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Advanced Engineering Mathematics 4th edition

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Dennis G. Zill and Warren S. Wright
Publisher: Jones and Bartlett Learning

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Table of Contents

  • Chapter 1: Introduction to Differential Equations
    • 1.1: Definitions and Terminology
    • 1.2: Initial-Value Problems
    • 1.3: Differential Equations as Mathematical Models
    • 1: Review Questions (21)
    • 1: Test Bank (18)

  • Chapter 2: First-Order Differential Equations
    • 2.1: Solutions Curves Without a Solution
    • 2.2: Separable Equations
    • 2.3: Linear Equations
    • 2.4: Exact Equations
    • 2.5: Solutions by Substitutions
    • 2.6: A Numerical Method
    • 2.7: Linear Models
    • 2.8: Nonlinear Models
    • 2.9: Modeling with Systems of First-Order Des
    • 2: Review Questions (30)
    • 2: Test Bank (12)

  • Chapter 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 Equation
    • 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
    • 3: Review Questions (38)
    • 3: Test Bank (7)

  • Chapter 4: The Laplace Transform
    • 4.1: Definition of the Laplace Transform
    • 4.2: The Inverse Transform and Transforms of Derivatives
    • 4.3: Translation Theorems
    • 4.4: Additional Operational Properties
    • 4.5: The Dirac Delta Function
    • 4.6: Systems of Linear Differential Equations
    • 4: Review Questions (35)
    • 4: Test Bank (12)

  • Chapter 5: Series Solutions of Linear Differential Equations
    • 5.1: Solutions about Ordinary Points
    • 5.2: Solutions about Singular Points
    • 5.3: Special Functions
    • 5: Review Questions (13)
    • 5: Test Bank (4)

  • Chapter 6: Numerical Solutions of Ordinary Differential Equations
    • 6.1: Euler Methods and Error Analysis
    • 6.2: Runge-Kutta Methods
    • 6.3: Multistep Methods
    • 6.4: Higher-Order Equations and Systems
    • 6.5: Second-Order Boundary-Value Problems
    • 6: Review Questions (8)
    • 6: Test Bank

  • Chapter 7: Vectors
    • 7.1: Vectors in 2-Space
    • 7.2: Vectors in 3-Space
    • 7.3: Dot Product
    • 7.4: Cross Product
    • 7.5: Lines and Planes in 3-Space
    • 7.6: Vector Spaces
    • 7.7: Gram-Schmidt Orthogonalization Process
    • 7: Review Questions (38)
    • 7: Test Bank (6)

  • Chapter 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: Cryptography
    • 8.14: An Error-Correcting Code
    • 8.15: Method of Least Squares
    • 8.16: Discrete Compartmental Models
    • 8: Review Questions (36)
    • 8: Test Bank (9)

  • Chapter 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
    • 9: Review Questions (47)
    • 9: Test Bank (8)

  • Chapter 10: Systems of Linear Differential Equations
    • 10.1: Theory of Linear Systems
    • 10.2: Homogeneous Linear Systems
    • 10.3: Solution by Diagonalization
    • 10.4: Nonhomogeneous Linear Systems
    • 10.5: Matrix Exponential
    • 10: Review Questions (15)
    • 10: Test Bank (2)

  • Chapter 11: Systems of Nonlinear Differential Equations
    • 11.1: Autonomous Systems
    • 11.2: Stability of Linear Systems
    • 11.3: Linearization and Local Stability
    • 11.4: Autonomous Systems as Mathematical Models
    • 11.5: Periodic Solutions, Limit Cycles, and Global Stability
    • 11: Review Questions (13)
    • 11: Test Bank (9)

  • Chapter 12: Orgthogonal Functions and Fourier Series
    • 12.1: Orgthogonal Functions
    • 12.2: Fourier Series
    • 12.3: Fourier Cosine and Sine Series
    • 12.4: Complex Fourier Series
    • 12.5: Sturn-Liouville Problem
    • 12.6: Bessel and Legendre Series
    • 12: Review Questions (15)
    • 12: Test Bank (8)

  • Chapter 13: Boundary-Value Problems in Rectangular Coordinates
    • 13.1: Separable Partial Differential Equations
    • 13.2: Classical PDEs and Boundary-Value Problems
    • 13.3: Heat Equation
    • 13.4: Wave Equation
    • 13.5: Laplace's Equation
    • 13.6: Nonhomogeneous BVPs
    • 13.7: Orthogonal Series Expansions
    • 13.8: Fourier Series in Two Variables
    • 13: Review Questions (9)
    • 13: Test Bank (8)

  • Chapter 14: Boundary-Value Problems in Other Coordinate Systems
    • 14.1: Problems in Polar Coordinates
    • 14.2: Problems in Cylindrical Coordinates
    • 14.3: Problems in Spherical Coordinates
    • 14: Review Question (6)
    • 14: Test Bank

  • Chapter 15: Integral Transform Method
    • 15.1: Error Function
    • 15.2: Applications of the Laplace Transform
    • 15.3: Fourier Integral
    • 15.4: Fourier Transforms
    • 15.5: Fast Fourier Transform
    • 15: Review Questions (9)
    • 15: Test Bank (3)

  • Chapter 16: Numerical Solutions of Partial Differential Equations
    • 16.1: Laplace's Equation
    • 16.2: The Heat Equation
    • 16.3: The Wave Equation
    • 16: Review Question (3)
    • 16: Test Bank (4)

  • Chapter 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
    • 17: Review Questions (36)
    • 17: Test Bank (7)

  • Chapter 18: Integration in the Complex Plane
    • 18.1: Contour Integrals
    • 18.2: Cauchy-Goursat Theorem
    • 18.3: Independence of Path
    • 18.4: Cauchy's Integral Formulas
    • 18: Review Questions (29)
    • 18: Test Bank

  • Chapter 19: Series and Residues
    • 19.1: Sequences and Series
    • 19.2: Taylor Series
    • 19.3: Laurent Series
    • 19.4: Zeros and Poles
    • 19.5: Residues and Residue Theorem
    • 19.6: Evaluation of Real Integrals
    • 19: Review Questions (33)
    • 19: Test Bank (6)

  • Chapter 20: Conformal Mappings
    • 20.1: Complex Functions as Mappings
    • 20.2: Conformal Mappings
    • 20.3: Linear Fractional Transformations
    • 20.4: Schwarz-Christoffel Transformations
    • 20.5: Poisson Integral Formulas
    • 20.6: Applications
    • 20: Review Questions (16)
    • 20: Test Bank

  • Chapter 21: Statistics and Probability
    • 21: Statistics and Probability (34)

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Group Quantity Questions
Chapter 1: Introduction to Differential Equations
R 21 001 002 003 004 005 006 007 008 009 010 011 012 015 016 017 019 020 022 027 028 029
TB 18 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018
Chapter 2: First-Order Differential Equations
R 30 001 002 003 004 005 006 008 009 011 012 013 014 015 016 017 018 019 022 024 025 026 027 028 031 033 036 037 038 039 040
TB 12 001 002 003 004 005 006 007 008 009 010 011 012
Chapter 3: Higher-Order Differential Equations
R 38 001 002 003 004 005 006 007 008 009 010 013 014 015 016 017 020 021 022 024 025 026 027 028 029 033 035 036 037 038 041 042 043 045 047 048 049 055 056
TB 7 001 002 003 004 005 006 007
Chapter 4: The Laplace Transform
R 35 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 020 021 022 025 026 027 028 029 030 031 032 033 034 037 038 039 040 041
TB 12 001 002 003 004 005 006 007 008 009 010 011 012
Chapter 5: Series Solutions of Linear Differential Equations
R 13 001 002 003 005 006 009 010 013 015 016 017 019 020
TB 4 027 028 029 030
Chapter 6: Numerical Solutions of Ordinary Differential Equations
R 8 001 002 003 004 005 006 007 008
Chapter 7: Vectors
R 38 001 002 004 005 006 008 009 010 012 013 014 016 017 018 020 021 022 024 025 026 028 029 030 031 032 034 036 037 039 040 042 044 045 046 047 048 049 050
TB 6 025 026 027 028 029 030
Chapter 8: Matrices
R 36 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 026 027 029 030 031 032 035 036 037 039 040 042 044 046 047 048 049
TB 9 001 002 003 004 005 006 007 008 009
Chapter 9: Vector Calculus
R 47 001 002 004 005 006 008 009 010 012 013 014 016 017 018 020 021 022 024 026 027 028 030 031 032 036 038 039 040 041 042 043 044 047 049 051 052 053 055 056 057 058 059 060 061 063 064 065
TB 8 023 024 025 026 027 028 029 030
Chapter 10: Systems of Linear Differential Equations
R 15 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015
TB 2 005 006
Chapter 11: Systems of Nonlinear Differential Equations
R 13 001 002 003 004 005 006 007 008 009 010 013 014 016
TB 9 022 023 024 025 026 027 028 029 030
Chapter 12: Orgthogonal Functions and Fourier Series
R 15 001 002 003 004 005 006 007 008 009 010 013 014 015 016 020
TB 8 001 002 003 004 005 006 007 008
Chapter 13: Boundary-Value Problems in Rectangular Coordinates
R 9 001 003 005 007 008 009 012 013 014
TB 8 001 002 003 004 005 006 007 008
Chapter 14: Boundary-Value Problems in Other Coordinate Systems
R 6 001 002 003 004 007 009
Chapter 15: Integral Transform Method
R 9 001 002 004 006 007 008 013 016 017
TB 3 028 029 030
Chapter 16: Numerical Solutions of Partial Differential Equations
R 3 001 002 003
TB 4 027 028 029 030
Chapter 17: Functions of a Complex Variable
R 36 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 027 028 029 030 031 032 033 034 035 036 038
TB 7 024 025 026 027 028 029 030
Chapter 18: Integration in the Complex Plane
R 29 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029
Chapter 19: Series and Residues
R 33 001 002 003 004 005 006 007 008 009 010 011 012 013 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034
TB 6 001 002 003 004 005 006
Chapter 20: Conformal Mappings
R 16 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 018
Chapter 21: Statistics and Probability
21.8 10 007 009 010 012 018 019 023 025 028 031
21.23 7 001 003 005 010 013 019 020
21.49 7 001 003 005 008 011 017 029
21.57 6 001 003 007 008 012 017
21.60 4 002 003 006 012
Total 607  
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