*AP Calculus: BC* @ Hialeah Gardens High School.

Carlos Sotuyo. Email: csotuyo@imathesis.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 e
^{x}, sinx, cosx. - Find a Taylor polynomial by using substitution. Ex: e
^{2x}, sin2x^{}, cos(x/2), etc. Note: Taylor series can be added, subtracted, and multiplied by constants and powers of, and the resulting series will also be Taylor series. Example: To find a series for*x*, simply substitute*cos 2x*in for each*2x*in the Taylor series for*x*.*cos x* - Find the expansion of e
^{ix}, compare the result to the expansion of sin x and cos x and relate the result to: e^{ix}= 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.**

**January 2012.**

- 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:

Vector valued functions.

Motion along a curve: problems involving position, velocity and acceleration of a particule on a 2-Dimensional space.Feb 20- and Beyond: REVIEW.

- Discussion of previous Calculus BC Exams,

Worksheet on integration: int by substitution, by parts, partial fractions. **AP Calc. Free Response Q & Sln 1989-1997.**

March 19-31:

Paul's Online notes. Excelent resources for calculus II (BC):Here!

Calculus I & II --AB & BC--

Professor S. Hollis,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.**