# Calculus Resources

**Does it all**

Wolframalpha

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

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

**Graphing Calculators**

Desmos.com

Desmos.com

Great Online Graphing Calculator

Graphing calculator Programs from Lin McMullin

Calculator Problems Powerpoint

Graphing calculator Programs from Lin McMullin

Calculator Problems Powerpoint

*Calculus*Review - Calculator

Textbook Website

Textbook Website

Worksheets

Simple Nice Worksheets from Univ of Arizona

Mastermathmentor

Calculus Maximus from Kevin Korpi's KorpisWorld

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

Principles of Calculus Modeling- From Dartmouth

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**

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

Constant Rule Lesson 1 Lesson from the Math Page

Constand Multiple Rule Lesson 1

Sum and Difference Rules Lesson from the Math Page

Product Rule Wiki Lesson from the Math Page

Chain Rule Wiki 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**

Visual Calculus Tutorial

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**

Equations of Motion

Volume Applet

Reimann Sums

Reimann Sums - Ted Coe Applet

Accumulation Function

Area Between Two Curves

David Little's Area Between Two Curves

**Volume**

Disk Method

Washer Method

Volumes of Revolution - from www.calculusapplets.com

Shell Method Applet GOOD VISUAL

**SHELL METHOD**

VIDEOS FROM KHAN ACADEMY

- Shell method to rotate around y-axis
- Shell method around a non-axis line
- Shell method around a non-axis line 2

Shell Method Applet GOOD VISUAL

**Known Cross Sections**

Volume Applet

Differential Equations

Differential Equations

Slope Fields

Wikipedia- Slope Fields

Slope Field Plotter- from Penn State

Slope Field Plotter- from Lawrenceville

Inverse Trig Calculus

Inverse Trig 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

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)

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

Inverse Trig Functions

**Calculus BC Resources****Functions and Graphs**

Parametric, Polar and Vector Functions**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)

Integration by Parts

Integration by Parts

Integration by Simple Partial Fractions

Partial Fractions

Improper Integrals (as limits of definite integrals)

L'Hospital Applied to Integrals

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