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Using Excel to plot numerical and analytical forms of the diffusion equation

Anne Lightbody
,
University of New Hampshire
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This activity was selected for the On the Cutting Edge Exemplary Teaching Collection

Resources in this top level collection a) must have scored Exemplary or Very Good in all five review categories, and must also rate as “Exemplary” in at least three of the five categories. The five categories included in the peer review process are

  • Scientific Accuracy
  • Alignment of Learning Goals, Activities, and Assessments
  • Pedagogic Effectiveness
  • Robustness (usability and dependability of all components)
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For more information about the peer review process itself, please see http://serc.carleton.edu/NAGTWorkshops/review.html.



This page first made public: Jun 29, 2010

Summary

This computer-based assignment forces students to compare and contrast integral and differential forms of the conservation of mass equation, as well as analytical and numerical approaches to solution. Students are given a text description of a simple environmental problem (a conservative tracer diffusing in a one-dimensional system with no-flux boundaries) and are then required to first write equations that describe the system and then implement these equations in an Excel spreadsheet or Matlab m-file. Students then use their spreadsheets/m-files to compare different solution methods and must communicate these results in short text answers.

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Context

Audience

Undergraduate hydrology class introducing students to basic physical transport processes (advection, diffusion, dispersion) and chemical reactions (first-order reactions, boundary sources and sinks) in surface water, ground water, and atmospheric systems. The class has 3 hours of lecture and one hour of recitation per week; there is no associated laboratory.

Skills and concepts that students must have mastered

Before beginning this exercise, students must be able to:

How the activity is situated in the course

One out of eight homework assignments, occurring somewhere near the middle of the class. Previous homeworks included developing a two-box numerical model of a lake and plotting Gaussian curves. One variation is to assign the problem over two weeks, allowing students to receive feedback on their proposed approach before using those equations to develop a computer model.

Goals

Content/concepts goals for this activity

Higher order thinking skills goals for this activity

Other skills goals for this activity

Description of the activity/assignment

This computer-based assignment forces students to compare and contrast integral and differential forms of the conservation of mass equation, as well as analytical and numerical approaches to solution. Students are given a text description of a simple environmental problem (a conservative tracer diffusing in a one-dimensional system with no-flux boundaries) and are then required to first write equations that describe the system and then implement these equations in an Excel spreadsheet or Matlab m-file. Students then use their spreadsheets/m-files to compare different solution methods and must communicate these results in short text answers.

Determining whether students have met the goals

Examine student written answers and computer spreadsheet/m-file to determine whether they (a) wrote the correct set-up equations (Parts A-C), (b) completed the assigned computer tasks correctly (Parts D & E), and (c) provided reasonable answers to follow-up questions asking for further reflection.

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