Differential Equations: From Calculus to Dynamical Systems 2nd edition

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Virginia W. Noonburg
Publisher: Mathematical Association of America

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  • Chapter 1: Introduction to Differential Equations
    • 1.1: Basic Terminology (10)
    • 1.2: Families of Solutions, Initial-Value Problems (6)
    • 1.3: Modeling with Differential Equations (2)

  • Chapter 2: First-order Differential Equations
    • 2.1: Separable First-order Equations (12)
    • 2.2: Graphical Methods, the Slope Field (7)
    • 2.3: Linear First-order Differential Equations (8)
    • 2.4: Existence and Uniqueness of Solutions (2)
    • 2.5: More Analytic Methods for Nonlinear First-order Equations (10)
    • 2.6: Numerical Methods (6)
    • 2.7: Autonomous Equations, the Phase Line (5)

  • Chapter 3: Second-order Differential Equations
    • 3.1: General Theory of Homogeneous Linear Equations (8)
    • 3.2: Homogeneous Linear Equations with Constant Coefficients (7)
    • 3.3: The Spring-mass Equations (5)
    • 3.4: Nonhomogeneous Linear Equations (13)
    • 3.5: The Forced Spring-mass System (3)
    • 3.6: Linear Second-order Equations with Non-constant Coefficients (5)
    • 3.7: Autonomous Second-order Differential Equations (5)

  • Chapter 4: Linear Systems of First-order Differential Equations
    • 4.1: Introduction to Systems (6)
    • 4.2: Matrix Algebra (9)
    • 4.3: Eigenvalues and Eigenvectors (4)
    • 4.4: Analytic Solutions of the Linear System x′ = Ax (8)
    • 4.5: Large Linear Systems; the Matrix Exponential (6)

  • Chapter 5: Geometry of Autonomous Systems
    • 5.1: The Phase Plane for Autonomous Systems (2)
    • 5.2: Geometric Behavior of Linear Autonomous Systems (9)
    • 5.3: Geometric Behavior of Nonlinear Autonomous Systems (2)
    • 5.4: Bifurcations for Systems (1)
    • 5.5: Student Projects

  • Chapter 6: Laplace Transforms
    • 6.1: Definition and Some Simple Laplace Transforms (8)
    • 6.2: Solving Equations, the Inverse Laplace Transform (9)
    • 6.3: Extending the Table (11)
    • 6.4: The Unit Step Function (10)
    • 6.5: Convolution and the Impulse Function (4)

  • Chapter 7: Introduction to Partial Differential Equations
    • 7.1: Solving Partial Differential Equations (3)
    • 7.2: Orthogonal Functions and Trigonometric Fourier Series (9)
    • 7.3: Boundary-Value Problems: Sturm-Liouville Equations (4)

  • Chapter 8: Solving Second-order Partial Differential Equations
    • 8.1: Classification of Linear Second-order Partial Differential Equations (9)
    • 8.2: The 1-dimensional Heat Equation (4)
    • 8.3: The 1-dimensional Wave Equation (4)
    • 8.4: Numerical Solution of Parabolic and Hyperbolic Equations (3)
    • 8.5: Laplace's Equation (2)
    • 8.6: Student Project: Harvested Diffusive Logistic Equation (3)


Differential Equations: From Calculus to Dynamical Systems: Second Edition is a new edition of Virginia Noonburg's bestselling text. A thoroughly modern textbook for the sophomore-level differential equations course, the book includes two new chapters on partial differential equations, making it usable for a two-semester sequence. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme.

Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The book's clear and inviting exposition makes it ideal for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature. The WebAssign component of this text features immediate student feedback and question links to an eBook.

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Group Quantity Questions
Chapter 1: Introduction to Differential Equations
1.1 10 002 004 006 008 010 012 014 016 018 020
1.2 6 002 004 006 008 010 012
1.3 2 002 003
Chapter 2: First-order Differential Equations
2.1 12 002 004 006 008 010 012 014 016 018 020 022 024
2.2 7 002 004 006 008 010 012 014
2.3 8 002 004 006 008 010 012 014 016
2.4 2 004 006
2.5 10 002 004 006 008 010 012 014 016 018 020
2.6 6 002 004 006 008 010 012
2.7 5 002 004 006 008 010
Chapter 3: Second-order Differential Equations
3.1 8 002 004 006 008 010 012 014 016
3.2 7 002 004 006 008 010 012 014
3.3 5 002 004 006 008 010
3.4 13 002 004 006 008 010 012 014 016 018 020 022 024 026
3.5 3 002 004 006
3.6 5 002 004 006 008 010
3.7 5 002 004 006 008 010
Chapter 4: Linear Systems of First-order Differential Equations
4.1 6 002 004 006 008 010 012
4.2 9 002 004 006 008 010 012 014 016 018
4.3 4 002 004 006 008
4.4 8 002 004 006 008 010 012 016 020
4.5 6 002 004 006 008 010 012
Chapter 5: Geometry of Autonomous Systems
5.1 2 002 004
5.2 9 002 004 006 008 010 012 014 016 018
5.3 2 002 004
5.4 1 002
Chapter 6: Laplace Transforms
6.1 8 002 004 006 008 010 012 014 016
6.2 9 002 004 006 008 010 012 014 016 018
6.3 11 002 004 006 008 010 012 014 016 018 020 022
6.4 10 002 004 006 008 010 012 014 016 018 020
6.5 4 002 004 006 008
Chapter 7: Introduction to Partial Differential Equations
7.1 3 002 004 006
7.2 9 002 004 006 008 010 012 014 016 018
7.3 4 002 004 006 008
Chapter 8: Solving Second-order Partial Differential Equations
8.1 9 002 004 006 008 010 012 014 016 018
8.2 4 002 004 006 008
8.3 4 002 004 006 008
8.4 3 002 004 006
8.5 2 002 004
8.6 3 002 004 006
Total 244