Parametric Equations-Arc Length (Feb 18)

Finding the length of the segment between two points on the curve is the most accurate way we can use to find the arc length between the two points. We can then relate this to the Pythagorean Theorem, and set up a definite integral using this idea to find the arc length. SORRY THIS IS SO LATE!!!

Parametric Motion 2/19/09

Today in class we discussed Parametric Motion dealing with finding position, velocity, speed, and/or distance at a certain time or time interval from a parametric equation.

2/23/09 Notes

Today in class we briefly discussed/reviewed translations in polar equations. We also learned about differentiating polar equations and how to apply it.

Notes Feb 20

Polar equations. Today we talked about graphing polar equations. We went over the different shapes to expect along with converting to rect. eqn's.

2/17/09 Notes

Today we took second derivatives of parametric equations and used them to find concavity.

2/16/09 notes

Today we covered parametric equations, graphing them and solving them. We also talked about velocity and speed and the two basic parametric things we should be able to recognize. In class, we did a problem on finding the slope of a tangent line of the equation.

Missing Days

I just wanted to put up a post to note what happened between Michael's previous post and Sabrina's post to be...

On Tuesday, Feb 10, we reviewed differential equations and looked at some application problems.

On Wednesday, Feb 11, there was a test over differential equations, improper integrals, some new techniques of integration (including integration by parts and by partial fractions), slope fields and Euler's method. The test average was 90.1.

On Thursday, Feb 12 we hunted space monsters.

There was no school on Friday, Feb 13, and that brings us to Monday the 16th.

Improper Integrals

Today we learned how to solve improper integrals, which are definite integrals that are based off of limits. The most important concept was that improper integrals that equal infinity have diverging graphs, and those that equal a rational number have converging graphs.

Class Notes, Friday the Sixth Oh-Nine

Friday's topics involved solving integrals using calculus. Our main method was integration by partial fractions - using algebra to break up, via factoring, an otherwise un-integralable denominator. Other forms of attack included breaking a fraction into smaller parts by distributing the numerator and completing the square.

Notes February 5

Today we continued working with u and dv, but it got a bit trickier. We completed two problems, which took a while to complete and had many steps.

Integration by Parts

Today we learned integration by parts. We can use this when integration by substitution (the one using u) doesn't work.

Today we just used the logistic model from yesterday in class, generated a slope value and found out what the logistic model would look like if we started with different values.