Book description
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.
Table of contents
- Cover Page
- Title Page
- Copyright Page
- Contents
- Preface
-
PART 1 Ordinary Differential Equations
- 1 Introduction to Differential Equations
- 2 First-Order Differential Equations
-
3 Higher-Order Differential Equations
- 3.1 Theory of Linear 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
- 3.9 Linear Models: Boundary-Value Problems
- 3.10 Green’s Functions
- 3.11 Nonlinear Models
- 3.12 Solving Systems of Linear Equations
- Chapter 3 in Review
- 4 The Laplace Transform
- 5 Series Solutions of Linear Differential Equations
- 6 Numerical Solutions of Ordinary Differential Equations
-
PART 2 Vectors, Matrices, and Vector Calculus
- 7 Vectors
-
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
- 8.7 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
- Chapter 8 in 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
- Chapter 9 in Review
- PART 3 Systems of Differential Equations
- PART 4 Partial Differential Equations
-
PART 5 Complex Analysis
-
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
- 19 Series and Residues
- 20 Conformal Mappings
-
17 Functions of a Complex Variable
- Appendices
- Answers to Selected Odd-Numbered Problems
- Index
Product information
- Title: Advanced Engineering Mathematics, 6th Edition
- Author(s):
- Release date: August 2016
- Publisher(s): Jones & Bartlett Learning
- ISBN: 9781284105971
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