How to do Anti-Derivatives (i.e. Integrals)

We have been using derivatives since the first couple days of school. We should be getting comfortable with the notion that derivatives tell you slopes of tangent lines to curves, and in a practical sense allow us to find velocity and acceleration just by knowing a position function with respect to time. That is, v = ds/dt, and a = dv/dt. And hopefully this has made sense as we have worked with motion graphs and tried to see how these three motion graphs connect.

But a problem came up when we start with acceleration, and need to find velocity and position. We must figure out a way to 'undo' the derivatives, or in other words, find an anti-derivative. This video introduces the concept, and graphically this is equivalent to finding the area below a curve.  I hope this helps.

Lessons for classes

I am VERY sorry to be out again with a flu-like illness, but here are some things we can still accomplish.

Periods 3-4: Tension problems are notorious for their detail, but with some practice and thinking about them systematically, are quite doable. Check out this video and take notes to get a technique down that we will use for just about any more complex, multi-object system we encounter, so we can find 'internal forces' of the system.

Periods 1-2, 8-9: We mentioned that the key quantity for everything in E&M is electric charge. All charges, whether a single particle or a charged balloon, produce TWO physical quantities: electric fields and electric potential (better known as voltage; this is not the same as potential energy!). Fields are vectors, and potential is a scalar. Check out this video for an introduction for finding total voltage and net electric fields from a system of point charges. Take notes, and see if you can work through the practice problems.

Everyone can also find a science article of interest and provide a summary - we do this every so often so you can have a chance to check out some current, cutting edge topics and get a sense of some very cool things going on out in the world! It can be from a Scientific American (please return at some point!) or online, and can be from any discipline.

Have a Happy Friday and weekend, and see you Monday.  :-)

Quizzam Review

What is on the first Quizzam?

Vector addition - find components, add to get total x, y; create final right triangle
Vector multiplication: dot product, cross product
Examples of vectors vs. scalars
Constant speed problems
Constant acceleration problems
Basic projectile problems
Derivatives - v = dx/dt, a = dv/dt
Instantaneous vs. average velocity, acceleration
Anti-derivatives (integration)
Motion graphs - sketch, interpret
Relative motion (e.g. airplane flying with a cross wind, boat across a river)
Standard deviation for multiple trials