Multivariable Calculus Online

 

Technology and Tradition in a Common Context

While there is a great deal that is new and different about the textbook Multivariable Calculus Online, we have taken great pains to make the everyday experience of students predictable, familiar, and inviting.  To better illustrate this idea, let’s look at how technology and tradition mix in this online format.  

The textbook is divided into 5 chapters with 7 to 9 sections in each chapter (along with an optional “capstone” experience that explores the inverse square law). Each section is divided into 4 subsections, a set of exercises, a Maple worksheet, and an online tool related to the section.  The subsections resemble subsections in a traditional textbook in that there are definitions, theorems, and worked examples.  However, the figures and illustrations in the textbook are frequently in the form of applets, animations, and interactive tools.

Similarly, the exercise sets contain only pencil and paper activities, so that students' online experiences retain the flavor of a traditional calculus course.  Our desire is for the online venue itself to be the medium that allows a natural mixing of technology with tradition, thus eliminating any need for contrived uses of technology.  

Student use of technology is concentrated in the online tools and the Maple worksheets.  The online tools allow exploration of one or more concepts introduced in the section, and the Maple worksheets allow application of the concepts in a software environment.  Many of the pencil and paper exercise sets suggest ways that the online tool can enhance the exercises, and many of the tools produce separate windows and stand-alone data sets which can be collected and graded.  

Also, the tools were created to produce Maple-style output and require Maple syntax, and one of our goals is to create a version of the text in which the tools produce Mathematica-style output and require Mathematica Syntax.  Such uniformity makes the use of the technology less demanding after the first couple of weeks of the course.

The Maple worksheets (and eventually Mathematica notebooks) are intended to be a lecture supplement.  This not only enhances the lecture but also introduces the role chosen for Maple in that section.  Correspondingly, each Maple worksheet contains a set of graded exercises that build upon the lecture material and are suitable for usage as daily assignments. 

At the end of each chapter is a comprehensive review which includes a set of graded Maple questions that range from take-home test problems to extended projects.  We have found that carefully designed tests that mix Maple usage with pencil and paper calculations are no more taxing or time-consuming than traditional calculus exams. 

 

In addition, there are answers to selected odd exercises, much like in a traditional textbook.  We have tried to design the text to allow an instructor to determine the desired balance of technology and traditional problem-solving, with the view of having this same balance during assessment as well.