Basic Integration Review*Reviewed integrals
*Reviewed mean value theorem for derivatives
*Reviewed Mean Value Theorem
*Reviewed the first and second fundamental theorems of calculus
*Worked through multiple practice problems
*Also worked with u-substitutions Practice problems were pretty easy. Glad to have review with u-substitutions.
Slope Fields, Euler's Method, Growth and DecaySlope Fields:
- Determine if f(x) is a solution of a Differential Eq.
- Construct part of a slope field
- Determine correct slope field
- Look for slope at axes Euler's (pron. Oiler's) Method:
- Start with initial point (x0, y0)
- Use appr. step size (delta x)
- Find dy/dx
- find dy (dy/dx * delta x)
- new point is (x + dx, y + dy) NEED TO SEPARATE VARS. ALWAYS.
Learned growth and decay formulas. Appreciated review of growth and decay functions.
Infinite Series*Reviewed different types of series
* reviewed tests for convergence and divergence
* reviewed difference between sequences and series Glad for review on the different tests, and on geometric series.
Taylor Series & Power SeriesOverview: Appreciated the review on LaGrange Error Bounds, but remembered most other stuff. Need to review power series for transcendental functions. *Taylor Polynomials are polynomial approximations of transcendental functions
*Maclaurin Series = Taylor series centered at 0.
*Actual Error: |Rn(x)| = |f(x) - Pn(x)|
*LaGrange Error Bound: next derivative of z times (x -center) to the next power all over (n + 1)!
- z = a convenient maximum error.
- for example, use 1 for sin or cos
TestingTests to practice for the AP
Looked at practice examsWent over practice tests. Didn't do horribly, but could have done better.
Shell & Disk MethodsGlad for review.
Was pretty confident before, now I hope not to lose any points on questions involving these.
Advanced Integration TechniquesReviewed partial fractions and u-substitions. I had forgotten about some of the u-substitution tricks, and was glad for the review. remembered partial fractions pretty well.
best of all... NO TRIG SUB ON TEST!
THE TESTSurprisingly easy. Had maybe 2 or 3 multiple choice questions on series and part of a free response involved the ratio test. Some integration and derivatives, but nothing too difficult. One problem was almost like exponential growth, but not quite. Will be very dissapointed if I recieve anything less than a 5.