TITLE: Examples of open ended calculus "class project" ideas
QUESTION [7 upvotes]: I have instructed calculus I an II, each once, at the college level and would like to emphasize that math is not just about memorizing formulas and concepts for a test and that applied math is not a bunch of contrived word problems. I would like to encourage my students to do a a "final project" the next time I teach the course (or at least the next time I have a bit more power to set the curriculum). For those of you who have done this before, what types of questions have you asked? and what were the students solutions like? Did you find your projects were manageable enough with just the calculus they learned and some basic research about whatever topic they chose? The next time you teach calculus will you do it again? I'd like to have at least one or two theory and application choices, plus an option for them to choose their own topic (requiring my approval for this option).

REPLY [5 votes]: I have done something like this with ordinary degree students. I will just show you what I have done it may give you some ideas.
I think the better students enjoyed the projects but some of them might have been too long.
The project titles were:

Nowhere-Continuous Functions
Intermediate Value Theorem
Fixing Nasty Functions and making them Nice
Continuity
Leaving Cert Questions
L’Hopital’s Rule
Linear Algebra
Differentiation
Extrema of Functions of Several Variables with an Application to Statistics
Riemann Sums
Further Techniques of Trigonometric Integration
The Natural Exponential Function as a Power Series
and The Most Beautiful Formula in Mathematics
The Area & Volume of familiar Shapes & Solids
Euler’s Method of Numerical Solution of Differential
Equations
The Length of the Monza Circuit
Dynamical Systems

You can find projects 1-9 here, projects 10-15 here and project 16 is question 3 in here.