MVC Portfolio

This page is dedicated to the Course Portfolio to Multivariable Calculus. While not new, it is still an evolving page with items being added/changed frequently. It should provide a central location where students can find information regarding this semester-long assignment. If you have any suggestions for this page, please let me know. Click here to go back to the Multivariable page.

What Is It?

The Course Portfolio is essentially a cumulative assessment documenting your mastery of the main multivariable calculus topics presented in class. Each student's portfolio is unique to him or her - written in your own words, this document reflects on work done in the course and provides specific examples your academic strengths.

What is its purpose?

The Course Portfolio actually serves several purposes. For one, the finished document provides a final assessment for the course, much like a typical final examination does. Instead of "showing off" what you know on a 90-minute written exam, however, you get to do so in a semester-long activity!

The process of writing the portfolio also encourages you to reflect on the multivariable calculus material throughout the semester, which in turn allows you to gain a better understanding of the topics as the semester continues.

A third purpose (and the one that you probably care most about) involves evidence that you have mastered a typical college-level multivariable calculus course. As you know, there is no AP Exam for this course, so college credit and/or exemption is not common. The portfolio can be used in college as an argument for not repeating the course and moving on to a differential equations course. More on that later...

What goes in it?

While your portfolio is unique to your design, all portfolios must contain three main pieces - an introduction, chapter summaries with sample material, and a collection of your chapter exams. You are more than welcome to include other material - assignments, quizzes, additional narratives, etc. - as long as it does not distract from the purposes mentioned.

What is the process of creating it?

Most of the creation process deals with the five chapters of material, each containing a summary of the lessons in class and at least one problem and solution related to that material.

Each summary is a collaborative process that the entire class will participate in (this is a little different from previous classes, hence the difference in the example portfolios below). For each chapter, I will outline the main topics to include (other topics can be added, of course), then the class will write and revise the actual text through a wiki.

Even though the wiki makes the collaboration process easier, it does have the drawback of not being equation and graph friendly. Therefore, once the class is relatively satisfied with the text part of the introduction, it will need to be transferred to a "rough draft" Word document. Then MathType and Maple can be used to create and include the mathematical expressions and graphs. I will review this version, make comments throughout, and repost it for all to see. At this point, students will take the commented document and individually edit it for their "final draft".

The problems to be included in each chapter are created on a more individual basis. Students choose a problem related to the material (which needs to be approved by me), and then type up a "rough draft" solution. I will review it, checking all calculations, and then return it with comments. Based on that, students write a "final draft" to be included in the final portfolio.

Once the chapters are complete, students will write an introduction unique to their portfolio that basically describes what the whole thing is about (its philosophy, what is included, etc.). On the last day, everyone will piece together the introduction, chapter summaries and problems, and the course's exams into one big stack. Finally, we will bind the portfolios in class - arguably the most rewarding part of the whole process!

Chapter Requirements

We will discuss in greater detail the samples to include in each chapter, but below is a list of a few key points you might want to consider. When choosing what work to include, try to find a balance of mathematical theory and application. Also consider the graphs or other illustrations needed to complement your examples.

Chapter 9

	an application involving vector calculations, such as a the dot or cross product
	an example requiring lines and planes in space
	a discussion on three-dimensional surfaces

Chapter 10

	an analysis of a space curve (arc length, curvature, TNB-frame, or the normal and osculating planes)
	a discussion on the parametric representation of surfaces

Chapter 11

	a discussion on calculus concepts with respect to multivariate functions (limits, continuity, partial derivatives, etc.)
	an application using linearization, differentials, or the chain rule
	a discussion on the relationship between the directional derivative and the gradient vector
	a sample of function optimization (relative and absolute extreme values, Lagrange multipliers, etc.)

Chapter 12

	a discussion on the concept of the iterated integral
	an application requiring a double integral, including surface area
	an application requiring a triple integral (including cylindrical or spherical coordinates)

Chapter 13

	a discussion on the concept of the line and/or the surface integral
	a discussion on the Fundamental Theorem of Line Integrals
	an application using a surface integral
	an example demonstrating Green's Theorem, Stokes Theorem, or the Divergence Theorem

A Few Writing Tips

Writing a book (that's essentially what you will be doing here) isn't easy... toss in the fact that your chapter summaries will include a boatload of mathematics makes it considerably more difficult. You will find out quickly that the actual mathematics is a piece of cake, but explaining your work is a bit more time consuming. Here are a few tips to get you started, and we will discuss formatting in greater detail after the first rough draft is returned.

	Stay consistent with your writing applications. I suggest Word for the main document, MathType for the equations, and Maple for the graphs.
	Choose a formatting style and stick with it - you want the look of your entire portfolio to be consistent.
	You will save yourself a ton of time in the editing process if you will remember the following: italicize all variables. There are exceptions, of course, but I'd suggest getting used to the Ctrl-I keystroke early.
	Concerning your mathematical calculations, don't get bogged down in the "grunt work". For example, consider writing the definite integral setup followed by its value - the intermediate evaluation steps aren't always necessary.
	Write mathematical notation vertically for an easier read (step 1 on line 1, step 2 on line 2, etc.). A good rule of thumb is there should be only one equal sign per line.

Some Helpful Resources

I'll add more as I think of things to include!

	Here is a tip sheet for formatting your portfolio work.
	Here are some samples of previous students' portfolios: Coogan, Kovacs, Norman, Semenova, Chen.
	Here are some suggestions for approaching your university's mathematics department for course exemption.

"Final" Introductions

Here is where I will place the group's collaborative chapter introductions (I figure this is more efficient than the file storage site we've been using). Each one will still have comments that you as an individual should review before printing and publishing this in your portfolio.

	Chapter 9
	Chapter 10
	Chapter 11
	Chapter 12