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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


If you can't explain it simply, you don't understand it well enough.
Albert Einstein


Topic outline for Calc AB & BC (pages 6 to 12 of the course description): pdf.

The AP Calculus AB Exam

The AP Calculus BC Exam

University Houston, Lectures  for AP Calculus

College Board: Multiple choice questions collection (AB/BC)

AP Calculus AB Free Response Notebook

Peterson’s Master AP Calculus AB & BC.

The AP Calculus Problem Book by Chuck Garner, Ph.D

teachingcalculus.com A blog for calculus teachers and students by Lin McMullin. Highly recommended !



MATHISPOWER4U tutorials: Algebra, Calculus I, II, III, differentail eq, set theory, logic, etc.


&

Prof. R. Delaware, Kansas' Univ. College Algebra

Prof. R. Delaware, Kansas' Univ. Calculus I

Calculus I Lectures, NYU. Prof. M. Leingang.

Multivariable Calculus,  by Prof. Larry K. Norris



Polar graphs

Draw function graphs

Graphics for Complex Analysis

Complex Function Grapher

Investigating Parent Functions

Cheat Sheets and Tables by professor Dawkins
Just trig cheat sheet, click here.




Single variable Calculus MIT OpenCourseWare

History of Mathematics in 50 Minutes by Mathematics Professor John Dersch (video lecture).

Math History 9: Calculus by Prof Wildberger. University of New South Wales, Australia.

The Fibonacci sequence. Audio, BBC. Video.

Let’s begin  with a pair of rabbits.  Assume that that rabbits begin to reproduce two months after their own birth.  This is, after reaching the age of two months each pair produces one male and one female, and another pair each month thereafter. Also assume that no rabbit dies. This is the sequence of numbers of rabbits generated by the original pair of rabbits:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,  …

The Fibonacci Sequence!

The Golden Ratio and The Fibonacci Numbers

Notes & Assignments:

Week 12/05 --12/16.

  1. Discuss tests of covergence for Series.
  2. Taylor - Maclaurin Series.
  3. Find the Taylor expansion for a given trascendental function, such as ex, sinx, cosx.
  4. 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.
  5. 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



  6. Find Taylor/Maclaurin series expansions by integration or differentiation of power series. Ex: ln(1-x), arctan x etc.
  7. The Binomial Series expansion.
  8. Background: Integration by partial fractions, Improper integrals, Geometric Series.
  9. Strategies for testing Series, by Stewart: test the following series for convergence or divergence, #1 to #34. Solutions included.
  10. Summary of Convergence Tests for Series pdf.
  11. Testing Series Convergence: Series Tests flowchart.

    January 2012.

  12. The binomial series. Text book p. 683
  13. Radius of convergence of power series. Text book p662-665
  14. Remainder estimation theorem. Text book p656-657
  15. Estimating the Value of a Series.
  16. Teacher notes MS Word. PDF here.
  17. Practice. Worksheet.

Jan 23 to Feb 3rd:

  1. Parametric equations.
  2. Derivatives. Arc length.
  3. Practice: Text book p763: AB/BC Calculus prep questions 1 thru 6.


    Feb 6 thru 10:

  4. Polar coordinates. Graphs.
  5. Area in polar coordinates.
  6. Practice: Text book p763: AB/BC Calculus prep questions 7 thru 10.
  7. 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.
  1. Discussion of previous Calculus BC Exams,
    Worksheet on integration: int by substitution, by parts, partial fractions.
  2. AP Calc. Free Response Q & Sln 1989-1997.

March 19-31:
Paul's Online notes. Excelent resources for calculus II (BC): Here !



Professor S. Hollis,
Calculus I & II --AB & BC-- videos, online.

  1. Discussion of previous exams free response questions.
  2. Related rate problems -- worksheet.
  3. 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.
  4. April 2nd thru May 9: Discussion of previous exams.
  5. TI 83 program for taylor series, click here.
  6. TI 84 plus online manual.
  7. TI 89 online manual.
  8. Check left column of this page under College Board logo:
    Recommended: on-line question collections.
    FRIDAYS at 2.30pm --tutoring program room 3126 !
  9. On line Resources, Calculus AP:
    Piecewise Functions:  Investigating Differentiability

  10. Calculus.org Resources For The Calculus Student:
  11. Study.com   AP Calculus AB & BC: Exam Prep
  12. Exams, MIT Calculus Open Courseware

  13. Univ California at Davis: CONTINUITY OF FUNCTIONS OF ONE VARIABLE.
    Questions & Solutions.