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Advanced Engineering Mathematics 4th edition

Textbook Cover

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


Access is contingent on use of this textbook in the instructor's classroom.

  • Chapter 1: Introduction to Differential Equations
    • 1.1: Definitions and Terminology (6)
    • 1.2: Initial-Value Problems (6)
    • 1.3: Differential Equations as Mathematical Models (6)
    • 1: Review Questions (21)
    • 1: Test Bank (18)

  • Chapter 2: First-Order Differential Equations
    • 2.1: Solutions Curves Without a Solution (6)
    • 2.2: Separable Equations (6)
    • 2.3: Linear Equations (6)
    • 2.4: Exact Equations (6)
    • 2.5: Solutions by Substitutions (6)
    • 2.6: A Numerical Method (3)
    • 2.7: Linear Models (6)
    • 2.8: Nonlinear Models (6)
    • 2.9: Modeling with Systems of First-Order Des (3)
    • 2: Review Questions (30)
    • 2: Test Bank (12)

  • Chapter 3: Higher-Order Differential Equations
    • 3.1: Theory of Linear Equations (5)
    • 3.2: Reduction of Order (6)
    • 3.3: Homogeneous Linear Equations with Constant Coefficients (7)
    • 3.4: Undetermined Coefficients (7)
    • 3.5: Variation of Parameters (7)
    • 3.6: Cauchy-Euler Equation (6)
    • 3.7: Nonlinear Equations (4)
    • 3.8: Linear Models: Initial-Value Problems (7)
    • 3.9: Linear Models: Boundary-Value Problems (6)
    • 3.10: Green's Functions (6)
    • 3.11: Nonlinear Models (3)
    • 3.12: Solving Systems of Linear Equations (6)
    • 3: Review Questions (38)
    • 3: Test Bank (7)

  • Chapter 4: The Laplace Transform
    • 4.1: Definition of the Laplace Transform (7)
    • 4.2: The Inverse Transform and Transforms of Derivatives (7)
    • 4.3: Translation Theorems (10)
    • 4.4: Additional Operational Properties (9)
    • 4.5: The Dirac Delta Function (4)
    • 4.6: Systems of Linear Differential Equations (5)
    • 4: Review Questions (35)
    • 4: Test Bank (12)

  • Chapter 5: Series Solutions of Linear Differential Equations
    • 5.1: Solutions about Ordinary Points (3)
    • 5.2: Solutions about Singular Points (3)
    • 5.3: Special Functions (3)
    • 5: Review Questions (13)
    • 5: Test Bank (4)

  • Chapter 6: Numerical Solutions of Ordinary Differential Equations
    • 6.1: Euler Methods and Error Analysis (4)
    • 6.2: Runge-Kutta Methods (4)
    • 6.3: Multistep Methods (2)
    • 6.4: Higher-Order Equations and Systems (3)
    • 6.5: Second-Order Boundary-Value Problems (3)
    • 6: Review Questions (8)
    • 6: Test Bank

  • Chapter 7: Vectors
    • 7.1: Vectors in 2-Space (4)
    • 7.2: Vectors in 3-Space (3)
    • 7.3: Dot Product (3)
    • 7.4: Cross Product (3)
    • 7.5: Lines and Planes in 3-Space (2)
    • 7.6: Vector Spaces (2)
    • 7.7: Gram-Schmidt Orthogonalization Process (2)
    • 7: Review Questions (38)
    • 7: Test Bank (6)

  • Chapter 8: Matrices
    • 8.1: Matrix Algebra (2)
    • 8.2: Systems of Linear Algebraic Equations (2)
    • 8.3: Rank of a Matrix (2)
    • 8.4: Determinants (2)
    • 8.5: Properties of Determinants (2)
    • 8.6: Inverse of a Matrix (2)
    • 8.7: Cramer's Rule (2)
    • 8.8: The Eigenvalue Problem (2)
    • 8.9: Powers of Matrices (2)
    • 8.10: Orthogonal Matrices (2)
    • 8.11: Approximation of Eigenvalues (2)
    • 8.12: Diagonalization (2)
    • 8.13: Cryptography (2)
    • 8.14: An Error-Correcting Code (2)
    • 8.15: Method of Least Squares (2)
    • 8.16: Discrete Compartmental Models (1)
    • 8: Review Questions (36)
    • 8: Test Bank (9)

  • Chapter 9: Vector Calculus
    • 9.1: Vector Functions (6)
    • 9.2: Motion on a Curve (6)
    • 9.3: Curvature and Components of Acceleration (5)
    • 9.4: Partial Derivatives (7)
    • 9.5: Directional Derivative (6)
    • 9.6: Tangent Planes and Normal Lines (3)
    • 9.7: Curl and Divergence (6)
    • 9.8: Line Integrals (6)
    • 9.9: Independence of the Path (6)
    • 9.10: Double Integrals (6)
    • 9.11: Double Integrals in Polar Coordinates (6)
    • 9.12: Green's Theorem (6)
    • 9.13: Surface Integrals (6)
    • 9.14: Stokes' Theorem (5)
    • 9.15: Triple Integrals (7)
    • 9.16: Divergence Theorem (4)
    • 9.17: Change of Variables in Multiple Integrals (5)
    • 9: Review Questions (47)
    • 9: Test Bank (8)

  • Chapter 10: Systems of Linear Differential Equations
    • 10.1: Theory of Linear Systems (4)
    • 10.2: Homogeneous Linear Systems (5)
    • 10.3: Solution by Diagonalization (3)
    • 10.4: Nonhomogeneous Linear Systems (4)
    • 10.5: Matrix Exponential (3)
    • 10: Review Questions (15)
    • 10: Test Bank (2)

  • Chapter 11: Systems of Nonlinear Differential Equations
    • 11.1: Autonomous Systems (4)
    • 11.2: Stability of Linear Systems (4)
    • 11.3: Linearization and Local Stability (4)
    • 11.4: Autonomous Systems as Mathematical Models (3)
    • 11.5: Periodic Solutions, Limit Cycles, and Global Stability (1)
    • 11: Review Questions (13)
    • 11: Test Bank (9)

  • Chapter 12: Orgthogonal Functions and Fourier Series
    • 12.1: Orgthogonal Functions (4)
    • 12.2: Fourier Series (4)
    • 12.3: Fourier Cosine and Sine Series (4)
    • 12.4: Complex Fourier Series (2)
    • 12.5: Sturn-Liouville Problem (2)
    • 12.6: Bessel and Legendre Series (2)
    • 12: Review Questions (15)
    • 12: Test Bank (8)

  • Chapter 13: Boundary-Value Problems in Rectangular Coordinates
    • 13.1: Separable Partial Differential Equations (4)
    • 13.2: Classical PDEs and Boundary-Value Problems (3)
    • 13.3: Heat Equation (3)
    • 13.4: Wave Equation (4)
    • 13.5: Laplace's Equation (2)
    • 13.6: Nonhomogeneous BVPs (2)
    • 13.7: Orthogonal Series Expansions (2)
    • 13.8: Fourier Series in Two Variables (2)
    • 13: Review Questions (9)
    • 13: Test Bank (8)

  • Chapter 14: Boundary-Value Problems in Other Coordinate Systems
    • 14.1: Problems in Polar Coordinates (2)
    • 14.2: Problems in Cylindrical Coordinates (2)
    • 14.3: Problems in Spherical Coordinates (2)
    • 14: Review Question (6)
    • 14: Test Bank

  • Chapter 15: Integral Transform Method
    • 15.1: Error Function (1)
    • 15.2: Applications of the Laplace Transform (3)
    • 15.3: Fourier Integral (3)
    • 15.4: Fourier Transforms (3)
    • 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 (2)
    • 16.2: The Heat Equation (2)
    • 16.3: The Wave Equation (2)
    • 16: Review Question (3)
    • 16: Test Bank (4)

  • Chapter 17: Functions of a Complex Variable
    • 17.1: Complex Numbers (4)
    • 17.2: Powers and Roots (4)
    • 17.3: Sets in the Complex Plane (2)
    • 17.4: Functions of a Complex Variable (3)
    • 17.5: Cauchy-Riemann Equations (2)
    • 17.6: Exponential and Logarithmic Functions (4)
    • 17.7: Trigonometric and Hyperbolic Functions (2)
    • 17.8: Inverse Trigonometric and Hyperbolic Functions (2)
    • 17: Review Questions (36)
    • 17: Test Bank (7)

  • Chapter 18: Integration in the Complex Plane
    • 18.1: Contour Integrals (2)
    • 18.2: Cauchy-Goursat Theorem (2)
    • 18.3: Independence of Path (2)
    • 18.4: Cauchy's Integral Formulas (3)
    • 18: Review Questions (29)
    • 18: Test Bank

  • Chapter 19: Series and Residues
    • 19.1: Sequences and Series (2)
    • 19.2: Taylor Series (2)
    • 19.3: Laurent Series (2)
    • 19.4: Zeros and Poles (2)
    • 19.5: Residues and Residue Theorem (1)
    • 19.6: Evaluation of Real Integrals (2)
    • 19: Review Questions (33)
    • 19: Test Bank (6)

  • Chapter 20: Conformal Mappings
    • 20.1: Complex Functions as Mappings (2)
    • 20.2: Conformal Mappings (2)
    • 20.3: Linear Fractional Transformations (2)
    • 20.4: Schwarz-Christoffel Transformations (2)
    • 20.5: Poisson Integral Formulas (1)
    • 20.6: Applications (2)
    • 20: Review Questions (16)
    • 20: Test Bank

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

Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

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GRAY questions are under development


Group Quantity Questions
Chapter 1: Introduction to Differential Equations
1.R 21 001 002 003 004 005 006 007 008 009 010 011 012 015 016 017 019 020 022 027 028 029
1.TB 18 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018
1.1 6 003 009 019 027 037 050
1.2 6 001 007 015 023 033 037
1.3 6 001 007 013 017 023 027
Chapter 2: First-Order Differential Equations
2.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
2.TB 12 001 002 003 004 005 006 007 008 009 010 011 012
2.1 6 001 005 013 019 025 038
2.2 6 001 009 017 023 030 045
2.3 6 001 009 017 024 029 038
2.4 6 001 009 017 025 029 035
2.5 6 005 011 019 023 029 038
2.6 3 003 009 012
2.7 6 005 013 021 031 039 048
2.8 6 003 006 009 013 017 025
2.9 3 004 007 011
Chapter 3: Higher-Order Differential Equations
3.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
3.TB 7 001 002 003 004 005 006 007
3.1 5 001 009 019 023 036
3.2 6 001 005 009 013 016 019
3.3 7 001 009 015 023 029 037 051
3.4 7 001 009 017 025 031 037 045
3.5 7 001 005 010 013 017 021 025
3.6 6 001 009 017 023 029 035
3.7 4 003 007 011 015
3.8 7 001 008 017 025 033 045 049
3.9 6 004 007 011 015 019 027
3.10 6 001 007 013 019 027 039
3.11 3 001 007 016
3.12 6 001 005 009 013 017 021
Chapter 4: The Laplace Transform
4.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
4.TB 12 001 002 003 004 005 006 007 008 009 010 011 012
4.1 7 001 005 009 013 019 027 035
4.2 7 001 005 013 021 029 035 041
4.3 10 001 009 017 025 031 041 049 055 063 073
4.4 9 001 009 015 019 027 037 045 049 057
4.5 4 003 007 011 014
4.6 5 003 007 011 015 019
Chapter 5: Series Solutions of Linear Differential Equations
5.R 13 001 002 003 005 006 009 010 013 015 016 017 019 020
5.TB 4 027 028 029 030
5.1 3 011 021 029
5.2 3 005 011 025
5.3 3 007 013 047
Chapter 6: Numerical Solutions of Ordinary Differential Equations
6.R 8 001 002 003 004 005 006 007 008
6.1 4 003 007 011 017
6.2 4 003 007 011 015
6.3 2 004 007
6.4 3 003 007 011
6.5 3 003 007 012
Chapter 7: Vectors
7.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
7.TB 6 025 026 027 028 029 030
7.1 4 001 009 023 037
7.2 3 014 025 041
7.3 3 001 016 039
7.4 3 001 013 047
7.5 2 001 031
7.6 2 011 027
7.7 2 005 017
Chapter 8: Matrices
8.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
8.TB 9 001 002 003 004 005 006 007 008 009
8.1 2 011 021
8.2 2 025 037
8.3 2 007 016
8.4 2 013 029
8.5 2 017 031
8.6 2 025 051
8.7 2 011 014
8.8 2 005 017
8.9 2 009 017
8.10 2 017 024
8.11 2 006 012
8.12 2 011 035
8.13 2 006 009
8.14 2 009 021
8.15 2 005 008
8.16 1 002
Chapter 9: Vector Calculus
9.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
9.TB 8 023 024 025 026 027 028 029 030
9.1 6 010 015 019 025 033 041
9.2 6 003 007 011 015 021 025
9.3 5 003 007 011 015 020
9.4 7 012 017 021 025 043 054 057
9.5 6 008 014 023 031 035 043
9.6 3 013 021 033
9.7 6 004 009 016 019 021 028
9.8 6 001 009 015 023 029 034
9.9 6 001 010 013 017 021 025
9.10 6 001 013 023 035 051 059
9.11 6 001 007 013 022 027 033
9.12 6 001 007 011 019 025 029
9.13 6 001 009 019 025 029 037
9.14 5 001 005 009 011 015
9.15 7 001 009 019 035 043 051 059
9.16 4 001 003 007 011
9.17 5 001 005 013 017 027
Chapter 10: Systems of Linear Differential Equations
10.R 15 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015
10.TB 2 005 006
10.1 4 001 007 011 017
10.2 5 001 013 021 029 041
10.3 3 001 005 008
10.4 4 003 010 014 031
10.5 3 001 012 019
Chapter 11: Systems of Nonlinear Differential Equations
11.R 13 001 002 003 004 005 006 007 008 009 010 013 014 016
11.TB 9 022 023 024 025 026 027 028 029 030
11.1 4 001 009 019 023
11.2 4 001 007 011 015
11.3 4 003 011 021 036
11.4 3 001 010 016
11.5 1 014
Chapter 12: Orgthogonal Functions and Fourier Series
12.R 15 001 002 003 004 005 006 007 008 009 010 013 014 015 016 020
12.TB 8 001 002 003 004 005 006 007 008
12.1 4 001 005 009 018
12.2 4 001 005 009 013
12.3 4 001 011 025 035
12.4 2 001 008
12.5 2 001 009
12.6 2 001 015
Chapter 13: Boundary-Value Problems in Rectangular Coordinates
13.R 9 001 003 005 007 008 009 012 013 014
13.TB 8 001 002 003 004 005 006 007 008
13.1 4 001 005 009 017
13.2 3 001 005 009
13.3 3 001 004 007
13.4 4 001 003 005 009
13.5 2 001 011
13.6 2 001 010
13.7 2 002 004
13.8 2 001 005
Chapter 14: Boundary-Value Problems in Other Coordinate Systems
14.R 6 001 002 003 004 007 009
14.1 2 001 012
14.2 2 005 013
14.3 2 005 010
Chapter 15: Integral Transform Method
15.R 9 001 002 004 006 007 008 013 016 017
15.TB 3 028 029 030
15.1 1 006
15.2 3 003 014 022
15.3 3 001 007 013
15.4 3 002 013 019
Chapter 16: Numerical Solutions of Partial Differential Equations
16.R 3 001 002 003
16.TB 4 027 028 029 030
16.1 2 001 005
16.2 2 001 011
16.3 2 001 005
Chapter 17: Functions of a Complex Variable
17.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
17.TB 7 024 025 026 027 028 029 030
17.1 4 001 009 017 033
17.2 4 003 015 021 033
17.3 2 001 011
17.4 3 001 015 027
17.5 2 015 025
17.6 4 001 014 029 040
17.7 2 001 015
17.8 2 001 010
Chapter 18: Integration in the Complex Plane
18.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
18.1 2 001 018
18.2 2 009 017
18.3 2 003 011
18.4 3 001 009 017
Chapter 19: Series and Residues
19.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
19.TB 6 001 002 003 004 005 006
19.1 2 001 019
19.2 2 002 027
19.3 2 001 013
19.4 2 003 013
19.5 1 001
19.6 2 003 011
Chapter 20: Conformal Mappings
20.R 16 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 018
20.1 2 001 011
20.2 2 001 019
20.3 2 001 009
20.4 2 001 006
20.5 1 001
20.6 2 001 011
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 1107  

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