Advanced Engineering Mathematics, 7th Edition
- Length: 1064 pages
- Edition: 7
- Language: English
- Publisher: Jones & Bartlett Learning
- Publication Date: 2020-12-15
- ISBN-10: 1284206246
- ISBN-13: 9781284206241
- Sales Rank: #748208 (See Top 100 Books)
This package includes the printed hardcover book and access to the Navigate Companion Website. The seventh edition of Advanced Engineering Mathematics provides learners with a modern and comprehensive compendium of topics that are most often covered in courses in engineering mathematics, and is extremely flexible to meet the unique needs of courses ranging from ordinary differential equations, to vector calculus, to partial differential equations. Acclaimed author, Dennis G. Zill’s accessible writing style and strong pedagogical aids, guide students through difficult concepts with thoughtful explanations, clear examples, interesting applications, and contributed project problems.
Cover Title Page Copyright Page Contents Preface 1 Introduction to Differential Equations 1.1 Definitions and Terminology 1.2 Initial-Value Problems 1.3 Differential Equations as Mathematical Models Chapter 1 in 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 Chapter 2 in 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 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 DEs Chapter 3 in Review 4 The Laplace Transform 4.1 Definition of the Laplace Transform 4.2 Inverse Transforms 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 Dirac Delta Function 4.6 Systems of Linear Differential Equations Chapter 4 in Review 5 Series Solutions of Linear 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 Chapter 5 in 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 Chapter 6 in 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 Chapter 7 in Review 8 Matrices 8.1 Matrix Algebra 8.2 Systems of Linear 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 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 Error-Correcting Code 8.16 Method of Least Squares 8.17 Discrete Compartmental Models Chapter 8 in Review 9 Vector Calculus 9.1 Vector Functions 9.2 Motion on a Curve 9.3 Curvature 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 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 Chapter 9 in 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 Chapter 10 in 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 Chapter 11 in Review 12 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 Chapter 12 in 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 Higher-Dimensional Problems Chapter 13 in Review 14 Boundary-Value Problems in Other Coordinate Systems 14.1 Polar Coordinates 14.2 Cylindrical Coordinates 14.3 Spherical Coordinates Chapter 14 in Review 15 Integral Transforms 15.1 Error Function 15.2 Laplace Transform 15.3 Fourier Integral 15.4 Fourier Transforms 15.5 Finite Fourier Transforms 15.6 Fast Fourier Transform Chapter 15 in Review 16 Numerical Solutions of Partial Differential Equations 16.1 Laplace’s Equation 16.2 Heat Equation 16.3 Wave Equation Chapter 16 in 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 Chapter 17 in Review 18 Integration in the Complex Plane 18.1 Contour Integrals 18.2 Cauchy–Goursat Theorem 18.3 Independence of Path 18.4 Cauchy’s Integral Formulas Chapter 18 in 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 Residue Theorem 19.6 Evaluation of Real Integrals Chapter 19 in 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 Chapter 20 in Review Appendices A Integral-Defined Functions B Derivative and Integral Formulas C Laplace Transforms D Conformal Mappings Answers to Selected Odd-Numbered Problems Index
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