Advanced Engineering Mathematics / Dennis G. Zill

It includes Appendix, Answers to Selected Odd-Numbered Problems and Index Pages

Modern and comprehensive, the new sixth edition of award-winning author, Dennis G. Zill’s Advanced Engineering Mathematics is a 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. A key strength of this best-selling text is the author’s emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. An accessible writing style and robust pedagogical aids guide students through difficult concepts with thoughtful explanations, clear examples, interesting applications, and contributed project problems.

Contents:

Preface

Part 1: Ordinary Differential Equations

Chapter 1: Introduction to Differential Equations• Definitions and Terminology • Initial-Value Problems • Differential Equations as Mathematical Models • Chapter 1 in Review

Chapter 2: First-Order Differential Equations• Solution Curves Without a Solution • Direction Fields • Autonomous First-Order DEs • Separable Equations • Linear Equations • Exact Equations • Solutions by Substitutions • A Numerical Method • Linear Models • Nonlinear Models • Modeling with Systems of First-Order DEs • Chapter 2 in Review

Chapter 3: Higher-Order Differential Equations• Theory of Linear Equations • Initial-Value and Boundary-Value Problems • Homogeneous Equations • Nonhomogeneous Equations • Reduction of Order • Homogeneous Linear Equations with Constant Coefficients • Undetermined Coefficients • Variation of Parameters • Cauchy-Euler Equations • Nonlinear Equations • Linear Models: Initial-Value Problems • Spring/Mass Systems: Free Undamped Motion • Spring/Mass Systems: Free Damped Motion • Spring/Mass Systems: Driven Motion • Series Circuit Analogue • Linear Models: Boundary-Value Problems • Green’s Functions • Initial-Value Problems • Boundary-Value Problems • Nonlinear Models • Solving Systems of Linear Equations • Chapter 3 in Review

Chapter 4: The Laplace Transform • Definition of the Laplace Transform • The Inverse Transform and Transforms of Derivatives • Inverse Transforms • Transforms of Derivatives • Translation Theorems • Translation on the s-axis • Translation on the t-axis • Additional Operational Properties • Derivatives of Transforms • Transforms of Integrals • Transform of a Periodic Function • The Dirac Delta Function • Systems of Linear Differential Equations • Chapter 4 in Review

Chapter 5: Series Solutions of Linear Differential Equations • Solutions about Ordinary Points • Review of Power Series • Power Series Solutions • Solutions about Singular Points • Special Functions • Bessel Functions • Legendre Functions • Chapter 5 in Review

Chapter 6: Numerical Solutions of Ordinary Differential Equations • Euler Methods and Error Analysis • Runge-Kutta Methods • Multistep Methods • Higher-Order Equations and Systems • Second-Order Boundary-Value Problems • Chapter 6 in Review

Part 2: Vectors, Matrices, and Vector Calculus

Chapter 7: Vectors • Vectors in 2-Space • Vectors in 3-Space • Dot Product • Cross Product • Lines and Planes in 3-Space • Vector Spaces • Gram-Schmidt Orthogonalization Process • Chapter 7 in Review

Chapter 8: Matrices • Matrix Algebra • Systems of Linear Algebraic Equations • Rank of a Matrix • Determinants • Properties of Determinants • Inverse of a Matrix • Finding the Inverse • Using the Inverse to Solve Systems • Cramer’s Rule • The Eigenvalue Problem • Powers of Matrices • Orthogonal Matrices • Approximation of Eigenvalues • Diagonalization • LU-Factorization • Cryptography • An Error-Correcting Code • Method of Least Squares • Discrete Compartmental Models • Chapter 8 in Review

Chapter 9: Vector Calculus • Vector Functions • Motion on a Curve • Curvature and Components of Acceleration • Partial Derivatives • Directional Derivative • Tangent Planes and Normal Lines • Curl and Divergence • Line Integrals • Independence of the Path • Double Integrals • Double Integrals in Polar Coordinates • Green’s Theorem • Surface Integrals • Stokes’ Theorem • Triple Integrals • Divergence Theorem • Change of Variables in Multiple Integrals • Chapter 9 in Review

Part 3: Systems of Differential Equations

Chapter 10: Systems of Linear Differential Equations• Theory of Linear Systems • Homogeneous Linear Systems • Distinct Real Eigenvalues • Repeated Eigenvalues • Complex Eigenvalues • Solution by Diagonalization • Nonhomogeneous Linear Systems • Undetermined Coefficients • Variation of Parameters • Diagonalization • Matrix Exponential • Chapter 10 in Review

Chapter 11: Systems of Nonlinear Differential Equations • Autonomous Systems • Stability of Linear Systems • Linearization and Local Stability • Autonomous Systems as Mathematical Models
• Periodic Solutions, Limit Cycles, and Global Stability • Chapter 11 in Review

Part 4: Partial Differential Equations

Chapter 12: Orthogonal Functions and Fourier Series• Orthogonal Functions • Fourier Series • Fourier Cosine and Sine Series • Complex Fourier Series • Sturm-Liouville Problem • Bessel and Legendre Series • Fourier-Bessel Series • Fourier-Legendre Series • Chapter 12 in Review

Chapter 13: Boundary-Value Problems in Rectangular Coordinates • Separable Partial Differential Equations • Classical PDEs and Boundary-Value Problems • Heat Equation • Wave Equation • Laplace’s Equation • Nonhomogeneous Boundary-Value Problems • Orthogonal Series Expansions • Fourier Series in Two Variables • Chapter 13 in Review

Chapter 14: Boundary-Value Problems in Other Coordinate Systems • Polar Coordinates • Cylindrical Coordinates • Spherical Coordinates • Chapter 14 in Review

Chapter 15: Integral Transform Method • Error Function • Applications of the Laplace Transform • Fourier Integral • Fourier Transforms • Fast Fourier Transform • Chapter 15 in Review

Chapter 16: Numerical Solutions of Partial Differential Equations • Laplace’s Equation • Heat Equation • Wave Equation • Chapter 16 in Review

Part 5: Complex Analysis

Chapter 17: Functions of a Complex Variable • Complex Numbers • Powers and Roots • Sets in the Complex Plane • Functions of a Complex Variable • Cauchy—Riemann Equations • Exponential and Logarithmic Functions • Trigonometric and Hyperbolic Functions • Inverse Trigonometric and Hyperbolic Functions • Chapter 17 in Review

Chapter 18: Integration in the Complex Plane• Contour Integrals • Cauchy-Goursat Theorem
• Independence of the Path • Cauchy’s Integral Formulas • Chapter 18 in Review

Chapter 19: Series and Residues • Sequences and Series • Taylor Series • Laurent Series • Zeros and Poles • Residues and Residue Theorem • Evaluation of Real Integrals • Chapter 19 in Review

Chapter 20: Conformal Mappings • Complex Functions as Mappings • Conformal Mappings
• Linear Fractional Transformations • Schwarz-Christoffel Transformations • Poisson Integral Formulas • Applications • Chapter 20 in Review

Appendices • I Derivative and Integral Formulas • II Gamma Function • III Table of Laplace Transforms • IV Conformal Mappings

Answers to Selected Odd-Numbered Problem

Index