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A First Course in Differential Equations with Modeling Applications 12th edition

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Dennis Zill
Publisher: Cengage Learning

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  • Zill A First Course in Differential Equations with Modeling Applications 12e v2

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

  • Chapter 1: Introduction to Differential Equations
    • 1.1: Definitions and Terminology (49)
    • 1.2: Initial-Value Problems (51)
    • 1.3: Differential Equations as Mathematical Models (28)
    • 1: Chapter 1 in Review (26)

  • Chapter 2: First-Order Differential Equations
    • 2.1: Solution Curves without a Solution (31)
    • 2.2: Separable Equations (50)
    • 2.3: Linear Equations (57)
    • 2.4: Exact Equations (44)
    • 2.5: Solutions by Substitutions (39)
    • 2.6: A Numerical Method (12)
    • 2: Chapter 2 in Review (21)

  • Chapter 3: Modeling with First-Order Differential Equations
    • 3.1: Linear Models (51)
    • 3.2: Nonlinear Models (29)
    • 3.3: Modeling with Systems of First-Order DEs (18)
    • 3: Chapter 3 in Review (8)

  • Chapter 4: Higher-Order Differential Equations
    • 4.1: Theory of Linear Equations (40)
    • 4.2: Reduction of Order (28)
    • 4.3: Homogeneous Linear Equations with Constant Coefficients (67)
    • 4.4: Undetermined Coefficients—Superposition Approach (47)
    • 4.5: Undetermined Coefficients—Annihilator Approach (60)
    • 4.6: Variation of Parameters (36)
    • 4.7: Cauchy-Euler Equations (53)
    • 4.8: Green's Functions (34)
    • 4.9: Solving Systems of Linear DEs by Elimination (20)
    • 4.10: Nonlinear Differential Equations (20)
    • 4: Chapter 4 in Review (32)

  • Chapter 5: Modeling with Higher-Order Differential Equations
    • 5.1: Linear Models: Initial-Value Problems (54)
    • 5.2: Linear Models: Boundary-Value Problems (34)
    • 5.3: Nonlinear Models (19)
    • 5: Chapter 5 in Review (10)

  • Chapter 6: Series Solutions of Linear Equations
    • 6.1: Review of Power Series (37)
    • 6.2: Solutions About Ordinary Points (28)
    • 6.3: Solutions About Singular Points (30)
    • 6.4: Special Functions (41)
    • 6: Chapter 6 in Review (17)

  • Chapter 7: The Laplace Transform
    • 7.1: Definition of the Laplace Transform (47)
    • 7.2: Inverse Transforms and Transforms of Derivatives (44)
    • 7.3: Operational Properties I (73)
    • 7.4: Operational Properties II (68)
    • 7.5: The Dirac Delta Function (20)
    • 7.6: Systems of Linear Differential Equations (22)
    • 7: Chapter 7 in Review (37)

  • Chapter 8: Systems of Linear Differential Equations
    • 8.1: Theory of Linear Systems (20)
    • 8.2: Homogeneous Linear Systems (57)
    • 8.3: Nonhomogeneous Linear Systems (38)
    • 8.4: Matrix Exponential (28)
    • 8: Chapter 8 in Review (15)

  • Chapter 9: Numerical Solutions of Ordinary Differential Equations
    • 9.1: Euler Methods and Error Analysis (17)
    • 9.2: Runge-Kutta Methods (13)
    • 9.3: Multistep Methods (6)
    • 9.4: Higher-Order Equations and Systems (10)
    • 9.5: Second-Order Boundary-Value Problems (12)
    • 9: Chapter 9 in Review (8)

  • Chapter A: Appendices
    • A.A: Integral-Defined Functions (7)
    • A.B: Matrices (60)

  • 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, 12th Edition, by Dennis Zill balances analytical, qualitative, and quantitative approaches to differential equation studies. Designed to engage students from various majors, it offers useful pedagogical tools, including numerous examples, clear explanations, insightful "Remarks" boxes, and helpful definitions. Written in an accessible and supportive style, this book provides a comprehensive overview of the topics typically covered in a first course in differential equations. In this edition, we've enhanced the focus on piecewise-linear differential equations involving nonelementary integrals.

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Group Quantity Questions
Chapter A: Appendices
A.A 7 001 002 007 008 021 025 026
A.B 60 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 016.EP 017 018 019 019.EP 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 008 009 010
CR.2 12 001 002 003 004 005 006 007.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 26 001 002 003 004 005 006 007 008 009 010 011 012 015 016 017 018 019 020 022 024 028 032 042 042.EP 043 044
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1.2 51 001 002 003.MI 003.MI.SA 004 004.EP 005 007 008 009 009.EP 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 028 028.EP 030 033 034 035 037 039 039.EP 041 042 042.EP 043 044 046 048 051
1.3 28 001 002 003 005 006 007 008 009 010.MI 010.MI.SA 012 013 014 014.EP 015 016 017 018 018.EP 019 021 023 025 026 027 028 038 039
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
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2.2 50 PJT.001 001 001.EP 002 003 004 004.EP 005 007 007.EP 008 009 010.MI 010.MI.SA 011 012 013 015 017 017.EP 018 019 020 021 022 023 023.EP 024 025.MI 025.MI.SA 026 027 027.EP 028 030 031 032 033 035 035.EP 037 040 042 045 050 051 053 059 061 063
2.3 57 001 003 004 005 005.EP 006 007 007.EP 008.MI 008.MI.SA 009 009.EP 010 011 011.EP 012 013 013.EP 015 015.EP 017 017.EP 018 019 019.EP 021 022 023 023.EP 024 024.EP 025.MI 025.MI.SA 026 027 028 028.EP 029 031 032 032.EP 033 034 038 038.EP 039 042 042.EP 044 045 047 049 050 053 054 060 501.XP
2.4 44 001 001.EP 003 004 004.EP 005 006 007 008 009 009.EP 010 011 012 013.MI 013.MI.SA 015 016 017 019 021 021.EP 023.MI 023.MI.SA 024 025 025.EP 027 028 029 030 030.EP 033 034 034.EP 035 036 036.EP 037 040 041 044 046 047
2.5 39 001 002 003 003.EP 004 004.EP 005 007 007.EP 009 010 011.MI 011.MI.SA 012 012.EP 013 015 015.EP 017 018 019 020 020.EP 021.MI 021.MI.SA 022 023 023.EP 025 026 027 028 029 030 032 034 037 038 040
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 51 PJT.001 001 002 002.EP 003.MI 003.MI.SA 004 004.EP 005 006 007 008 009 011 011.EP 012 013 014 015 016 017.MI 017.MI.SA 018 019 019.EP 021 022 023 024 024.EP 025 027 028 029 029.EP 031 031.EP 033 034 035 035.EP 036 037 039 040 041 043 045 046 047 050
3.2 29 PJT.001 001 002.MI 002.MI.SA 003 003.EP 004 005 007 008 010 011.MI 011.MI.SA 012 013 014 015 015.EP 017 018 019 020 021 022 023 028 029 030 035
3.3 18 PJT.001 001 002 003 004 007 008 009 009.EP 010 011 012 013 014 015 016 019 022
Chapter 4: Higher-Order Differential Equations
4.R 32 001 002 003 004 006 008 011 012 018 019 020 021 022 023 026 027 028 030 031 032 033 034 035 036 041 043 044 045 046 049 050 051
4.1 40 PJT.001 001 002 003 004 007 009 010 012 013 014 015 015.EP 016 016.EP 017 017.EP 018 018.EP 019 019.EP 020 021 021.EP 022 022.EP 023 024 025 026 027.MI 027.MI.SA 028 029 031 034 036 038 039 042
4.2 28 001 002 003 005 007.MI 007.MI.SA 008 008.EP 009 009.EP 010 011 011.EP 012 013 013.EP 014 015 016 019.MI 019.MI.SA 020 020.EP 021 022 022.EP 024 026
4.3 67 001 002 003 004 005.MI 005.MI.SA 007 008 009 009.EP 010 010.EP 011 013 013.EP 014 015 017 018 019 019.EP 021 022 023 023.EP 024 024.EP 025.MI 025.MI.SA 026 027 027.EP 029 032 033 033.EP 034 035 037.MI 037.MI.SA 038 039 039.EP 040 041 042 043 044 045 047 049 050 051 053 054 055 057 058 059 060 061 061.EP 062 065 067 069 501.XP
4.4 47 001 003 003.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 019.MI.SA 021 023 024 025 025.EP 027 029 029.EP 030 031.MI 031.MI.SA 033 034 035 037 038 039 039.EP 041 042 045 046 047 048 050 501.XP
4.5 60 001 002 003 004 005 007 009 011 013 015 017.MI 017.MI.SA 018 019 021 022 023 024 025 026 027 029 030 031 033 034 035 035.EP 036 037 039.MI 039.MI.SA 040 041 041.EP 042 043 043.EP 045 047 049 049.EP 051 052 053 055 056 057 058 059 061 063 063.EP 065 065.EP 066 067 068 069 071
4.6 36 001 001.EP 003 004 004.EP 005 007 008 009 009.EP 010 010.EP 011 013.MI 013.MI.SA 015 016 017 019 019.EP 021.MI 021.MI.SA 023 023.EP 024 025 027 028 031 032 033 034 035 038 039 040
4.7 53 001 001.EP 002 003 004 005 005.EP 006 007 007.EP 009 010 011 013 013.EP 014 015 016 017 019 019.EP 020 021.MI 021.MI.SA 022 023 025 026 027 029 030 031 032 033 034 034.EP 035 037 039 040 041 041.EP 042 043 045 045.EP 046 047 049 051 053 055 059
4.8 34 001 003 004 004.EP 005 007 007.EP 008 009 011 012 013 015 016 017 019 019.EP 020 021.MI 021.MI.SA 023 024 025 027 028 029 031 032 033 035 039 041 042 043
4.9 20 PJT.001 001 002.MI 002.MI.SA 003 005 006 007 009 010 011 012 013 015 017 018 019 021 022 023
4.10 20 002 003.MI 003.MI.SA 004 004.EP 005 006 008 008.EP 009 010 011 012 012.EP 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 54 PJT.001 001 001.EP 002 003 003.EP 004 005 006 006.EP 007 008 010 012 012.EP 013 014 017 019 020 021 022 023 025.MI 025.MI.SA 026 027 027.EP 029 031 032 033 034 034.EP 035 036 037 040 041 043 044 051 053 054 054.EP 055 056 058 058.EP 059 060 062 063 064
5.2 34 001 001.EP 002 003 003.EP 004 005 005.EP 006 007 007.EP 008 009 010 011 012 013 014 015 016 017 018 019 020 021 023 026 027 029 030 034 036 038 041
5.3 19 PJT.001 001 002 003 004 005 006 007 008 009 010 011 014 016 017 018 020 021 023
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 37 001 001.EP 002 003 003.EP 005 005.EP 006 007 009 010 011 012 013 013.EP 015 017 019 020 021 023 024 025 026 026.EP 027.MI 027.MI.SA 028 028.EP 029 029.EP 035 036 037 037.EP 038 040
6.2 28 001 002 003 005 005.EP 007 007.EP 008 009.MI 009.MI.SA 010 011 012 012.EP 013 015 015.EP 016 017 018 019 019.EP 020.MI 020.MI.SA 021 023 024 025
6.3 30 001 003 004 005 006 007 009 010 011 012 013 014 015.MI 015.MI.SA 016 016.EP 017 018 018.EP 019 021 022 022.EP 023 025 027 027.EP 031 032 035
6.4 41 PJT.001 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 029 032 033 034 036 043 046 048 049 050 051 057 058 059
Chapter 7: The Laplace Transform
7.R 37 003 004 005 006 007 008 009 010 011 012 013 014 021 022 023 024 027 032 033 034 036 041 042 043 044 045 046 047 048 053 054 059 062 063 064 065 066
7.1 47 001 001.EP 002 002.EP 003 003.EP 005 005.EP 006 007 008.MI 008.MI.SA 009 009.EP 011 013 014 014.EP 015 017 018 019 021 022 023 024 025 026 027 030 031.MI 031.MI.SA 033 035 036 037 039 041 044 047 049 054 058 059 061 502.XP 503.XP
7.2 44 001 003 004 005 007 008 009 010 011 013 014 015 017 018 019 020 021 023 024 025 027 028 029 031 032 035 035.EP 037.MI 037.MI.SA 038 038.EP 039 040 040.EP 041 043 044 045 047 047.EP 049 049.EP 055 501.XP
7.3 73 PJT.001 001 003 004 005 006 007 008 009 011 012 013 014 015 016 017 018 019 021 022 023 025 025.EP 026 027 028 029.MI 029.MI.SA 031 032 032.EP 033 035.MI 035.MI.SA 037 037.EP 038 040 041 042 043 044 045 047 049 050 051 053 057 059 059.EP 061 062 062.EP 063 065 067 067.EP 071 071.EP 072 073 073.EP 075 076.MI 076.MI.SA 077 079 079.EP 081 085 089 092
7.4 68 001 003 004 005 006.MI 006.MI.SA 007 008 009 009.EP 010 011 011.EP 013.MI 013.MI.SA 014 014.EP 015 017 017.EP 018 020 021 023 024 026 027 027.EP 028 029 030 031 032 033 034 035 036 037 039 040 041 043 043.EP 044 047 048 048.EP 049 050 051 051.EP 052 053 055 056 061 061.EP 063 064 065 066 067 071 074 075 076 079 081
7.5 20 001 001.EP 002 003 005 006 007.MI 007.MI.SA 009 009.EP 010 011 011.EP 012 014 015 017 018 020 021
7.6 22 001 002.MI 002.MI.SA 003 003.EP 004 005 005.EP 006 007 008 009 009.EP 010 011 011.EP 012 013 014 015 017 019
Chapter 8: Systems of Linear Differential Equations
8.R 15 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015
8.1 20 001 005 006 007 008 009 010 011 017 018 019 021 022 023 024 025 027 028 029 032
8.2 57 PJT.001 001 001.EP 003 003.EP 004 004.EP 005 005.EP 006 007 007.EP 008 009 010 011 013 013.EP 014 016.MI 016.MI.SA 017 021.MI 021.MI.SA 022 023 023.EP 024 024.EP 025 026 027 027.EP 028 028.EP 029 031 031.EP 032 033 035.MI 035.MI.SA 036 037 037.EP 038 038.EP 039 039.EP 040 041 043 044 045 047 047.EP 048
8.3 38 PJT.001 001.MI 001.MI.SA 002 002.EP 003 003.EP 005 005.EP 006 007 007.EP 009 009.EP 010 012 013 013.EP 014 016 017 017.EP 018 018.EP 019 021 021.EP 023 025 027 028 028.EP 029 031 032 033 034 035
8.4 28 001 001.EP 002 003 004 005 006 007 008 009 009.EP 010 011 012 014 015.MI 015.MI.SA 016 016.EP 017 020 021 022 023 025 027 029 031
Chapter 9: Numerical Solutions of Ordinary Differential Equations
9.R 8 001 002 003 004 005 006 007 008
9.1 17 PJT.001 001 002 003 004 005 006 007 008 009 010 011 012 013 014 017 021
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 10 001 002 003 004 005 006 007 008 009 011
9.5 12 001 002 003 004 005 006 007 008 009 010 012 014
Total 1949  

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