AP Calculus: BC @ Hialeah Gardens High School.
Carlos Sotuyo. Email: email@example.com
The art of teaching is the art of assisting discovery.
Mark Van Doren
Notes & Assignments:
Week 12/05 --12/16.
- Discuss tests of covergence for Series.
- Taylor - Maclaurin Series.
- Find the Taylor expansion for a given trascendental function, such as ex, sinx, cosx.
- Find a Taylor polynomial by using substitution. Ex: e2x, sin2x, cos(x/2), etc. Note: Taylor series can be added, subtracted, and multiplied by constants and powers of x, and the resulting series will also be Taylor series. Example: To find a series for cos 2x, simply substitute 2x in for each x in the Taylor series for cos x.
- Find the expansion of eix, compare the result to the expansion of sin x and cos x and relate the result to: eix = cos x + isin x
- Find Taylor/Maclaurin series expansions by integration or differentiation of power series. Ex: ln(1-x), arctan x etc.
- The Binomial Series expansion.
- Background: Integration by partial fractions, Improper integrals, Geometric Series.
- Strategies for testing Series, by Stewart: test the following series for convergence or divergence, #1 to #34. Solutions included.
- Summary of Convergence Tests for Series pdf.
- Testing Series Convergence: Series Tests flowchart.
- The binomial series. Text book p. 683
- Radius of convergence of power series. Text book p662-665
- Remainder estimation theorem. Text book p656-657
- Estimating the Value of a Series.
- Teacher notes MS Word. PDF here.
- Practice. Worksheet.
Jan 23 to Feb 3rd:
- Parametric equations.
- Derivatives. Arc length.
- Practice: Text book p763: AB/BC Calculus prep questions 1 thru 6.
Feb 6 thru 10:
- Polar coordinates. Graphs.
- Area in polar coordinates.
- Practice: Text book p763: AB/BC Calculus prep questions 7 thru 10.
- Paul online notes. Examples.
Feb 13-17:Feb 20- and Beyond: REVIEW.
Vector valued functions.
Motion along a curve: problems involving position, velocity and acceleration of a particule on a 2-Dimensional space.
- Discussion of previous Calculus BC Exams,
Worksheet on integration: int by substitution, by parts, partial fractions.
- AP Calc. Free Response Q & Sln 1989-1997.
Paul's Online notes. Excelent resources for calculus II (BC): Here !
Professor S. Hollis, Calculus I & II --AB & BC-- videos, online.
- Discussion of previous exams free response questions.
- Related rate problems -- worksheet.
- Area between curves, volumen of a solid of revolutions.
Ex 1 thru 6, also 17 & 18 p 454. Page 465 ex 1 thru 10
and page 474 1 tru 4, and 17, 18, 27, 28.
- April 2nd thru May 9: Discussion of previous exams.
- TI 83 program for taylor series, click here.
- TI 84 plus online manual.
- TI 89 online manual.
- Check left column of this page under College Board logo:
Recommended: on-line question collections.
FRIDAYS at 2.30pm --tutoring program room 3126 !
- On line Resources, Calculus AP:
Piecewise Functions: Investigating Differentiability
- Calculus.org Resources For The Calculus Student:
- Study.com AP Calculus AB & BC: Exam Prep
- Exams, MIT Calculus Open Courseware
- Univ California at Davis: CONTINUITY OF FUNCTIONS OF ONE VARIABLE.
Questions & Solutions.