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
. Highly recommended ! teachingcalculus.com A blog for calculus teachers and students by Lin McMullin
: Algebra, Calculus I, II, III, differentail eq, set theory, logic, etc. MATHISPOWER4U
Prof. R. Delaware, Kansas' Univ. College Algebra
Prof. R. Delaware, Kansas' Univ. Calculus I
Calculus I Lectures, NYU. Prof. M. Leingang.
, by Prof. Larry K. Norris Multivariable Calculus
Draw function graphs
Graphics for Complex Analysis
Complex Function Grapher
Investigating Parent Functions
by professor Dawkins Cheat Sheets and Tables
Just trig cheat sheet, click here.
Single variable Calculus MIT OpenCourseWare
by Mathematics Professor John Dersch (video lecture). History of Mathematics in 50 Minutes
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.
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.
: test the following series for convergence or divergence, #1 to #34. Solutions included. Strategies for testing Series, by Stewart
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 .
Jan 23 to Feb 3rd:
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.
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.
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,
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.