Advanced Engineering Mathematics, 7th Edition

Advanced Engineering Mathematics, 7th Edition

by Dennis G. Zill
Released December 2020
Publisher(s): Jones & Bartlett Learning
ISBN: 9781284206258

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Book description


This package includes the printed hardcover book and access to the Navigate 2 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.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Contents
  5. Preface
  6. 1 Introduction to Differential Equations
    1. 1.1 Definitions and Terminology
    2. 1.2 Initial-Value Problems
    3. 1.3 Differential Equations as Mathematical Models
    4. Chapter 1 in Review
  7. 2 First-Order Differential Equations
    1. 2.1 Solution Curves Without a Solution
      1. 2.1.1 Direction Fields
      2. 2.1.2 Autonomous First-Order DEs
    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
  8. 3 Higher-Order Differential Equations
    1. 3.1 Theory of Linear Equations
      1. 3.1.1 Initial-Value and Boundary-Value Problems
      2. 3.1.2 Homogeneous Equations
      3. 3.1.3 Nonhomogeneous Equations
    2. 3.2 Reduction of Order
    3. 3.3 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
      1. 3.8.1 Spring/Mass Systems: Free Undamped Motion
      2. 3.8.2 Spring/Mass Systems: Free Damped Motion
      3. 3.8.3 Spring/Mass Systems: Driven Motion
      4. 3.8.4 Series Circuit Analogue
    9. 3.9 Linear Models: Boundary-Value Problems
    10. 3.10 Green’s Functions
      1. 3.10.1 Initial-Value Problems
      2. 3.10.2 Boundary-Value Problems
    11. 3.11 Nonlinear Models
    12. 3.12 Solving Systems of Linear DEs
    13. Chapter 3 in Review
  9. 4 The Laplace Transform
    1. 4.1 Definition of the Laplace Transform
    2. 4.2 Inverse Transforms and Transforms of Derivatives
      1. 4.2.1 Inverse Transforms
      2. 4.2.2 Transforms of Derivatives
    3. 4.3 Translation Theorems
      1. 4.3.1 Translation on the s-axis
      2. 4.3.2 Translation on the t-axis
    4. 4.4 Additional Operational Properties
      1. 4.4.1 Derivatives of Transforms
      2. 4.4.2 Transforms of Integrals
      3. 4.4.3 Transform of a Periodic Function
    5. 4.5 Dirac Delta Function
    6. 4.6 Systems of Linear Differential Equations
    7. Chapter 4 in Review
  10. 5 Series Solutions of Linear Equations
    1. 5.1 Solutions about Ordinary Points
      1. 5.1.1 Review of Power Series
      2. 5.1.2 Power Series Solutions
    2. 5.2 Solutions about Singular Points
    3. 5.3 Special Functions
      1. 5.3.1 Bessel Functions
      2. 5.3.2 Legendre Functions
    4. Chapter 5 in Review
  11. 6 Numerical Solutions of Ordinary Differential Equations
    1. 6.1 Euler Methods and Error Analysis
    2. 6.2 Runge–Kutta Methods
    3. 6.3 Multistep Methods
    4. 6.4 Higher-Order Equations and Systems
    5. 6.5 Second-Order Boundary-Value Problems
    6. Chapter 6 in Review
  12. 7 Vectors
    1. 7.1 Vectors in 2-Space
    2. 7.2 Vectors in 3-Space
    3. 7.3 Dot Product
    4. 7.4 Cross Product
    5. 7.5 Lines and Planes in 3-Space
    6. 7.6 Vector Spaces
    7. 7.7 Gram–Schmidt Orthogonalization Process
    8. Chapter 7 in Review
  13. 8 Matrices
    1. 8.1 Matrix Algebra
    2. 8.2 Systems of Linear Equations
    3. 8.3 Rank of a Matrix
    4. 8.4 Determinants
    5. 8.5 Properties of Determinants
    6. 8.6 Inverse of a Matrix
      1. 8.6.1 Finding the Inverse
      2. 8.6.2 Using the Inverse to Solve Systems
    7. 8.7 Cramer’s Rule
    8. 8.8 Eigenvalue Problem
    9. 8.9 Powers of Matrices
    10. 8.10 Orthogonal Matrices
    11. 8.11 Approximation of Eigenvalues
    12. 8.12 Diagonalization
    13. 8.13 LU-Factorization
    14. 8.14 Cryptography
    15. 8.15 Error-Correcting Code
    16. 8.16 Method of Least Squares
    17. 8.17 Discrete Compartmental Models
    18. Chapter 8 in Review
  14. 9 Vector Calculus
    1. 9.1 Vector Functions
    2. 9.2 Motion on a Curve
    3. 9.3 Curvature
    4. 9.4 Partial Derivatives
    5. 9.5 Directional Derivative
    6. 9.6 Tangent Planes and Normal Lines
    7. 9.7 Curl and Divergence
    8. 9.8 Line Integrals
    9. 9.9 Independence of Path
    10. 9.10 Double Integrals
    11. 9.11 Double Integrals in Polar Coordinates
    12. 9.12 Green’s Theorem
    13. 9.13 Surface Integrals
    14. 9.14 Stokes’ Theorem
    15. 9.15 Triple Integrals
    16. 9.16 Divergence Theorem
    17. 9.17 Change of Variables in Multiple Integrals
    18. Chapter 9 in Review
  15. 10 Systems of Linear Differential Equations
    1. 10.1 Theory of Linear Systems
    2. 10.2 Homogeneous Linear Systems
      1. 10.2.1 Distinct Real Eigenvalues
      2. 10.2.2 Repeated Eigenvalues
      3. 10.2.3 Complex Eigenvalues
    3. 10.3 Solution by Diagonalization
    4. 10.4 Nonhomogeneous Linear Systems
      1. 10.4.1 Undetermined Coefficients
      2. 10.4.2 Variation of Parameters
      3. 10.4.3 Diagonalization
    5. 10.5 Matrix Exponential
    6. Chapter 10 in Review
  16. 11 Systems of Nonlinear Differential Equations
    1. 11.1 Autonomous Systems
    2. 11.2 Stability of Linear Systems
    3. 11.3 Linearization and Local Stability
    4. 11.4 Autonomous Systems as Mathematical Models
    5. 11.5 Periodic Solutions, Limit Cycles, and Global Stability
    6. Chapter 11 in Review
  17. 12 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
      1. 12.6.1 Fourier–Bessel Series
      2. 12.6.2 Fourier–Legendre Series
    7. Chapter 12 in Review
  18. 13 Boundary-Value Problems in Rectangular Coordinates
    1. 13.1 Separable Partial Differential Equations
    2. 13.2 Classical PDEs and Boundary-Value Problems
    3. 13.3 Heat Equation
    4. 13.4 Wave Equation
    5. 13.5 Laplace’s Equation
    6. 13.6 Nonhomogeneous Boundary-Value Problems
    7. 13.7 Orthogonal Series Expansions
    8. 13.8 Higher-Dimensional Problems
    9. Chapter 13 in Review
  19. 14 Boundary-Value Problems in Other Coordinate Systems
    1. 14.1 Polar Coordinates
    2. 14.2 Cylindrical Coordinates
    3. 14.3 Spherical Coordinates
    4. Chapter 14 in Review
  20. 15 Integral Transforms
    1. 15.1 Error Function
    2. 15.2 Laplace Transform
    3. 15.3 Fourier Integral
    4. 15.4 Fourier Transforms
    5. 15.5 Finite Fourier Transforms
    6. 15.6 Fast Fourier Transform
    7. Chapter 15 in Review
  21. 16 Numerical Solutions of Partial Differential Equations
    1. 16.1 Laplace’s Equation
    2. 16.2 Heat Equation
    3. 16.3 Wave Equation
    4. Chapter 16 in Review
  22. 17 Functions of a Complex Variable
    1. 17.1 Complex Numbers
    2. 17.2 Powers and Roots
    3. 17.3 Sets in the Complex Plane
    4. 17.4 Functions of a Complex Variable
    5. 17.5 Cauchy–Riemann Equations
    6. 17.6 Exponential and Logarithmic Functions
    7. 17.7 Trigonometric and Hyperbolic Functions
    8. 17.8 Inverse Trigonometric and Hyperbolic Functions
    9. Chapter 17 in Review
  23. 18 Integration in the Complex Plane
    1. 18.1 Contour Integrals
    2. 18.2 Cauchy–Goursat Theorem
    3. 18.3 Independence of Path
    4. 18.4 Cauchy’s Integral Formulas
    5. Chapter 18 in Review
  24. 19 Series and Residues
    1. 19.1 Sequences and Series
    2. 19.2 Taylor Series
    3. 19.3 Laurent Series
    4. 19.4 Zeros and Poles
    5. 19.5 Residue Theorem
    6. 19.6 Evaluation of Real Integrals
    7. Chapter 19 in Review
  25. 20 Conformal Mappings
    1. 20.1 Complex Functions as Mappings
    2. 20.2 Conformal Mappings
    3. 20.3 Linear Fractional Transformations
    4. 20.4 Schwarz–Christoffel Transformations
    5. 20.5 Poisson Integral Formulas
    6. 20.6 Applications
    7. Chapter 20 in Review
  26. Appendices
    1. A Integral-Defined Functions
    2. B Derivative and Integral Formulas
    3. C Laplace Transforms
    4. D Conformal Mappings
  27. Answers to Selected Odd-Numbered Problems
  28. Index

Product information

  • Title: Advanced Engineering Mathematics, 7th Edition
  • Author(s): Dennis G. Zill
  • Release date: December 2020
  • Publisher(s): Jones & Bartlett Learning
  • ISBN: 9781284206258