## 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.

1. Cover Page
2. Title Page
4. Contents
5. Preface
6. PART 1 Ordinary Differential Equations
1. 1 Introduction to Differential Equations
2. 2 First-Order Differential Equations
1. 2.1 Solution Curves Without a Solution
2. 2.2 Separable Equations
3. 2.3 Linear Equations
4. 2.4 Exact Equations
5. 2.5 Solutions by Substitutions
6. 2.6 A Numerical Method
7. 2.7 Linear Models
8. 2.8 Nonlinear Models
9. 2.9 Modeling with Systems of First-Order DEs
10. Chapter 2 in Review
3. 3 Higher-Order Differential Equations
1. 3.1 Theory of Linear Equations
2. 3.2 Reduction of Order
3. 3.3 Homogeneous Linear Equations with Constant Coefficients
4. 3.4 Undetermined Coefficients
5. 3.5 Variation of Parameters
6. 3.6 Cauchy–Euler Equations
7. 3.7 Nonlinear Equations
8. 3.8 Linear Models: Initial-Value Problems
9. 3.9 Linear Models: Boundary-Value Problems
10. 3.10 Green’s Functions
11. 3.11 Nonlinear Models
12. 3.12 Solving Systems of Linear Equations
13. Chapter 3 in Review
4. 4 The Laplace Transform
1. 4.1 Definition of the Laplace Transform
2. 4.2 The Inverse Transform and Transforms of Derivatives
3. 4.3 Translation Theorems
5. 4.5 The Dirac Delta Function
6. 4.6 Systems of Linear Differential Equations
7. Chapter 4 in Review
5. 5 Series Solutions of Linear Differential Equations
1. 5.1 Solutions about Ordinary Points
2. 5.2 Solutions about Singular Points
3. 5.3 Special Functions
4. Chapter 5 in Review
6. 6 Numerical Solutions of Ordinary Differential Equations
7. PART 2 Vectors, Matrices, and Vector Calculus
1. 7 Vectors
2. 8 Matrices
3. 9 Vector Calculus
8. PART 3 Systems of Differential Equations
1. 10 Systems of Linear Differential Equations
1. 10.1 Theory of Linear Systems
2. 10.2 Homogeneous Linear Systems
3. 10.3 Solution by Diagonalization
4. 10.4 Nonhomogeneous Linear Systems
5. 10.5 Matrix Exponential
6. Chapter 10 in Review
2. 11 Systems of Nonlinear Differential Equations
9. PART 4 Partial Differential Equations
1. 12 Orthogonal Functions and Fourier Series
1. 12.1 Orthogonal Functions
2. 12.2 Fourier Series
3. 12.3 Fourier Cosine and Sine Series
4. 12.4 Complex Fourier Series
5. 12.5 Sturm–Liouville Problem
6. 12.6 Bessel and Legendre Series
7. Chapter 12 in Review
2. 13 Boundary-Value Problems in Rectangular Coordinates
3. 14 Boundary-Value Problems in Other Coordinate Systems
4. 15 Integral Transform Method
5. 16 Numerical Solutions of Partial Differential Equations
10. PART 5 Complex Analysis
1. 17 Functions of a Complex Variable
2. 18 Integration in the Complex Plane
3. 19 Series and Residues
4. 20 Conformal Mappings
11. Appendices
12. Answers to Selected Odd-Numbered Problems
13. Index

## Product information

• Title: Advanced Engineering Mathematics, 6th Edition
• Author(s): Dennis G. Zill
• Release date: August 2016
• Publisher(s): Jones & Bartlett Learning
• ISBN: 9781284105971