# A First Course in Differential Equations with Modeling Applications 11th edition

Dennis Zill
Publisher: Cengage Learning

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• Zill A First Course in Differential Equations with Modeling Applications 11e

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• Chapter 1: Introduction to Differential Equations
• 1.1: Definitions and Terminology (27)
• 1.2: Initial-Value Problems (40)
• 1.3: Differential Equations as Mathematical Models (23)
• 1: Chapter 1 in Review (26)

• Chapter 2: First-Order Differential Equations
• 2.1: Solution Curves Without a Solution (23)
• 2.2: Separable Equations (36)
• 2.3: Linear Equations (38)
• 2.4: Exact Equations (33)
• 2.5: Solutions by Substitutions (28)
• 2.6: A Numerical Method (12)
• 2: Chapter 2 in Review (21)

• Chapter 3: Modeling with First-Order Differential Equations
• 3.1: Linear Models (42)
• 3.2: Nonlinear Models (20)
• 3.3: Modeling with Systems of First-Order DEs (15)
• 3: Chapter 3 in Review (8)

• Chapter 4: Higher-Order Differential Equations
• 4.1: Preliminary Theory—Linear Equations (32)
• 4.2: Reduction of Order (27)
• 4.3: Homogeneous Linear Equations with Constant Coefficients (51)
• 4.4: Undetermined Coefficients—Superposition Approach (44)
• 4.5: Undetermined Coefficients—Annihilator Approach (51)
• 4.6: Variation of Parameters (26)
• 4.7: Cauchy-Euler Equations (35)
• 4.8: Green's Functions (32)
• 4.9: Solving Systems of Linear DEs by Elimination (19)
• 4.10: Nonlinear Differential Equations (18)
• 4: Chapter 4 in Review (32)

• Chapter 5: Modeling with Higher-Order Differential Equations
• 5.1: Linear Models: Initial-Value Problems (38)
• 5.2: Linear Models: Boundary-Value Problems (24)
• 5.3: Nonlinear Models (12)
• 5: Chapter 5 in Review (10)

• Chapter 6: Series Solutions of Linear Equations
• 6.1: Review of Power Series (32)
• 6.2: Solutions About Ordinary Points (22)
• 6.3: Solutions About Singular Points (25)
• 6.4: Special Functions (22)
• 6: Chapter 6 in Review (17)

• Chapter 7: The Laplace Transform
• 7.1: Definition of the Laplace Transform (37)
• 7.2: Inverse Transforms and Transforms of Derivatives (36)
• 7.3: Operational Properties I (54)
• 7.4: Operational Properties II (51)
• 7.5: The Dirac Delta Function (16)
• 7.6: Systems of Linear Differential Equations (20)
• 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 (49)
• 8.3: Nonhomogeneous Linear Systems (36)
• 8.4: Matrix Exponential (16)
• 8: Chapter 8 in Review (15)

• Chapter 9: Numerical Solutions of Ordinary Differential Equations
• 9.1: Euler Methods and Error Analysis (13)
• 9.2: Runge-Kutta Methods (13)
• 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 A: Appendices
• A.A: Integral-Defined Functions (7)
• A.B: Matrices (58)

• Chapter CR: Calculus Review
• CR.1: Factoring Polynomials (10)
• CR.2: Partial Fractions (12)
• CR.3: The Product and Quotient Rules of Differentiation (10)
• CR.4: Derivatives of Exponential and Logarithmic Functions (10)
• CR.5: Derivatives of Trigonometric Functions (10)
• CR.6: The Chain Rule of Differentiation (10)
• CR.7: Implicit Differentiation (10)
• CR.8: Derivatives and the Shape of a Graph (10)
• CR.9: The Substitution Rule of Integration (12)
• CR.10: Integration by Parts (10)
• CR.11: Trigonometric Integrals and Substitutions (12)
• CR.12: Improper Integrals (10)

A First Course in Differential Equations with Modeling Applications, 11th Edition, by Dennis Zill strikes a balance between analytical, qualitative, and quantitative approaches to the study of differential equations. This proven resource speaks to students of varied majors through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, and definitions. It provides a thorough overview of the topics typically taught in a first course in differential equations written in a straightforward, readable, and helpful style. The WebAssign component for this title engages students with many features, and links to a complete eBook.

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• Expanded Problem (EP) questions are expanded versions of existing questions that include intermediary steps to guide the student to the final answer.
• Course Packs with ready-to-use assignments built by subject matter experts specifically for this textbook are designed to save you time, and can be easily customized to meet your teaching goals.
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## 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.

##### Question Group Key
EP - Expanded Problem
MI - Master It Tutorial
MI.SA - Stand Alone Master It
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 58 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032.MI 032.MI.SA 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047.MI 047.MI.SA 048 049 050 051 052 053 054 055 056
Chapter CR: Calculus Review
CR.1 10 001.MI 002 003 004 005 006 007.MI 008.MI 009.MI 010.MI
CR.2 12 001 002 003.MI 004 005.MI 006.MI 007.MI 008 009.MI 010.MI 011.MI 012
CR.3 10 001 002 003 004.MI 005 006 007 008 009 010
CR.4 10 001 002 003 004 005 006 007 008 009 010
CR.5 10 001 002.MI 003 004 005 006 007 008 009 010
CR.6 10 001 002 003 004 005 006 007 008 009 010
CR.7 10 001 002 003 004 005 006 007 008 009 010
CR.8 10 001 002 003 004.MI 005 006 007 008 009 010
CR.9 12 001.MI 002 003.MI 004 005.MI 006 007.MI 008.MI 009 010 011 012
CR.10 10 001 002.MI 003 004 005.MI 006 007 008 009 010
CR.11 12 001.MI 002 003 004 005 006 007 008 009 010 011 012
CR.12 10 001 002 003 004 005 006 007 008 009 010
Chapter 1: Introduction to Differential Equations
1.R 26 001 002 003 004 005 006 007 008 009 010 011 012 015 016 017 018 019 020 022 024 028 032 038 038.EP 039 040
1.1 27 001 002 003 004 005 007 009 011 012 013 015 017 018 019 021 023 026 031 034 036 037 042 045 054 058 058.EP 060
1.2 40 001 003.MI 003.MI.SA 004 004.EP 007 008 009 011 012 012.EP 013 015 017 017.EP 018 018.EP 019 019.EP 021 021.EP 022 022.EP 023 023.EP 024 024.EP 025 025.EP 026 026.EP 030 033 034 037 039 041 042 043 046
1.3 23 001 002 005 006 007 008 009 010.MI 010.MI.SA 013 014 014.EP 015 016 017 018 018.EP 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 23 PJT.001 001 002 003 004 005 007 009 010 011 013 014 015 016 019 021 023 025 027 030 031 038 040
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2.3 38 001 003 004 005 007 008.MI 008.MI.SA 009 009.EP 011 011.EP 012 013 015 015.EP 017 017.EP 018 019 019.EP 021 022 023 024 024.EP 025.MI 027 028 028.EP 029 031 033 034 038 038.EP 039 052 501.XP
2.4 33 001 001.EP 003 004 004.EP 005 007 008 009 009.EP 010 011 012 013.MI 013.MI.SA 015 017 019 021 021.EP 023.MI 024 025 025.EP 027 028 029 030 031 032 033 035 038
2.5 28 001 003 003.EP 004 004.EP 005 007 007.EP 009 010 011.MI 011.MI.SA 012 013 015 017 018 019 021.MI 022 023 025 026 027 029 030 036 038
2.6 12 001 001.EP 002 003 004 005 006 007 009 010 011 012
Chapter 3: Modeling with First-Order Differential Equations
3.R 8 004 007 008 010 012 012.EP 013 014
3.1 42 PJT.001 001 002 003.MI 003.MI.SA 004 005 006 007 008 009 009.EP 010 011 012 013 014 015.MI 016 017 019 020 021 022 022.EP 023 025 026 027 029 029.EP 031 032 033 034 035 037 041 043 044 045 048
3.2 20 PJT.001 001 002.MI 003 003.EP 004 006 008 009.MI 009.MI.SA 010 011 013 013.EP 015 017 019 020 021 027
3.3 15 PJT.001 001 002 004 007 008 009 009.EP 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 32 PJT.001 001 002 004 009 010 013 014 015 015.EP 016 016.EP 017 017.EP 018 018.EP 019 019.EP 021 021.EP 022 022.EP 023 025 026 027.MI 027.MI.SA 028 029 034 036 040
4.2 27 001 002 003 005 007.MI 008 008.EP 009 009.EP 010 011 011.EP 012 013 013.EP 014 015 016 017.MI 017.MI.SA 018 018.EP 019 020 020.EP 022 024
4.3 51 001 003 004 005.MI 007 009 010 010.EP 011 013 013.EP 014 015 017 018 019 019.EP 021 023 023.EP 024 024.EP 025.MI 026 027 029 030 031 031.EP 032 033 035.MI 035.MI.SA 036 037 038 039 040 041 043 045 047 049 050 051 053 055 056 057 058 061
4.4 44 001 003 003.EP 005 006.MI 006.MI.SA 007 007.EP 009 010 010.EP 011 013 014 014.EP 015 017 017.EP 018 019.MI 021 023 024 025 025.EP 027 028 029 029.EP 030 031.MI 033 034 035 037 038 039 041 042 045 046 047 048 050
4.5 51 001 003 004 005 007 009 015 017.MI 019 021 022 023 024 025 026 027 029 030 031 033 034 035 035.EP 037 039.MI 041 041.EP 042 043 043.EP 045 047 049 049.EP 051 052 053 055 057 058 059 061 063 063.EP 065 065.EP 066 067 068 069 071
4.6 26 001 001.EP 003 004 004.EP 005 007 009 009.EP 010 010.EP 011.MI 011.MI.SA 013 014 015 017 019.MI 020 021 027 028 029 030 031 034
4.7 35 001 001.EP 003 004 005 005.EP 006 007 007.EP 009 010 011 013 013.EP 015 016 017 019 019.EP 020 021.MI 022 023 025 027 029 031 032 033 035 037 037.EP 038 039 041
4.8 32 001 003 004 004.EP 005 007 007.EP 008 009 011 012 013 015 016 017 019 020 021.MI 023 024 025 027 028 029 031 032 033 035 039 041 042 043
4.9 19 PJT.001 001 002.MI 003 005 006 007 009 010 011 012 013 015 017 018 019 021 022 023
4.10 18 002 003.MI 004 004.EP 005 006 008 008.EP 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 38 PJT.001 001 001.EP 002 003 003.EP 005 006 006.EP 008 012 014 019 021 023 025.MI 025.MI.SA 026 027 027.EP 029 031 033 034 034.EP 035 037 041 042 049 051 052 052.EP 053 056 057 060 061
5.2 24 001 001.EP 003 003.EP 005 005.EP 007 007.EP 009 010 011 012 013 014 015 016 017 018 020 021 027 029 036 041
5.3 12 PJT.001 001 002 003 004 007 008 009 010 016 017 018
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 32 001 001.EP 003 003.EP 005 005.EP 006 007 009 010 011 012 013 013.EP 015 017 019 021 023 025 026 026.EP 027.MI 028 028.EP 029 029.EP 035 036 037 037.EP 038
6.2 22 001 002 005 005.EP 007 007.EP 008 009.MI 009.MI.SA 011 012 013 015 016 017 018 019 020.MI 021 023 024 025
6.3 25 001 003 005 006 007 009 010 011 013 014 015.MI 015.MI.SA 016 016.EP 017 018 018.EP 019 021 022 023 025 027 031 032
6.4 22 PJT.001 001 002 003 004 005 007 008 009 010 011 012 013 015 016 017 019 023 024 026 036 049
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 37 001 001.EP 002 002.EP 003 003.EP 005 005.EP 006 007 008.MI 008.MI.SA 009 009.EP 011 013 014 015 017 018 019 021 023 024 025 026 027 030 031.MI 033 035 036 037 038 039 040 050
7.2 36 001 003 004 005 007 009 010 011 013 014 015 017 019 020 021 023 024 025 027 028 029 032 035 035.EP 037.MI 037.MI.SA 038 038.EP 039 040 040.EP 041 043 044 045 050
7.3 54 PJT.001 001 003 004 005 007 008 009 011 012 013 015 016 017 018 019 021 021.EP 023 024 025.MI 027 028 028.EP 029 031.MI 031.MI.SA 033 033.EP 034 037 039 040 041 043 045 046 047 049 053 055 057 059 061 063 064 065 065.EP 067 068.MI 069 071 073 077
7.4 51 001 003 004 005 006.MI 007 009 009.EP 010 011 011.EP 013.MI 013.MI.SA 014 014.EP 015 017 017.EP 018 023 023.EP 024 025 026 027 028 029 031 032 033 035 036 037 041 042 042.EP 043 045 045.EP 046 047 049 051 053 054 055 056 057 061 067 070
7.5 16 001 001.EP 002 003 005 006 007.MI 007.MI.SA 009 009.EP 010 011 011.EP 012 015 016
7.6 20 001 002.MI 002.MI.SA 003 003.EP 004 005 005.EP 007 008 009 009.EP 010 011 011.EP 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 49 PJT.001 001 001.EP 003 003.EP 004 004.EP 005 005.EP 007 007.EP 008 009 010 011 013 013.EP 014 016.MI 016.MI.SA 017 021.MI 023 023.EP 024 024.EP 025 027 027.EP 028 028.EP 029 031 031.EP 032 035.MI 035.MI.SA 037 037.EP 038 038.EP 039 039.EP 041 043 044 045 047 048
8.3 36 PJT.001 001.MI 001.MI.SA 002 002.EP 003 003.EP 005 005.EP 006 007 007.EP 009 009.EP 010 012 013 014 016 017 017.EP 018 018.EP 019 021 021.EP 023 025 027 028 029 031 032 033 034 035
8.4 16 001 002 003 004 005 007 008 009 010 012 015.MI 015.MI.SA 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 13 PJT.001 001 002 003 005 006 007 008 009 010 011 012 017
9.2 13 001 003 003.EP 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
Total 1598