# A First Course in Differential Equations with Modeling Applications, International Edition 10th edition

Dennis Zill
Publisher: Cengage Learning

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• Chapter 1: Introduction to Differential Equations
• 1.1: Definitions and Terminology (17)
• 1.2: Initial-Value Problems (18)
• 1.3: Differential Equations as Mathematical Models (18)
• 1: Review (20)

• Chapter 2: First-Order Differential Equations
• 2.1: Solution Curves Without a Solution (18)
• 2.2: Separable Equations (20)
• 2.3: Linear Equations (21)
• 2.4: Exact Equations (19)
• 2.5: Solutions by Substitutions (17)
• 2.6: A Numerical Method (7)
• 2: Review (18)

• Chapter 3: Modeling With First-Order Differential Equations
• 3.1: Linear Models (31)
• 3.2: Nonlinear Models (15)
• 3.3: Modeling with Systems of First-Order DEs (11)
• 3: Review (6)

• Chapter 4: Higher-Order Differential Equations
• 4.1: Preliminary Theory-Linear Equations (14)
• 4.2: Reduction of Order (12)
• 4.3: Homogeneous Linear Equations with Constant Coefficients (30)
• 4.4: Undetermined Coefficients-Superposition Approach (23)
• 4.5: Undetermined Coefficients-Annihilator Approach (34)
• 4.6: Variation of Parameters (15)
• 4.7: Cauchy-Euler Equation (21)
• 4.8: Green's Function (21)
• 4.9: Solving Systems of Linear DEs by Elimination (12)
• 4.10: Nonlinear Differential Equations (9)
• 4: Review (28)

• Chapter 5: Modeling With Higher-Order Differential Equations
• 5.1: Linear Models: Initial-Value Problems (22)
• 5.2: Linear Models: Boundary-Value Problems (18)
• 5.3: Nonlinear Models (6)
• 5: Review (4)

• Chapter 6: Series Solutions of Linear Equations
• 6.1: Review of Power Series (16)
• 6.2: Solutions About Ordinary Points (12)
• 6.3: Solutions About Singular Points (17)
• 6.4: Special Functions (13)
• 6: Review (13)

• Chapter 7: The Laplace Transform
• 7.1: Definition of the Laplace Transform (20)
• 7.2: Inverse Transforms and Transforms of Derivatives (22)
• 7.3: Operational Properties I (36)
• 7.4: Operational Properties II (29)
• 7.5: The Dirac Delta Function (8)
• 7.6: Systems of Linear Differential Equations (10)
• 7: Review (35)

• Chapter 8: Systems of Linear First-Order Differential Equations
• 8.1: Preliminary Theory-Linear Systems (12)
• 8.2: Homogeneous Linear Systems (21)
• 8.3: Nonhomogeneous Linear Systems (18)
• 8.4: Matrix Exponential (8)
• 8: Review (15)

• Chapter 9: Numerical Solutions of Ordinary Differential Equations
• 9.1: Euler Methods and Error Analysis (8)
• 9.2: Runge-Kutta Methods (8)
• 9.3: Multistep Methods (4)
• 9.4: Higher-Order Equations and Systems (6)
• 9.5: Second-Order Boundary-Value Problems (6)
• 9: Review (8)

• Chapter A: Appendixes
• A.1: Gamma Function
• A.2: Matrices
• A.3: Laplace Transforms

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Group Quantity Questions
Chapter 1: Introduction to Differential Equations
1.R 20 001 002 003 004 005 006 007 008 009 010 011 012 015 016 017 019 020 022 035 036
1.1 17 001 003 005 007 009 011 013 015 017 019 023 027 033 041 050 054 056
1.2 18 001 003 007 009 011 013 015 017 019 021 023 025 033 034 037 039 041 043
1.3 18 001 002 005 006 007 008 009 010 013 014 015 016 017 018 023 025 026 027
Chapter 2: First-Order Differential Equations
2.R 18 001 002 013 014 015 016 018 019 021 022 023 024 025 026 027 028 029 032
2.1 18 001 002 003 005 007 008 009 011 013 014 019 021 023 025 027 031 038 040
2.2 20 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 036 041 047 049 055
2.3 21 001 003 005 007 009 011 013 015 017 019 021 023 024 025 027 029 031 033 039 042 047
2.4 19 001 003 005 007 009 010 011 013 015 017 019 021 023 025 027 029 031 033 035
2.5 17 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 036 038
2.6 7 001 003 005 007 009 011 012
Chapter 3: Modeling With First-Order Differential Equations
3.R 6 004 005 006 009 011 012
3.1 31 001 002 003 004 005 006 007 009 010 011 012 013 014 015 016 017 019 020 021 022 023 026 029 031 033 035 037 039 041 043 046
3.2 15 001 002 003 004 006 008 009 010 011 013 015 017 019 021 027
3.3 11 001 002 004 005 006 007 008 009 010 011 013
Chapter 4: Higher-Order Differential Equations
4.R 28 001 002 003 004 011 012 015 016 017 018 019 022 023 024 026 027 028 029 030 031 035 037 038 039 040 043 044 045
4.1 14 001 004 009 013 015 017 019 021 023 025 027 029 036 040
4.2 12 001 003 005 007 009 011 013 015 016 017 019 022
4.3 30 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 039 041 043 045 047 049 051 053 055 057 061
4.4 23 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 039 041 045 047
4.5 34 001 003 005 007 009 015 017 019 021 023 025 027 029 031 033 035 037 039 041 043 045 047 049 051 053 055 057 059 061 063 065 067 069 071
4.6 15 001 003 005 007 009 011 013 015 017 019 021 023 025 027 030
4.7 21 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 039 041
4.8 21 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 039 041 043
4.9 12 001 003 005 007 009 011 013 015 017 019 021 023
4.10 9 003 005 007 009 011 013 015 017 019
Chapter 5: Modeling With Higher-Order Differential Equations
5.R 4 011 014 015 021
5.1 22 001 002 003 005 008 015 017 019 021 023 025 027 029 030 031 033 037 045 047 049 053 057
5.2 18 001 003 005 007 009 010 011 012 013 014 015 016 017 018 019 025 027 037
5.3 6 001 003 007 009 016 017
Chapter 6: Series Solutions of Linear Equations
6.R 13 001 002 003 005 006 009 010 013 015 016 017 019 020
6.1 16 001 003 005 007 009 011 013 015 017 021 023 025 027 029 035 037
6.2 12 001 005 007 009 011 013 015 017 019 021 023 025
6.3 17 001 003 005 007 008 009 011 013 015 017 019 021 023 025 027 031 032
6.4 13 001 003 005 007 009 011 013 015 017 019 023 026 047
Chapter 7: The Laplace Transform
7.R 35 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 020 021 022 025 026 027 028 029 030 031 032 033 034 039 040 041 042 043
7.1 20 001 003 005 007 009 011 013 015 017 019 021 023 025 027 031 033 035 037 039 051
7.2 22 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 039 041 044
7.3 36 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 037 039 041 043 045 047 049 053 055 057 059 061 063 065 067 069 071 073 077
7.4 29 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 037 039 041 043 045 047 049 051 053 057 063 066
7.5 8 001 003 005 007 009 011 013 014
7.6 10 001 003 005 007 009 011 013 015 017 019
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 12 001 003 005 007 009 011 013 015 017 019 021 023
8.2 21 001 003 005 007 009 011 013 015 019 021 023 025 027 029 033 035 037 039 041 043 045
8.3 18 001 003 005 007 009 010 011 015 017 019 021 023 025 027 029 030 031 033
8.4 8 001 003 005 007 009 012 015 017
Chapter 9: Numerical Solutions of Ordinary Differential Equations
9.R 8 001 002 003 004 005 006 007 008
9.1 8 001 003 005 007 009 011 012 017
9.2 8 001 003 005 007 009 011 013 015
9.3 4 003 004 005 007
9.4 6 001 003 006 007 009 011
9.5 6 001 003 005 007 009 012
Total 870