# Calculus Resources

Mr. Lange's Calculus Resources

Course Description
AP Calculus Course Description from College Board

Does it all

Wolframalpha

Graphing Calculators

Desmos.com

Great Online Graphing Calculator

Graphing calculator Programs from Lin McMullin

Calculator Problems Powerpoint  Calculus Review - Calculator

Textbook Website

Worksheets
Simple Nice Worksheets from Univ of Arizona

Mastermathmentor
Calculus Maximus from Kevin Korpi's KorpisWorld

AP Questions

Complete Calculus Classes

National Repository of Online Courses- Online Study with Videos
BLC Notes - Match the Stewart book nicely
Visual Calculus- A Hands-on way to learn
Karl's Calculus Tutor - An Interesting Take on Calculus
Paul's Online Calculus Notes - - Good Notes and Cheat Sheets
The Math Page- Good Resources for the basic for the first few weeks

The Calculus Page- Problem List

Precalculus Resources

Complete Tutorials

Purplemath - Focus on Intermediate and Advanced Topics
Regents Prep- Also Visit Algebra and Geometry
Intmath- Focus on Trig and Algebra

Videos

Brightstorm - Great great Videos
Dartmouth Videos -Good Examples
HoustonVideos
Roxanne Byrne u of Denver- Slideshows and Videos

Online Practice Tests

Functions and Transformations

Function Flyer- Graph any Function and examine how number changes transform the graph

Limits

Wikipedia:     Limit    Limit of a Function     One Sided Limit

Limits by Tables Tutorial 1- Hofsta

Graphical Interpretation of a Limit Tutorial- Hofstra

Finding Limits Algebraically Tutorial- Hofsta

Limits at Infinity:

Limits and Continuity Tutorial- Hofstra

Derivatives

Wikipedia  Derivative

Tangent Lines and Secant Lines

Average vs. Instantaneous Velocity

Average Rate of Change Tutorial- Hofstra

Derivative as Instantaneous Rate of Change Tutorial-Hofstra

Derivative as Slope of Tangent Line Tutorial-Hofstra

Deriviative Graphers-   Flash and Math

Graphing a Derivative with a Graphing Calculator Mathbits

Graph of the Derivative Given a Function- Applet/Plotter

Limit Definition of the Derivative: UC Davis Calculus Page

Sketching a Function Given Its Derivative - Mathdemos

Continuity and Differentiability- Zweigmedia Tutorial

Continuous and Differentiable - Calculus Applets

Derivative Rules

Differentiation Rules Wikipedia Entry

Constand Multiple Rule Lesson 1

Sum and Difference Rules Lesson from the Math Page

Derivative of any number to a variable Proof by Chain Rule  Lesson from the Math Page

Inverse Trig Derivatives

Logarithmic and Exponential Derivatives  Hofstra Tutorial SoftCalculus Tutorial  Intmath Tutorial  Brightstorm Videos

Implicit Differentiation

Implicit Differentiation Wiki

Tables of Derivatives

Here's a Nice One - Page One Only

Derivate  Graphs a function and finds the tangent line and the derivative at any point

Applications of Derivatives

Related Rates

Maxima and Minima

Global and Local Extrema Calculus Applets

Curve Analysis Applet

Integration

AntiDerivatives

Introduction to the Definite Integral

Fundamental Theorem of Calculus

Integration with U Substitution

Calculus Physics

Reimann Sums

Reimann Sums - Ted Coe Applet

Accumulation Function

Area Between Two Curves

Volume
Solids of Revolution- A great online study with Calculator Tips
A Cool Lathe Applet

Disk Method

Washer Method
Volumes of Revolution - from www.calculusapplets.com

SHELL METHOD

Applet from David Little

Shell Method Applet GOOD VISUAL

Known Cross Sections

Differential Equations

Slope Fields

Wikipedia- Slope Fields

Slope Field Plotter- from Penn State
Slope Field Plotter- from Lawrenceville

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

Cramming for the AP TEST

Calculus Jeopardy

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

http://al048.k12.sd.us/ -- Excellent Practice Exams

http://tozzo.net/CalculusAB.htm  Mr Tozzo has it all

Mr Kries's Collection   Lots of Exam Material