# Ordinary Differential Equations: From Calculus to Dynamical Systems 1st edition

Virginia W. Noonburg
Publisher: Mathematical Association of America

## eBook

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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)

Ordinary Differential Equations: From Calculus to Dynamical Systems by V.W. Noonburg presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. The book is aimed at students with a good calculus background that want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being flipped. The WebAssign component of this text features immediate student feedback and question links to an eBook.

## 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 Availability Color Key
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GRAY questions are under development

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 6 002 004 006 006 008 010 012
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 8 002 004 006 008 010 012 014 016 020
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
Total 203 (2)