Spring 2005

- Have a nice summer everyone!

- Problem Set 1
- Problem Set 1 Solutions (Part B)
- Problem Set 2
- Problem Set 2 Solutions (Part B)
- Problem Set 3
- Problem Set 3 Solutions (Part B)
- Midterm 1 Preparation
- Problem Set 4
- Problem Set 4 Solutions (Part B). Note that the version handed out in recitation had an error in Part B #2; this version has the correction.
- Midterm 1 Addendum (due Tuesday March 8)
- Midterm 1 Solutions (should be helpful for the assignment above)
- Problem Set 5
- Problem Set 5 Solutions (Part B)
- Problem Set 6
- Problem Set 6 Solutions (Part B)
- Problem Set 7
- Problem Set 7 Solutions (Part B)
- Midterm 2 Preparation
- Midterm 2 Solutions
- Problem Set 8
- Problem Set 9
- Problem Set 9 Solutions (Part B)
- Problem Set 10
- Problem Set 10 Solutions (Part B)
- Problem Set 11
- Problem Set 11 Solutions (Part B)
- Problem Set 12
- Problem Set 12 Solutions (Part C)
- Final Exam Preparation

Most of these are Java applets, which run interactively as plug-ins in your web browser. To use them you must have Java enabled in your browser preferences -- by default, it probably is already.

- Some Java applets from MIT's OpenCourseWare page for 18.013A:
- Function and Derivative Animations, by Przemyslaw Bogacki and Gordon Melrose (.avi files, can play e.g. with Windows Media Player)
- Java applets of secant lines and tangent lines (from IES, Manipula Math):
- Secant lines for a function with two non-differentiable points (applet by Daniel J. Heath)
- Animations of secant lines approaching (or not approaching) tangent lines
(by Douglas N. Arnold):
- at a point of differentiability
- at a point of non-differentiability (the one-sided derivatives don't match)
- at another point of non-differentiability (vertical tangent; the derivative is infinite)

- Constructing
functions that are continuous but
*nowhere differentiable*(!), applet from Maths Online - Chain rule applet (from a multimedia calculus course by Scott Sarra)
- First and second derivatives applet (by Scott Sarra)
- More first and second derivatives, with parameters you can tweak (applet from Maths Online)
- Derivatives of
*a*,^{x}*sin x*,*cos x*(applets by Daniel J. Heath) - Converging
to the number
*e*(applet from IES, Manipula Math); note that the simulation doesn't let you go far enough to approach that close to*e* - Zooming in on a tangent line (animation by Douglas N. Arnold)
- Linear
approximation of
*sin x*at 0 (applet from UBC Calculus Online) - Finding a function's extremum, applet from Maths Online
- Rolle's theorem and the mean value theorem (applet from IES, Manipula Math)
- Some nice integral applets (by Daniel J. Heath):
- Numerical Integration Simulation (by Joseph L. Zachary)
- Some applets on volumes of solids (from IES, Manipula Math):
- Direction field applet (by Scott Sarra)
- More direction field applets (from UBC Calculus Online)
- Yet another direction field applet (from IES, Manipula Math)
- Parametric equation applet (by Scott Sarra)
- Another parametric equation applet (from IES, Manipula Math)
- Cycloid animation (by Przemyslaw Bogacki and Gordon Melrose)
- Cycloid applet (from Maths Online)
- Computing arc length (animation by Przemyslaw Bogacki and Gordon Melrose)
- Approximating arc length (applet by Daniel J. Heath)
- Polar curve applet (from IES, Manipula Math)
- Several polar curve animations (by Przemyslaw Bogacki and Gordon Melrose):
- Converging and diverging series animations (by Przemyslaw Bogacki and Gordon Melrose):
- Numerical tools for computing sequences / series (from Maths Online)
- Taylor approximations (applet by Daniel J. Heath)
- Power series grapher