## General Information

Portfolio Problems are calculus problems that address some of the core ideas of the subject at a level of depth that is considerably greater than typical homework exercises. They combine conceptual understanding, computational skill, and effective problem solving to challenge and stretch your abilities.

**During the course, you will be completing twelve such problems that you will choose from a list given below**. These problems are put into six general areas that are grouped by theme. You will be expected to complete roughly 2–3 portfolio problems per week on the average.

## Guidelines for Portfolio Problems

- Portfolio problems are to be done **completely individually**. You may not receive or give help from any human, print, or electronic source on these problems with the exception of the instructor. Any evidence that you have received or given help on a portfolio problem will be treated as academic dishonesty.
- You may submit one initial draft of each problem to the instructor to receive ungraded, but extensive, feedback on your work. Initial drafts should be reasonably complete solutions. The feedback given will focus on the correctness of the math work that is in the solution and on the quality of the writing and presentation. **Feedback will not include hints for how to proceed or get started on a problem,** so in order to get the most out of the feedback you should have a reasonably complete solution.
- You may submit **no more than four initial drafts in any given week**. A “week” for this purpose starts and ends at noon on Sundays. Note that this means that if you procrastinate, you won’t be able to send a big package of solutions to me for feedback.
- **Portfolio Problems must be typed up using software that is capable of rendering mathematical notation**. Examples of such software include Microsoft Word (using Equation Editor), Google Docs (which also has an equation editor), and LaTeX (a mathematical typesetting language used commonly in math and science fields). *No handwritten work will be accepted, in either draft or final form*.
- Portfolio Problems must be written up according to a short manual of guidelines for writing, showing work, and formatting graphics. This manual is posted here and will remain at this location throughout the course. (You can also print it and keep it with you.)
- The final set of 12 completed portfolio problems is due at **9:00am on Monday, June 17**. The portfolio should be submitted as a single PDF file that contains a title page and all of your solutions. (You’ll receive instructions on how to merge PDF’s as we get closer to the due date.)
- In order to make sure you are progressing appropriately through the problems, **you will be required to submit two final drafts of problems before 9:00am on Friday, May 16** (the end of the second week of class) and then **two more final drafts of problems before 9:00am on Friday, May 23** (the end of the third week of class). This will ensure that you complete at least 1/3 of the portfolio by the halfway point of the course. After this, you will be allowed to work on the remaining problems at your own pace. If you complete more final drafts of problems by these due dates, just hold on to them until the final due date on June 17.
- All rough and final drafts are to be submitted as PDF’s, as email attachments sent to the special email address [[e-mail]](mailto:[e-mail]). Note that the style manual specifies that you should use a particular style for titling your documents; please abide by that style in order to prevent confusion.

## Grading of Portfolio Problems
Each Portfolio Problems will ultimately be graded on a scale from 0 to 8 according to the following rubric:

To give you a sense of what an excellent writeup vs. a “just OK” writeup vs. a bad writeup look like, I’ve completed Exercise 1.1 from your textbook four different ways:

- Here is what an excellent (grade = 8) solution would look like.
- Here is what a good, but not excellent (grade = 6) solution would look like.
- Here is what an acceptable, but significantly flawed (grade = 4) solution would look like.
- Here is what a poor (grade < 4) solution might look like, although there are many ways for a writeup to be poor.

## List of Portfolio Problems

All the numbers below refer to sections in the book and problems found in the Exercise sets at the end of each section.

### Group 1: Limits (choose ONE)

Section 1.2: 1, 2, 4

### Group 2: Basic Derivative Concepts (choose one from each section for a total of TWO)

Section 1.3: 2, 3
Section 1.4: 1, 3, 4

### Group 3: The Second Derivative (choose ONE)

Section 1.6: 2, 3

### Group 4: Derivative Computation

Choose ONE problem from section 2.3, ONE problem from section 2.5, and then ONE more problem from any other section besides 2.3 or 2.5 for a total of THREE:

Section 2.1: 3
Section 2.2: 1, 3
Section 2.3: 4, 5 (<- You must choose one of these)
Section 2.5: 3, 4 (<- You must choose one of these)
Section 2.7: 2
Section 2.8: 4

### Group 5: Applications of the Derivative (Choose one from each section for a total of FOUR)

Section 3.2: 2, 3
Section 3.3: 2, 3
Section 3.4: 1, 2, 3, 4
Section 3.5: 1, 2, 3, 5

### Group 6: Accumulation of Change (choose ONE)

4.2: 3, 4