Mr. Stephen Lange » Calculus Resources

Calculus Resources

Mr. Lange's Calculus Resources

Course Description
AP Calculus Course Description from College Board

Does it all

Calculus Applets-- Download them all to your computer from the folder  Java required

Graphing Calculators

Great Online Graphing Calculator

Graphing calculator Programs from Lin McMullin

Calculator Problems Powerpoint  Calculus Review - Calculator

Textbook Website
Simple Nice Worksheets from Univ of Arizona

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

Brightstorm - Great great Videos
Dartmouth Videos -Good Examples 
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


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

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 
                                                   Zweigmedia Tutorial

Deriviative Graphers-   Flash and Math
                                 Calculus Applets
Graphing a Derivative with a Graphing Calculator Mathbits
Graph of the Derivative Given a Function- Applet/Plotter
                                                           Tracing Game
                                                           Puzzle Game
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



Introduction to the Definite Integral

Fundamental Theorem of Calculus

Integration with U Substitution

Calculus Physics
Equations of Motion

Reimann Sums

Reimann Sums - Ted Coe Applet

Accumulation Function

Area Between Two Curves

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

Disk Method

Washer Method

Known Cross Sections
Volume Applet

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 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


    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
  -- Lots of good stuff (When you See, Powerpoint, Cheat Sheets)
 -- Excellent Practice Exams
  Mr Tozzo has it all
    Mr Kries's Collection   Lots of Exam Material