# Advanced Engineering Mathematics 5th edition

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

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• Chapter 1: Introduction to Differential Equations
• 1.1: Definitions and Terminology (14)
• 1.2: Initial-Value Problems (14)
• 1.3: Differential Equations as Mathematical Models (13)
• 1: Review (21)
• 1: Test Bank (18)

• Chapter 2: First-Order Differential Equations
• 2.1: Solution Curves Without a Solution (13)
• 2.2: Separable Equations (13)
• 2.3: Linear Equations (13)
• 2.4: Exact Equations (14)
• 2.5: Solutions by Substitutions (12)
• 2.6: A Numerical Method (6)
• 2.7: Linear Models (21)
• 2.8: Nonlinear Models (11)
• 2.9: Modeling with Systems of First-Order DEs (8)
• 2: Review (30)
• 2: Test Bank (12)

• Chapter 3: Higher-Order Differential Equations
• 3.1: Theory of Linear Equations (11)
• 3.2: Reduction of Order (10)
• 3.3: Homogeneous Linear Equations with Constant Coefficients (19)
• 3.4: Undetermined Coefficients (17)
• 3.5: Variation of Parameters (12)
• 3.6: Cauchy-Euler Equations (14)
• 3.7: Nonlinear Equations (8)
• 3.8: Linear Models: Initial-Value Problems (16)
• 3.9: Linear Models: Boundary-Value Problems (14)
• 3.10: Green's Functions (16)
• 3.11: Nonlinear Models (6)
• 3.12: Solving Systems of Linear Equations (9)
• 3: Review (38)
• 3: Test Bank (7)

• Chapter 4: The Laplace Transform
• 4.1: Definition of the Laplace Transform (14)
• 4.2: The Inverse Transform and Transforms of Derivatives (16)
• 4.3: Translation Theorems (24)
• 4.4: Additional Operational Properties (20)
• 4.5: The Dirac Delta Function (6)
• 4.6: Systems of Linear Differential Equations (8)
• 4: Review (35)
• 4: Test Bank (12)

• Chapter 5: Series Solutions of Linear Differential Equations
• 5.1: Solutions about Ordinary Points (8)
• 5.2: Solutions about Singular Points (11)
• 5.3: Special Functions (8)
• 5: Review (13)
• 5: Test Bank (4)

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

• Chapter 7: Vectors
• 7.1: Vectors in 2-Space (7)
• 7.2: Vectors in 3-Space (6)
• 7.3: Dot Product (6)
• 7.4: Cross Product (6)
• 7.5: Lines and Planes in 3-Space (5)
• 7.6: Vector Spaces (5)
• 7.7: Gram-Schmidt Orthogonalization Process (5)
• 7: Review (38)
• 7: Test Bank (6)

• Chapter 8: Matrices
• 8.1: Matrix Algebra (5)
• 8.2: Systems of Linear Algebraic Equations (5)
• 8.3: Rank of a Matrix (5)
• 8.4: Determinants (5)
• 8.5: Properties of Determinants (5)
• 8.6: Inverse of a Matrix (5)
• 8.7: Cramer's Rule (5)
• 8.8: The Eigenvalue Problem (5)
• 8.9: Powers of Matrices (5)
• 8.10: Orthogonal Matrices (5)
• 8.11: Approximation of Eigenvalues (4)
• 8.12: Diagonalization (4)
• 8.13: LU-Factorization (2)
• 8.14: Cryptography (4)
• 8.15: An Error-Correcting Code (4)
• 8.16: Method of Least Squares (4)
• 8.17: Discrete Compartmental Models (3)
• 8: Review (36)
• 8: Test Bank (9)

• Chapter 9: Vector Calculus
• 9.1: Vector Functions (9)
• 9.2: Motion on a Curve (9)
• 9.3: Curvature and Components of Acceleration (8)
• 9.4: Partial Derivatives (10)
• 9.5: Directional Derivative (9)
• 9.6: Tangent Planes and Normal Lines (6)
• 9.7: Curl and Divergence (9)
• 9.8: Line Integrals (9)
• 9.9: Independence of the Path (9)
• 9.10: Double Integrals (9)
• 9.11: Double Integrals in Polar Coordinates (9)
• 9.12: Green's Theorem (8)
• 9.13: Surface Integrals (8)
• 9.14: Stokes' Theorem (7)
• 9.15: Triple Integrals (9)
• 9.16: Divergence Theorem (6)
• 9.17: Change of Variables in Multiple Integrals (7)
• 9: Review (47)
• 9: Test Bank (8)

• Chapter 10: Systems of Linear Differential Equations
• 10.1: Theory of Linear Systems (8)
• 10.2: Homogeneous Linear Systems (15)
• 10.3: Solution by Diagonalization (5)
• 10.4: Nonhomogeneous Linear Systems (13)
• 10.5: Matrix Exponential (6)
• 10: Review (15)
• 10: Test Bank (2)

• Chapter 11: Systems of Nonlinear Differential Equations
• 11.1: Autonomous Systems (8)
• 11.2: Stability of Linear Systems (7)
• 11.3: Linearization and Local Stability (6)
• 11.4: Autonomous Systems as Mathematical Models (6)
• 11.5: Periodic Solutions, Limit Cycles, and Global Stability (3)
• 11: Review (13)
• 11: Test Bank (9)

• Chapter 12: Orthogonal Functions and Fourier Series
• 12.1: Orthogonal Functions (6)
• 12.2: Fourier Series (6)
• 12.3: Fourier Cosine and Sine Series (10)
• 12.4: Complex Fourier Series (4)
• 12.5: Sturm-Liouville Problem (4)
• 12.6: Bessel and Legendre Series (3)
• 12: Review (15)
• 12: Test Bank (8)

• Chapter 13: Boundary-Value Problems in Rectangular Coordinates
• 13.1: Separable Partial Differential Equations (8)
• 13.2: Classical PDEs and Boundary-Value Problems (5)
• 13.3: Heat Equation (5)
• 13.4: Wave Equation (7)
• 13.5: Laplace's Equation (5)
• 13.6: Nonhomogeneous BVPs (5)
• 13.7: Orthogonal Series Expansions (4)
• 13.8: Fourier Series in Two Variables (3)
• 13: Review (9)
• 13: Test Bank (8)

• Chapter 14: Boundary-Value Problems in Other Coordinate Systems
• 14.1: Problems in Polar Coordinates (4)
• 14.2: Problems in Cylindrical Coordinates (3)
• 14.3: Problems in Spherical Coordinates (4)
• 14: Review (6)
• 14: Test Bank

• Chapter 15: Integral Transform Method
• 15.1: Error Function (3)
• 15.2: Applications of the Laplace Transform (6)
• 15.3: Fourier Integral (5)
• 15.4: Fourier Transforms (6)
• 15.5: Fast Fourier Transform (2)
• 15: Review (9)
• 15: Test Bank (3)

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

• Chapter 17: Functions of a Complex Variable
• 17.1: Complex Numbers (6)
• 17.2: Powers and Roots (6)
• 17.3: Sets in the Complex Plane (4)
• 17.4: Functions of a Complex Variable (5)
• 17.5: Cauchy-Riemann Equations (4)
• 17.6: Exponential and Logarithmic Functions (6)
• 17.7: Trigonometric and Hyperbolic Functions (4)
• 17.8: Inverse Trigonometric and Hyperbolic Functions (4)
• 17: Review (36)
• 17: Test Bank (7)

• Chapter 18: Integration in the Complex Plane
• 18.1: Contour Integrals (4)
• 18.2: Cauchy-Goursat Theorem (4)
• 18.3: Independence of the Path (4)
• 18.4: Cauchy's Integral Formulas (5)
• 18: Review (29)
• 18: Test Bank

• Chapter 19: Series and Residues
• 19.1: Sequences and Series (4)
• 19.2: Taylor Series (4)
• 19.3: Laurent Series (4)
• 19.4: Zeros and Poles (4)
• 19.5: Residues and Residue Theorem (3)
• 19.6: Evaluation of Real Integrals (4)
• 19: Review (33)
• 19: Test Bank (6)

• Chapter 20: Conformal Mappings
• 20.1: Complex Functions as Mappings (4)
• 20.2: Conformal Mappings (4)
• 20.3: Linear Fractional Transformations (4)
• 20.4: Schwarz-Christoffel Transformations (4)
• 20.5: Poisson Integral Formulas (3)
• 20.6: Applications (4)
• 20: Review (16)
• 20: Test Bank

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Group Quantity Questions
Chapter 1: Introduction to Differential Equations
1.R 21 001 002 003 004 005 006 007 008 009 010 011 012 015 016 017 019 020 022 033 034 501.XP
1.TB 18 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018
1.1 14 001 003 007 009 013 017 019 023 027 033 041 050 054 056
1.2 14 001 007 009 013 015 019 023 025 033 034 037 039 041 043
1.3 13 001 005 007 008 010 013 015 017 018 023 025 026 027
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 13 001 004 005 009 011 013 019 021 023 025 027 031 038
2.2 13 001 005 009 011 015 017 021 023 027 029 032 037 047
2.3 13 001 005 009 011 015 017 021 024 025 029 035 038 043
2.4 14 001 003 007 009 011 015 017 021 025 027 029 031 033 035
2.5 12 003 005 009 011 015 019 021 023 027 029 036 037
2.6 6 001 003 007 009 011 012
2.7 21 001 003 005 006 009 011 013 014 016 017 019 021 023 029 031 035 037 039 041 043 048
2.8 11 001 003 004 006 011 012 015 017 019 021 027
2.9 8 001 004 007 009 010 012 013 015
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 11 001 004 009 015 019 021 023 025 027 036 040
3.2 10 001 005 007 009 013 015 016 017 019 022
3.3 19 001 005 009 011 015 017 021 023 027 029 033 037 039 041 043 047 051 055 060
3.4 17 001 003 007 009 013 017 019 023 025 029 031 033 035 037 039 041 045
3.5 12 001 003 005 009 010 013 015 017 021 023 025 028
3.6 14 001 003 007 009 013 017 019 023 025 029 043 045 047 049
3.7 8 003 005 007 009 011 013 015 017
3.8 16 001 003 006 008 015 017 021 025 027 030 031 033 037 045 049 053
3.9 14 001 004 005 007 012 013 015 017 018 020 021 027 029 039
3.10 16 001 003 005 007 009 013 015 019 021 025 027 031 033 035 039 043
3.11 6 001 003 007 009 019 501.XP
3.12 9 001 005 007 009 013 015 017 021 023
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 14 001 005 007 009 013 015 019 021 025 027 031 033 035 039
4.2 16 001 003 005 009 013 015 019 021 025 029 031 035 037 039 041 044
4.3 24 001 005 009 013 017 019 023 025 029 031 037 039 041 043 047 049 055 057 061 063 067 071 073 077
4.4 20 001 003 007 009 013 015 019 021 025 027 031 037 039 043 045 050 051 053 055 059
4.5 6 003 005 007 011 013 014
4.6 8 003 005 007 011 013 015 017 019
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 8 003 011 017 021 025 029 031 033
5.2 11 001 005 007 011 015 019 023 025 027 031 032
5.3 8 003 007 011 013 015 019 024 051
Chapter 6: Numerical Solutions of Ordinary Differential Equations
6.R 8 001 002 003 004 005 006 007 008
6.1 6 003 005 007 011 012 017
6.2 6 003 005 007 011 013 015
6.3 3 004 005 007
6.4 4 003 006 007 011
6.5 6 001 003 005 007 009 012
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 6 032 033 034 035 036 037
7.1 7 001 009 023 037 041 044 047
7.2 6 014 023 025 035 037 041
7.3 6 001 016 021 026 035 039
7.4 6 001 008 013 043 047 052
7.5 5 001 031 035 046 065
7.6 5 011 017 027 030 031
7.7 5 005 009 015 017 019
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 5 011 013 017 021 027
8.2 5 005 015 025 029 037
8.3 5 001 007 011 015 016
8.4 5 002 007 013 023 029
8.5 5 011 017 025 031 038
8.6 5 011 025 031 047 051
8.7 5 001 005 011 013 014
8.8 5 005 013 017 023 028
8.9 5 003 009 011 015 017
8.10 5 006 013 017 019 024
8.11 4 002 006 007 012
8.12 4 011 027 031 035
8.13 2 003 015
8.14 4 003 006 009 011
8.15 4 009 013 021 030
8.16 4 001 003 005 008
8.17 3 001 002 004
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 8 030 031 032 033 034 035 036 037
9.1 9 010 011 015 019 025 027 033 037 041
9.2 9 003 007 011 013 015 022 025 026 027
9.3 8 003 005 007 011 015 017 020 023
9.4 10 012 017 021 025 038 043 050 054 056 057
9.5 9 001 008 011 014 023 031 033 035 043
9.6 6 003 013 015 021 025 033
9.7 9 004 009 013 016 019 021 028 035 040
9.8 9 001 009 015 023 029 031 034 036 040
9.9 9 001 010 013 015 017 021 025 027 028
9.10 9 001 013 023 027 035 043 051 059 061
9.11 9 001 007 013 018 022 025 027 033 035
9.12 8 001 007 011 019 023 025 029 033
9.13 8 001 009 019 025 029 037 039 041
9.14 7 001 005 009 011 013 015 017
9.15 9 001 009 019 027 035 043 051 059 075
9.16 6 001 003 007 009 011 012
9.17 7 001 005 008 013 017 023 027
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 8 001 005 007 011 013 017 019 023
10.2 15 001 005 007 009 013 017 023 025 029 031 035 037 041 043 047
10.3 5 001 003 005 008 010
10.4 13 003 005 009 012 016 017 019 021 025 029 031 033 035
10.5 6 001 005 009 012 017 019
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 9 024 025 026 030 031 032 033 034 035
11.1 8 001 005 009 011 015 019 023 024
11.2 7 001 007 009 011 015 017 023
11.3 6 003 009 011 021 024 036
11.4 6 001 004 010 011 016 019
11.5 3 003 011 014
Chapter 12: Orthogonal 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 6 001 005 007 009 018 021
12.2 6 001 005 007 009 013 015
12.3 10 001 005 011 013 018 025 033 035 045 049
12.4 4 001 004 008 009
12.5 4 001 007 009 011
12.6 3 001 009 015
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 8 001 003 005 009 012 017 019 023
13.2 5 001 003 005 007 009
13.3 5 001 002 004 005 007
13.4 7 001 002 003 015 019 023 501.XP
13.5 5 001 005 009 011 015
13.6 5 001 003 007 010 017
13.7 4 002 003 004 007
13.8 3 001 003 005
Chapter 14: Boundary-Value Problems in Other Coordinate Systems
14.R 6 001 002 003 004 007 009
14.1 4 001 012 013 015
14.2 3 005 012 013
14.3 4 001 005 010 011
Chapter 15: Integral Transform Method
15.R 9 001 002 004 006 007 008 013 016 017
15.TB 3 034 035 036
15.1 3 006 007 009
15.2 6 003 011 014 021 022 025
15.3 5 001 003 007 013 017
15.4 6 002 005 010 013 015 019
15.5 2 003 008
Chapter 16: Numerical Solutions of Partial Differential Equations
16.R 3 001 002 003
16.TB 4 030 031 034 035
16.1 4 001 003 005 006
16.2 4 001 006 011 012
16.3 4 001 004 005 006
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 7 030 031 032 033 034 035 036
17.1 6 001 009 017 029 033 039
17.2 6 003 013 015 021 027 033
17.3 4 001 006 011 016
17.4 5 001 011 015 020 027
17.5 4 001 007 015 025
17.6 6 001 011 014 025 029 040
17.7 4 001 012 015 021
17.8 4 001 005 010 013
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 4 001 018 022 032
18.2 4 009 011 017 023
18.3 4 003 006 011 021
18.4 5 001 009 012 017 021
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 4 001 016 019 023
19.2 4 002 015 027 033
19.3 4 001 005 007 013
19.4 4 003 011 013 020
19.5 3 001 007 025
19.6 4 003 007 011 018
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 4 001 011 015 025
20.2 4 001 015 019 023
20.3 4 001 005 009 015
20.4 4 001 006 007 009
20.5 3 001 005 007
20.6 4 001 005 011 014
Total 1572