# Differential Equations with Boundary-Value Problems 9th edition

Dennis Zill
Publisher: Cengage Learning

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• Chapter 1: Introduction to Differential Equations
• 1.1: Definitions and Terminology (26)
• 1.2: Initial-Value Problems (28)
• 1.3: Differential Equations as Mathematical Models (20)
• 1: Chapter 1 In Review (25)

• Chapter 2: First-Order Differential Equations
• 2.1: Solution Curves Without a Solution (22)
• 2.2: Separable Equations (30)
• 2.3: Linear Equations (29)
• 2.4: Exact Equations (27)
• 2.5: Solutions by Substitutions (24)
• 2.6: A Numerical Method (11)
• 2: Chapter 2 In Review (21)

• Chapter 3: Modeling with First-Order Differential Equations
• 3.1: Linear Models (35)
• 3.2: Nonlinear Models (16)
• 3.3: Modeling with Systems of First-Order DEs (13)
• 3: Chapter 3 In Review (7)

• Chapter 4: Higher-Order Differential Equations
• 4.1: Preliminary Theory—Linear Equations (23)
• 4.2: Reduction of Order (20)
• 4.3: Homogeneous Linear Equations with Constant Coefficients (44)
• 4.4: Undetermined Coefficients—Superposition Approach (36)
• 4.5: Undetermined Coefficients—Annihilator Approach (45)
• 4.6: Variation of Parameters (21)
• 4.7: Cauchy-Euler Equations (29)
• 4.8: Green's Functions (30)
• 4.9: Solving Systems of Linear DEs by Elimination (18)
• 4.10: Nonlinear Differential Equations (16)
• 4: Chapter 4 In Review (32)

• Chapter 5: Modeling with Higher-Order Differential Equations
• 5.1: Linear Models: Initial-Value Problems (30)
• 5.2: Linear Models: Boundary-Value Problems (20)
• 5.3: Nonlinear Models (11)
• 5: Chapter 5 In Review (10)

• Chapter 6: Series Solutions of Linear Equations
• 6.1: Review of Power Series (23)
• 6.2: Solutions About Ordinary Points (19)
• 6.3: Solutions About Singular Points (22)
• 6.4: Special Functions (21)
• 6: Chapter 6 In Review (17)

• Chapter 7: The Laplace Transform
• 7.1: Definition of the Laplace Transform (31)
• 7.2: Inverse Transforms and Transforms of Derivatives (32)
• 7.3: Operational Properties I (48)
• 7.4: Operational Properties II (43)
• 7.5: The Dirac Delta Function (12)
• 7.6: Systems of Linear Differential Equations (15)
• 7: Chapter 7 In Review (37)

• Chapter 8: Systems of Linear First-Order Differential Equations
• 8.1: Preliminary Theory—Linear Systems (20)
• 8.2: Homogeneous Linear Systems (32)
• 8.3: Nonhomogeneous Linear Systems (26)
• 8.4: Matrix Exponential (15)
• 8: Chapter 8 In Review (15)

• Chapter 9: Numerical Solutions of Ordinary Differential Equations
• 9.1: Euler Methods and Error Analysis (12)
• 9.2: Runge-Kutta Methods (12)
• 9.3: Multistep Methods (6)
• 9.4: Higher-Order Equations and Systems (9)
• 9.5: Second-Order Boundary-Value Problems (10)
• 9: Chapter 9 In Review (8)

• Chapter 10: Systems of Nonlinear First-Order Differential Equations
• 10.1: Autonomous Systems (18)
• 10.2: Stability of Linear Systems (16)
• 10.3: Linearization and Local Stability (17)
• 10.4: Autonomous Systems as Mathematical Models (7)
• 10: Chapter 10 In Review (15)

• Chapter 11: Fourier Series
• 11.1: Orthogonal Functions (18)
• 11.2: Fourier Series (15)
• 11.3: Fourier Cosine and Sine Series (23)
• 11.4: Sturm-Liouville Problem (8)
• 11.5: Bessel and Legendre Series (10)
• 11: Chapter 11 In Review (16)

• Chapter 12: Boundary-Value Problems in Rectangular Coordinates
• 12.1: Separable Partial Differential Equations (19)
• 12.2: Classical PDEs and Boundary-Value Problems (10)
• 12.3: Heat Equation (5)
• 12.4: Wave Equation (12)
• 12.5: Laplace's Equation (13)
• 12.6: Nonhomogeneous Boundary-Value Problems (12)
• 12.7: Orthogonal Series Expansions (5)
• 12.8: Higher-Dimensional Problems (6)
• 12: Chapter 12 In Review (12)

• Chapter 13: Boundary-Value Problems in Other Coordinate Systems
• 13.1: Polar Coordinates (9)
• 13.2: Polar and Cylindrical Coordinates (6)
• 13.3: Spherical Coordinates (5)
• 13: Chapter 13 In Review (9)

• Chapter 14: Integral Transforms
• 14.1: Error Function (6)
• 14.2: Laplace Transform (13)
• 14.3: Fourier Integral (12)
• 14.4: Fourier Transforms (9)
• 14: Chapter 14 In Review (9)

• Chapter 15: Numerical Solutions of Partial Differential Equations
• 15.1: Laplace's Equation (6)
• 15.2: Heat Equation (5)
• 15.3: Wave Equation (5)
• 15: Chapter 15 In Review (3)

• Chapter A: Appendices
• A.A: Integral-Defined Functions (7)
• A.B: Matrices (56)

Differential Equations with Boundary-Value Problems, 9th edition, by Dennis G. Zill, published by Cengage Learning, provides a thorough treatment of topics typically covered in a first course in Differential Equations, as well as an introduction to boundary-value problems and partial differential equations. This proven and easy-to-understand book speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and more. The WebAssign component for this text engages students with immediate feedback, a complete eBook, and a question bank of end-of-section exercises.

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##### Question Group Key
XP - Extra Problem

##### Question Availability Color Key
BLACK questions are available now
GRAY questions are under development

Group Quantity Questions
Chapter A: Appendices
A.A 7 001 002 007 008 021 025 026
A.B 56 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056
Chapter 1: Introduction to Differential Equations
1.R 25 001 002 003 004 005 006 007 008 009 010 011 012 015 016 017 018 019 020 022 024 028 032 038 039 040
1.1 26 001 002 003 004 005 007 009 011 012 013 015 017 018 019 021 023 026 031 034 036 037 042 045 054 058 060
1.2 28 001 003 004 007 008 009 011 012 013 015 017 018 019 021 022 023 024 025 026 030 033 034 037 039 041 042 043 046
1.3 20 001 002 005 006 007 008 009 010 013 014 015 016 017 018 023 025 026 027 028 038
Chapter 2: First-Order Differential Equations
2.R 21 001 002 013 014 015 016 018 019 020 021 022 023 024 025 026 028 032 033 034 035 038
2.1 22 001 002 003 004 005 007 009 010 011 013 014 015 016 019 021 023 025 027 030 031 038 040
2.2 30 001 003 004 005 007 008 009 010 011 013 015 017 018 019 020 021 023 024 025 027 028 029 030 036 038 041 046 047 049 055
2.3 29 001 003 004 005 007 008 009 011 012 013 015 017 018 019 021 022 023 024 025 027 028 029 031 033 034 038 039 052 501.XP
2.4 27 001 003 004 005 007 008 009 010 011 012 013 015 017 019 021 023 024 025 027 028 029 030 031 032 033 035 038
2.5 24 001 003 004 005 007 009 010 011 012 013 015 017 018 019 021 022 023 025 026 027 029 030 036 038
2.6 11 001 002 003 004 005 006 007 009 010 011 012
Chapter 3: Modeling with First-Order Differential Equations
3.R 7 004 007 008 010 012 013 014
3.1 35 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 019 020 021 022 023 026 029 031 032 033 034 035 037 041 043 044 045 048
3.2 16 001 002 003 004 006 008 009 010 011 013 015 017 019 020 021 027
3.3 13 001 002 004 007 008 009 010 011 012 013 014 015 022
Chapter 4: Higher-Order Differential Equations
4.R 32 001 002 003 004 006 008 011 012 016 017 018 019 020 021 024 025 026 028 029 030 031 032 033 034 039 041 042 043 044 047 048 049
4.1 23 001 002 004 009 010 013 014 015 016 017 018 019 021 022 023 025 026 027 028 029 034 036 040
4.2 20 001 002 003 005 007 008 009 010 011 012 013 014 015 016 017 018 019 020 022 024
4.3 44 001 003 004 005 007 009 010 011 013 014 015 017 018 019 021 023 024 025 026 027 029 030 031 032 033 035 036 037 038 039 040 041 043 045 047 049 050 051 053 055 056 057 058 061
4.4 36 001 003 005 006 007 009 010 011 013 014 015 017 018 019 021 023 024 025 027 028 029 030 031 033 034 035 037 038 039 041 042 045 046 047 048 050
4.5 45 001 003 004 005 007 009 015 017 019 021 022 023 024 025 026 027 029 030 031 033 034 035 037 039 041 042 043 045 047 049 051 052 053 055 057 058 059 061 063 065 066 067 068 069 071
4.6 21 001 003 004 005 007 009 010 011 013 014 015 017 019 020 021 027 028 029 030 031 034
4.7 29 001 003 004 005 006 007 009 010 011 013 015 016 017 019 020 021 022 023 025 027 029 031 032 033 035 037 038 039 041
4.8 30 001 003 004 005 007 008 009 011 012 013 015 016 017 019 020 021 023 024 025 027 028 029 031 032 033 035 039 041 042 043
4.9 18 001 002 003 005 006 007 009 010 011 012 013 015 017 018 019 021 022 023
4.10 16 002 003 004 005 006 008 009 010 011 012 013 015 016 017 019 021
Chapter 5: Modeling with Higher-Order Differential Equations
5.R 10 011 012 014 015 016 018 020 021 022 026
5.1 30 001 002 003 005 006 008 012 014 019 021 023 025 026 027 029 031 033 034 035 037 041 042 049 051 052 053 056 057 060 061
5.2 20 001 003 005 007 009 010 011 012 013 014 015 016 017 018 020 021 027 029 036 041
5.3 11 001 002 003 004 007 008 009 010 016 017 018
Chapter 6: Series Solutions of Linear Equations
6.R 17 001 002 003 004 005 006 009 010 013 014 015 016 017 019 020 022 026
6.1 23 001 003 005 006 007 009 010 011 012 013 015 017 019 021 023 025 027 028 029 035 036 037 038
6.2 19 001 002 005 007 008 009 011 012 013 015 016 017 018 019 020 021 023 024 025
6.3 22 001 003 005 006 007 009 010 011 013 014 015 016 017 018 019 021 022 023 025 027 031 032
6.4 21 001 002 003 004 005 007 008 009 010 011 012 013 015 016 017 019 023 024 026 036 049
Chapter 7: The Laplace Transform
7.R 37 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 020 021 022 024 025 026 027 028 029 030 031 032 035 036 041 042 043 044 045 046
7.1 31 001 002 003 005 006 007 008 009 011 013 014 015 017 018 019 021 023 024 025 026 027 030 031 033 035 036 037 038 039 040 050
7.2 32 001 003 004 005 007 009 010 011 013 014 015 017 019 020 021 023 024 025 027 028 029 032 035 037 038 039 040 041 043 044 045 050
7.3 48 001 003 004 005 007 008 009 011 012 013 015 016 017 018 019 021 023 024 025 027 028 029 031 033 034 037 039 040 041 043 045 046 047 049 053 055 057 059 061 063 064 065 067 068 069 071 073 077
7.4 43 001 003 004 005 006 007 009 010 011 013 014 015 017 018 023 024 025 026 027 028 029 031 032 033 035 036 037 041 042 043 045 046 047 049 051 053 054 055 056 057 061 067 070
7.5 12 001 002 003 005 006 007 009 010 011 012 015 016
7.6 15 001 002 003 004 005 007 008 009 010 011 012 013 015 017 019
Chapter 8: Systems of Linear First-Order Differential Equations
8.R 15 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015
8.1 20 001 003 004 005 006 007 008 009 011 012 013 015 016 017 018 019 021 022 023 026
8.2 32 001 003 004 005 007 008 009 010 011 013 014 016 017 021 023 024 025 027 028 029 031 032 035 037 038 039 041 043 044 045 047 048
8.3 26 001 002 003 005 006 007 009 010 012 013 014 016 017 018 019 021 023 025 027 028 029 031 032 033 034 035
8.4 15 001 002 003 004 005 007 008 009 010 012 015 016 017 020 022
Chapter 9: Numerical Solutions of Ordinary Differential Equations
9.R 8 001 002 003 004 005 006 007 008
9.1 12 001 002 003 005 006 007 008 009 010 011 012 017
9.2 12 001 003 004 005 007 008 009 011 012 013 015 016
9.3 6 003 004 005 006 007 008
9.4 9 001 002 003 004 006 007 008 009 011
9.5 10 001 002 003 004 005 007 008 009 010 012
Chapter 10: Systems of Nonlinear First-Order Differential Equations
10.R 15 001 002 003 004 005 006 007 008 010 012 013 014 016 017 018
10.1 18 001 002 003 004 005 007 008 009 011 012 013 015 016 019 021 023 024 026
10.2 16 001 002 004 005 006 007 009 010 011 013 015 017 018 020 023 024
10.3 17 002 003 006 008 009 011 014 016 018 021 022 024 028 032 034 036 037
10.4 7 001 002 004 010 011 016 019
Chapter 11: Fourier Series
11.R 16 001 002 003 004 005 006 007 008 010 012 013 014 015 016 018 022
11.1 18 001 002 003 005 006 007 008 009 010 011 014 016 018 019 020 021 022 023
11.2 15 001 002 003 005 006 007 008 009 010 011 012 013 014 015 018
11.3 23 001 003 004 005 007 008 011 012 013 014 015 018 025 028 029 030 033 035 038 044 045 046 049
11.4 8 001 004 007 008 009 010 011 012
11.5 10 001 002 004 006 007 008 009 010 015 021
Chapter 12: Boundary-Value Problems in Rectangular Coordinates
12.R 12 001 002 003 005 006 007 008 009 012 013 014 016
12.1 19 001 002 003 005 006 007 008 009 012 014 015 017 018 019 020 021 023 024 025
12.2 10 001 002 003 005 006 007 008 009 010 012
12.3 5 001 002 004 005 007
12.4 12 001 002 003 004 006 008 015 017 021 022 501.XP 502.XP
12.5 13 001 003 004 005 007 008 009 011 012 013 014 015 016
12.6 12 001 002 003 004 005 006 007 010 013 014 017 018
12.7 5 002 003 004 007 008
12.8 6 001 002 003 004 005 006
Chapter 13: Boundary-Value Problems in Other Coordinate Systems
13.R 9 001 002 003 004 005 006 010 016 018
13.1 9 001 002 006 008 010 011 014 015 018
13.2 6 003 006 008 012 013 501.XP
13.3 5 001 005 006 009 011
Chapter 14: Integral Transforms
14.R 9 001 002 004 006 007 008 010 013 020
14.1 6 006 007 008 009 012 014
14.2 13 002 003 006 008 009 011 012 014 021 022 024 025 029
14.3 12 001 002 003 006 007 008 010 011 013 014 017 018
14.4 9 002 005 008 010 013 015 016 019 026
Chapter 15: Numerical Solutions of Partial Differential Equations
15.R 3 001 002 003
15.1 6 001 002 003 004 005 006
15.2 5 001 003 006 011 012
15.3 5 001 002 004 005 006
Total 1621