Volume of a solid

End of Watch

This weekend I went to the theater to see End of Watch, a film directed by David Ayer and starring Jake Gyllenhaal and Michael Pena.  I haven't been to see a movie in theaters since summer ended, so that alone was a treat.  Movies are so much more powerful when seen on a large screen with excellent sound, and I enjoy being in an environment where everyone focuses on the film instead of multitasking.

End of Watch tells the story of two officers in the LAPD.  The movie focuses on their professional lives dealing with money, drugs, guns, and criminals but occasionally steps back from the intensity of crime to show moments with the officers' families, and the times they spend just talking to each other.  While the film as a whole revolves around action, guns, and gangs, it was refreshing to see these lighthearted clips of a quinceanera, or Gyllenhall and Pena blabbing in their cop car.

The cinematic style of this movie certainly varied from the norm.  As a side element in the movie's plot, many characters carry around video cameras.  As a result, the majority of the film is captured from hand held cameras, some of which are portrayed as the characters' own cameras and some of which are merely echoing a documentary style.  At first I found this shaky quality of the film to be rather disorientating, but I soon became accustomed to the wobbly images and began to enjoy seeing what the characters where seeing.  There was also one really beautiful shot in the film where the cop car is driving towards the city at dusk, and the LA skyline and sunset are reflected in the hood of the car.  The double image that is created transformed a more cliche photograph into an intriguing kaleidoscope-aesthetic.

La Grange and Alternating Series Error- Tuesday, April 7

Today we learned about how to find an alternating series error and the La Grange error bound. Both of which are used to approximate a value of desired accuracy. Both methods require the use of the next term in the series to be used and compared to the one before it. The difference is that the alternating series error can only be used when there is an alternating series. The La Grange error bound requires a Taylor series in order to be used.

Notes 03-30-09

Today we continued with Power Series and focused on two particular types: Taylor Series and Maclaurin Series. We first defined the two sub-series, then particed constructing them given different conditions.

Power Series

Today in class, we learned about power series and how to write them. Some power series are centered at x=0. These series are defined as the infinite sum of A sub n (An) multiplied by x^n. Other series are centered at x=c and these are defined as the infinite sum of the An multiplied by (x-c)^n. When writing a power series we first make sure the given function is in the geometric series form of 1st term/ (1-ratio). Then, the rest is easy...you just write the first term in the series and multiply each of the following terms by the ratio. Remember, the absolute value of the ratio must be less than one and to find the values of the interval of convergence for the power series just solve that absolute value equation.

Pythagorean Tree

This is the video we recorded in class today showing the Pythagorean Tree fractal.

(Note that clicking on the link will take you away from the blog...)

Notes from Class March 23-7th Period

Today we learned the Ratio Test. We were able to determine convergence or divergence of a series by dividing its sequence of a(n+1) over a(n). We also derived e by using the Ratio Test. Notice how the Ratio Test is similar to the Geometric Series Rule (r in geometric series is term/previous term).