About the Book

Now with a full-color design, the new fourth edition of Zill"s Advanced Engineering Mathematics provides an in-depth overview of the many mathematical topics necessary for students planning a career in engineering or the sciences. A key strength of this text is Zill’s emphasis on differential equations as mathematical models, discussing the constructs and pitfalls of each. The Fourth edition is comprehensive, yet flexible, to meet the unique needs of various course offerings ranging from ordinary differential equations to vector calculus. New modern applications and projects, makes Zill’s classic text a must-have text and resource for Engineering Math students.

About the Author

Dennis G. Zill received a Ph.D. in Applied Mathematics from Iowa State University and is currently Professor of Mathematics and former chair of the Mathematics Department at Loyola Marymount University in Los Angeles. Warren S. Wright received his M.A. in mathematics from the University of Southern California and is currently professor of mathematics at Loyola Marymount University in Los Angeles.

Table of Contents:
Projects: Projects for Section 2.2: When Differential Equations Invaded Geometry: Inverse Tangent Problems in the 17th Century Projects for Section 2.5: Two properties of the sphere Projects for Section 2.7: Potassium-Argon Dating Projects for Section 2.8: Tricky timing: The Isochrones of Huygenes and Leibniz Projects for Section 3.8: Vibration control: Vibration Isolation Projects for Section 3.11: Vibration control: Vibration Absorbers Projects for Section 9.16: Minimal Surfaces Projects for Section 13.4: Making waves: Convection, Diffusion, and Traffic Flow Projects for Section 14.4: The uncertainity inequality in signal processing 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 • Non Homogeneous Equations • Reduction of Order • Homogenous Liner Equations with Constant Coefficients • Undetermined Coefficients • Variation of Parameters • Cauchy–Euler Equation • Nonlinear Equations • Linear Models: Initial-Value Problem: Spring/Mass Systems: Free Undamped Motion • Spring/Mass Systems: Free Damped Motion • Spring/Mass System: 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 Transform 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 • 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 Reviews Part 4: Partial Differential Equations • Chapter 12: Orthogonal Functions and Fourier Series • Orthogonal Functions • Fourier Series • Fourier Cosine and Sine Series • Complex Fourier Series • Strum–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 BVPs • Orthogonal Series Expansions • Fourier Series in Two Variables • Chapter 13 in Review Chapter 14: Boundary-Value Problems in Other Coordinate Systems • Problems in Polar Coordinates • Problems in Cylindrical Coordinates • Problems in 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 • The Heat Equation • The 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 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 Appendix 1: Derivative and Integral Formula • Appendix II: Gamma Function • Appendix III: Table of Laplace Transforms • Appendix IV: Conformal Mappings • Answers for Selected Odd-numbered Problems • Index