Rasmussen , C., K. Keene, J. Dunmye, and N. Fortune. 2017. Inquiry-Oriented Differential Equations.

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Abstract

Authors: Rasmussen , C., K. Keene, J. Dunmye, and N. Fortune.

Date of Publication:  20i7.

Title: Inquiry-Oriented Differential Equations.

Location: https://iode.wordpress.ncsu.edu

Accessed 5 January 2018.

This online text with both Student version and Teacher version (for the latter the instructor has to register) is freely available under the Creative Commons licenses and is funded by the National Science Foundation.

In response to the question, "What is Inquiry-Oriented Differential Equations?" the IODE team responds, "Inquiry-Oriented Differential Equations (IODE) is a first course in differential equations focused on understanding of the big ideas in first order, second order, nonlinear, and systems of differential equations. The course is designed as a full semester course and topics covered include solving ODEs; numerical, analytic and graphical solution methods; solutions and spaces of solutions; linear systems; linearization; qualitative analysis of both ODEs and linear systems of ODEs; structures of solution spaces." The site leaders go on to refine their terms, "Our use of the term inquiry includes the following three principles: deep engagement in mathematics, peer-to-peer interaction, instructor interest in and use of student thinking. For further reading on these principles of inquiry and inquiry-oriented instruction see the articles by Rasmussen et al. and Kuster et al."

The site offers a set of GeoGebra tools in support of the material in the online text. GeoGebra is a free downloadble software package with exceptional graphics and instructional capabilities.

This effort is a nice combination of reasonable and engaging applications to motive the differential equation concept under study, use of technology (GeoGebra), and careful step-by-step solution strategies for solving differential equations.

If you are considering saving your students a bundle of money by not having them buy a version n (for n large) of any of the available texts then this text is something you might well consider.

Here is the Table of Contents of the student version of the text materials:

Student Materials

PDF - One Document

IODE Student Materials

PDF - By Chapter

Cover Page

Unit 1: Qualitative and Graphical Approaches

Unit 2: A Numerical Approach

Unit 3: An Analytic Approach

Unit 4: Linear Differential Equations

Unit 5: Uniqueness of Solutions

Unit 6: Autonomous Differential Equations

Unit 7: Modeling with Autonomous Differential Equations

Unit 8: The Effect of Varying a Parameter in Autonomous Differential Equations

Unit 9: Introduction to Systems

Unit 10: Spring Mass System and Linear System

Unit 11: Damped and Undamped Linear Systems

Unit 12: Eigentheory Applied to Linear Systems

Unit 13: Second Order Linear Differential Equations

Unit 14: Nonlinear Systems

Cite this work

Researchers should cite this work as follows:

  • Brian Winkel (2018), "Rasmussen , C., K. Keene, J. Dunmye, and N. Fortune. 2017. Inquiry-Oriented Differential Equations.," https://simiode.org/resources/4383.

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