Advanced Engineering Mathematics, 6th Edition

Advanced Engineering Mathematics, 6th Edition

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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.

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Table of contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Contents
  5. Preface
  6. PART 1 Ordinary Differential Equations
    1. 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
      1. 2.1 Solution Curves Without a Solution
        1. 2.1.1 Direction Fields
        2. 2.1.2 Autonomous First-Order DEs
        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
          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
          1. 3.10.1 Initial-Value Problems
          2. 3.10.2 Boundary-Value Problems
          1. 4.1 Definition of the Laplace Transform
          2. 4.2 The Inverse Transform and Transforms of Derivatives
            1. 4.2.1 Inverse Transforms
            2. 4.2.2 Transforms of Derivatives
            1. 4.3.1 Translation on the s-axis
            2. 4.3.2 Translation on the t-axis
            1. 4.4.1 Derivatives of Transforms
            2. 4.4.2 Transforms of Integrals
            3. 4.4.3 Transform of a Periodic Function
            1. 5.1 Solutions about Ordinary Points
              1. 5.1.1 Review of Power Series
              2. 5.1.2 Power Series Solutions
              1. 5.3.1 Bessel Functions
              2. 5.3.2 Legendre Functions
              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
              1. 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
                1. 8.1 Matrix Algebra
                2. 8.2 Systems of Linear Algebraic 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
                  1. 9.1 Vector Functions
                  2. 9.2 Motion on a Curve
                  3. 9.3 Curvature and Components of Acceleration
                  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 the 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
                  1. 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
                      1. 10.4.1 Undetermined Coefficients
                      2. 10.4.2 Variation of Parameters
                      3. 10.4.3 Diagonalization
                      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
                      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
                          1. 12.6.1 Fourier–Bessel Series
                          2. 12.6.2 Fourier–Legendre Series
                          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 Fourier Series in Two Variables
                          9. Chapter 13 in Review
                          1. 14.1 Polar Coordinates
                          2. 14.2 Cylindrical Coordinates
                          3. 14.3 Spherical Coordinates
                          4. Chapter 14 in Review
                          1. 15.1 Error Function
                          2. 15.2 Applications of the Laplace Transform
                          3. 15.3 Fourier Integral
                          4. 15.4 Fourier Transforms
                          5. 15.5 Fast Fourier Transform
                          6. Chapter 15 in Review
                          1. 16.1 Laplace’s Equation
                          2. 16.2 Heat Equation
                          3. 16.3 Wave Equation
                          4. Chapter 16 in Review
                          1. 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
                            1. 18.1 Contour Integrals
                            2. 18.2 Cauchy–Goursat Theorem
                            3. 18.3 Independence of the Path
                            4. 18.4 Cauchy’s Integral Formulas
                            5. Chapter 18 in Review
                            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 Residues and Residue Theorem
                            6. 19.6 Evaluation of Real Integrals
                            7. Chapter 19 in Review
                            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
                            1. I Derivative and Integral Formulas
                            2. II Gamma Function
                            3. III Table of Laplace Transforms
                            4. IV Conformal Mappings
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                            Product information

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