3 Translation Theorems4.3.1 Translation on the s-axis4.3.2 Translation on the t-axis4.4 Additional Operational Properties4.4.1 Derivatives of Transforms4.4.2 Transforms of Integrals4.4.3 Transform of a Periodic Function4.5 The Dirac Delta Function4.6 Systems of Linear Differential EquationsChapter 4 in Review

5.1 Solutions about Ordinary Points5.1.1 Review of Power Series5.1.2 Power Series Solutions5.2 Solutions about Singular Points5.3 Special Functions5.3.1 Bessel Functions5.3.2 Legendre FunctionsChapter 5 in Review
6.1 Euler Methods and Error Analysis6.2 Runge–Kutta Methods6.3 Multistep Methods6.4 Higher-Order Equations and Systems6.5 Second-Order Boundary-Value ProblemsChapter 6 in Review
7.1 Vectors in 2-Space7.2 Vectors in 3-Space7.3 Dot Product7.4 Cross Product7.5 Lines and Planes in 3-Space7.6 Vector Spaces7.7 Gram–Schmidt Orthogonalization ProcessChapter 7 in Review
8.1 Matrix Algebra8.2 Systems of Linear Algebraic Equations8.3 Rank of a Matrix8.4 Determinants8.5 Properties of Determinants8.6 Inverse of a Matrix8.6.1 Finding the Inverse8.6.2 Using the Inverse to Solve Systems8.7 Cramer’s Rule8.8 The Eigenvalue Problem8.9 Powers of Matrices8.10 Orthogonal Matrices8.11 Approximation of Eigenvalues8.12 Diagonalization8.13 LU-Factorization8.14 Cryptography8.15 An Error-Correcting Code8.16 Method of Least Squares8.17 Discrete Compartmental ModelsChapter 8 in Review
9.1 Vector Functions9.2 Motion on a Curve9.3 Curvature and Components of Acceleration9.4 Partial Derivatives9.5 Directional Derivative9.6 Tangent Planes and Normal Lines9.7 Curl and Divergence9.8 Line Integrals9.9 Independence of the Path9.10 Double Integrals9.11 Double Integrals in Polar Coordinates9.12 Green’s Theorem9.13 Surface Integrals9.14 Stokes’ Theorem9.15 Triple Integrals9.16 Divergence Theorem9.17 Change of Variables in Multiple IntegralsChapter 9 in Review
10.1 Theory of Linear Systems10.2 Homogeneous Linear Systems10.2.1 Distinct Real Eigenvalues10.2.2 Repeated Eigenvalues10.2.3 Complex Eigenvalues10.3 Solution by Diagonalization10.4 Nonhomogeneous Linear Systems10.4.1 Undetermined Coefficients10.4.2 Variation of Parameters10.4.3 Diagonalization10.5 Matrix ExponentialChapter 10 in Review
11.1 Autonomous Systems11.2 Stability of Linear Systems11.3 Linearization and Local Stability11.4 Autonomous Systems as Mathematical Models11.5 Periodic Solutions, Limit Cycles, and Global StabilityChapter 11 in Review
12.1 Orthogonal Functions12.2 Fourier Series12.3 Fourier Cosine and Sine Series12.4 Complex Fourier Series12.5 Sturm–Liouville Problem12.6 Bessel and Legendre Series12.6.1 Fourier–Bessel Series12.6.2 Fourier–Legendre SeriesChapter 12 in Review
13.1 Separable Partial Differential Equations13.2 Classical PDEs and Boundary-Value Problems13.3 Heat Equation13.4 Wave Equation13.5 Laplace’s Equation13.6 Nonhomogeneous Boundary-Value Problems13.7 Orthogonal Series Expansions13.8 Fourier Series in Two VariablesChapter 13 in Review
14.1 Polar Coordinates14.2 Cylindrical Coordinates14.3 Spherical CoordinatesChapter 14 in Review
15.1 Error Function15.2 Applications of the Laplace Transform15.3 Fourier Integral15.4 Fourier Transforms15.5 Fast Fourier TransformChapter 15 in Review
16.1 Laplace’s Equation16.2 Heat Equation16.3 Wave EquationChapter 16 in Review
17.1 Complex Numbers17.2 Powers and Roots17.3 Sets in the Complex Plane17.4 Functions of a Complex Variable17.5 Cauchy–Riemann Equations17.6 Exponential and Logarithmic Functions17.7 Trigonometric and Hyperbolic Functions17.8 Inverse Trigonometric and Hyperbolic FunctionsChapter 17 in Review
18.1 Contour Integrals18.2 Cauchy–Goursat Theorem18.3 Independence of the Path18.4 Cauchy’s Integral FormulasChapter 18 in Review
19.1 Sequences and Series19.2 Taylor Series19.3 Laurent Series19.4 Zeros and Poles19.5 Residues and Residue Theorem19.6 Evaluation of Real IntegralsChapter 19 in Review
20.1 Complex Functions as Mappings20.2 Conformal Mappings20.3 Linear Fractional Transformations20.4 Schwarz–Christoffel Transformations20.5 Poisson Integral Formulas20.6 ApplicationsChapter 20 in Review

Overview

Modern and comprehensive, the new sixth edition of Zill’s Advanced Engineering Mathematics is a full compendium of topics that are most often covered in engineering mathematics courses, and is extremely flexible to meet the unique needs of courses ranging from ordinary differential equations to vector calculus. A key strength of this best-selling text is Zill’s emphasis on differential equation as mathematical models, discussing the constructs and pitfalls of each.