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Differential Equations
Today we discussed differential equations and applications such as slope fields, growth/decay, and logistics. A differential equation is really just any equation that involves derivatives. For exponential growth/decay, the key words to look for are "rate of change if proportional to the amount present". Also, you always must remember to seperate the variables! I was familiar with today's review because we did this last year too, but I will definitely review this topic again before the AP. -
Sequences and Series
Today we reviewed sequences and series. The difference between the two is that for a series you add up the partial sum of the sequence. There are many different types of series that we learned, such as geometric, p- series, and alternating series. The main question that we will answer is: does the series converge or diverge? Each type of series has it's own way of determining convergence, so it's important to remember those conditions. -
Integration by Parts
I wasn't in class today, so I reviewed integration by parts on my own. It is another way to evaluate an integral. It is helpful to remember the acronym LIPET when choosing the expression for "u". LIPET stands for Logs, Inverse trig, Polynomials, Exponentials, and Trig. Whichever expression you didn't choose as u, now becomes the v. You then can more easily evaluate the integral. -
Definition of the Derivative
Today I reviewed the definition of the derivative, which was a calc AB topic. It is a way to find the derivative if you can't use the power rule, quotient rule, or any other easy way. You usually won't have to use it on the AP test, unless they give you the formula and ask you to identify the function. -
Trig
Today I reviewed some basic trig concepts and trig identities. This could be useful for trig substitution (not on the AP test) and other derivative/integration applications. -
L'hopitals rule
Today I reviewed L'hopitals rule. It can be used when you get a n indeterminate form. You keep taking the derivative of f(x) over g(x) until there is no no undefined value. -
Euler's Method
I reviewed Euler's method today. This is useful when you are attempting to solve differential equations when you are given a starting value. Calculuate the slope (dy/dx), then dy=dy/dx(delta x), then add the change in x and y and continue the process until the specified value. -
Geometric Series
Today I reviewed geometric series. If the absolute value of r is less than 1, then the series converges. It converges to a/(1-r). If the absolute value of r is greater than or equal to 1 than the series diverges. -
Maclaurin Series
Today I reviewed some common maclaurin series that are helpful to know. I studied e^x, sin(x), cos(x), ln(x), etc. It is helpful to know these by memory so that you can save time on the test. -
Parametrics
Today I reviewed parametrics, such as the arc length formula, derivatives, and vectors. i also studied how to find the minimum or maximum values. This could be useful on the free response or maybe the multiple choice section of the ap test. -
AP test review-KYSC
Today I reviewed a little bit of everything that I am not too comftorable with. I spent some time going over the KYSC sheet, and just reviewing basic inverse trig, formulas, etc. I'm feeling prepared and ready to go for tomorrow. -
GAME DAY
Today was the AP test. I thought the multiple choice was unexpectedly easy, but I had some trouble with the last free response about series. I probably should have studied series more... but I think I will get a passing grade, if not a 4 or a 5!
