Calculus Resources

Inverse Trig Calculus
Inverse Trig Functions

Calculus BC Resources

Functions and Graphs

Parametric, Polar and Vector Functions

Plane Curves and Parametrics

Polar Coordinates and Graphs

DERIVATIVES
Derivatives of Paramtric Polar and Vector Functions

Analysis of Planar Curves in Parametric Form

Polar Form and Vector Form including Velocity and Acceleration

Differentials and Newtons Method
Differentials and Newton's method

Numerical Solutions of differential equations using Euler's Method

L'Hospital's Rule in determining limits and convergence of improper integrals and series
Application of Integrals: Models

Area of a region bounded by polar curves
Area in Polar Coordinates

Integrals

Application of Integrals
Center of Mass and Centroid
Center of mass of a rod and centroid of a planar region

The arc length of a curve (including a curve in parametric form)

Antiderivatives by Substitution of Variables (Including Change of Limits for Definite Integrals)

Trig Powers and Trig Substitution


Integration by Parts
Integration by Parts


Integration by Simple Partial Fractions
Partial Fractions

Improper Integrals (as limits of definite integrals)

Improper Integrals

L'Hospital Applied to Integrals

L'Hopital's Rule

Solving Logistic Differential Equations and Usint Them in Modeling

V. Polynomial Approximations and Series

Concept of series

A series is defined as a sequence of partial sums, and convergence is defined in terms of the limit of the sequence of partial sums. Technology can be used to explore convergence and divergence.
Series of constants

Motivating examples, including decimal expansion  Geometric series with applications
  The harmonic series

Alternating series with error bound

Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series

The ratio test for convergence and divergence

Comparing series to test for convergence or divergence

Taylor series 

Taylor polynomial approximation with graphical demonstration of convergence (for example, viewing graphs of various Taylor polynomials of the sine function approximating the sine curve)

Maclaurin series and the general Taylor series centered at x = a

  Maclaurin series for the functions ex, sin x, cos x, and 1/(1 -x)

  Formal manipulation of Taylor series and shortcuts to computing

Taylor series, including substitution, differentiation, anti-differentiation, and the formation of new series from known

Functions defined by power series

•   Radius and interval of convergence of power series
•   Lagrange error bound for Taylor polynomials

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Calculus Jeopardy

 

www.jamesrahn.com  -- Lots of good stuff (When you See, Powerpoint, Cheat Sheets)