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Anti-Derivatives and Integration
First we reviewed anti-derivatives, including the general forms for trig and inverse trig functions. I felt very comfortable with most of the basic integration formulas; however, I definitely will look over the inverse trig formulas more closely. We also reviewed the FTC which I feel very comfortable with, but I want to review the Second FTC again, particularly when both bounds are variables. In general, I feel comfortable with messy integration, but I will look over the various techniques again -
Differential Equations, Slope Fields, Eulers, etc.
I am confident in my ability to separate variables, integrate and find the general solution for a differential equation. I also am comfortable sketching the slope field for a given differential equation. However, I'm not great at sketching the particular solution. It should be easy, but for some reasons I have problems with it, so I will definitely practice with that. One thing I definitely need to revisit are the various forms of logistic growth models and exponential growth/decay. -
Sequences and Series
Overall, I'm comfortable with determining convergence and divergence. It's importnant to remember that for a series, the sequence within the series must approach zero in order for it to converge. However, a sequence itself can approach any number and converge. Another concept that I want to look over is "boundedness" and whether or not a function is monotonic. To determine if it's monotonic, just look at the slope (f'(x)) over the interval. -
Sequences and Series Continued...
In general, the ratio test is go-to tool (tells absolute convergence). If the absolute value of a series converges, then the series converges absolutely; however, if the series converges, but the absolute value diverges, then it is conditionally convergent (ex. the alt. harmonic). We also reviewed the basic form of a Taylor Series. The approximation gets more accurate as n increases and you approach the center. I still struggle with the Lagrange remainder, specifically the "max value" concept. -
Power Series
Unlike a Taylor Series, a Power Series continues infinitely (remember the "+..."). The domain of the series are the numbers for which the series converges. We also discussed how to find the interval/radius of convergence. The ratio test is the best way, If the limit is 0, then the series converges for all x, but if the limit is infinity, it converges only at the center. If you need to find the IOC/ROC for the deriv./integral the endpoints are the same, but you need to test for inclusiveness. -
Advanced Integration
If you know the basic formulas, you can solve the majority of tricky integ. problems. Clever tricks...If the highest degree in the numerator is = or > than the denominator, do long division. Partial fractions can also make like really easy when you have binomials and trinomials in fractions. And thanks to the product rule, we can do IBP, but only when ALL OTHER OPTIONS have been considered (approx 8-10 sec. of thought). Use LIPET to determine u and v. Also, use L'Hopitals for IND forms. -
Volume and Area of Known Cross-Sections
This should be the problem that you can guarentee a "9" on. Just remember the formulas for the various methods and draw in you rectangles. Remember: "Parashell", "Perpendiskular". Also be sure to use the appropriate bounds. For areas of known cross-sections, use the function to write the area of the base (know the formulas for basic shapes). Then, take the integral of the "area" of the base. (Think- area is units squared and volume is cubed, integration takes you from one to the other) -
Polar Equations
There are 4 basic formulas to know: x=rcos(t), y=rsin(t), tan(t)=y/x, r^2=x^2+y^2. WIth these, you manipulate from polar to rectangular and vice versa. There are four major application/follow-up questions for a polar graph: slope, area, arc length, surface area. Remember those formulas!! Overall, I feel pretty comfortable with polar stuff. Sometimes converting the equations ca be challenging, and I really need to think about the area problems, but with sufficient time I can find the answer. -
Polar Graphs/Equations Test
I felt good about most of the test. There was one conversion problem that I really struggled with, but other than that it wasn't terrible. I was really happy that I was able to calculate (or at least I think) the area one. Those always confuse me a little. There were also a few multiple choice questions that I was unsure of, but overall I was happy with my performance. -
Practice Problems (Multiple Choice and FRQs)
Today I completed 18 multiple choice practice questions and 2 free-response questions. The free-response problems were fine, and most of the multiple choice were straight-forward. I will review some of the series information again just to make the converge/diverge problems go faster. -
Take Home Test Debrief
The take home test went really well! I'm feeling pretty good about the BIG GAME! I just want to review my KYSC sheet, particularly some of the trig conversions. -
The Pre-Game
Today I just went over my "What should you do when you see..." sheet and looked over my KYSC paper. I also went over the HHHs paper to reassure myself that I do indeed know calculus. (And of course went to be early and ate blueberrires for extra brain power). I feel confident about tomorrow! -
The BIG GAME Evaluation
Overall, I felt pretty good. The multiple choice w/ calculator was really easy; I even had time to check every answer twice. The non-calc multiple choice was more difficult, but there were only a handful of unclear questions. The free-response was signiicantly more difficult than MC (which I found odd), but the last question in particular was very challenging. It should have been easy, but the wording was very confusing and I just could not determine what they wanted me to find.
