Exploration of slopes of secant lines and tangent lines. The average and instantaneous rate of change is calculated with the difference quotient. Day 1 is an independent activity located here:

Exploration of slopes of secant lines and tangent lines. The average and instantaneous rate of change is calculated with the difference quotient.<br/> Day 1 is an independent activity <a href="http://www.uhigh.ilstu.edu/math/thompson/sketchpad/apcalc/2.4_The%20Leaning%20Tower%20of%20Pisa.doc" rel="nofollow" target="_blank">located here</a>:

2.4 day 2 

Euler's method to approximate the value of a function given a differential equation and initial point is explored.

Euler's Method (BC only)

We explore the integral test to determine convergence.  The harmonic series is revisited.

10.5 (BC only)  Integral Test for Convergence

We explore the comparison test and the ratio test to determine convergence.  The area inside polar functions is also explored as well as their slopes.

10.4 (BC only) Convergence and Polar functions

We explore the error bound for Taylor polynomials.

10.3 (BC only)  Taylor Polynomials and error bound

We explore creating Taylor polynomials.  We also center them at other values and create new polynomials from given ones.

10.2 (BC only)  Taylor Polynomials day 2

10.2 (BC only)  Taylor Polynomials

8.5  day 2  Work from pumping

Some example problems involving force and work. Lifting a leaky bucket and pumping to fill a tank.

8.5  day 1 Work done lifting a leaky bucket

We explore geometric series.  We create new power series from known ones by differentiation and integration.  The power series for e^x is explored.  We also write pi as an infinite series produced by integrating term by term of a problem producing an inverse tangent.

10.1 (BC only)  Power Series

AP Calculus lessons University High School Normal,IL

Dr Thompson's AP Calculus University High School

4.2 Implicit Differentiation

Methods of disks and washers are explored in calculating the volume of a solid. Revolution around a line not an axis is explored.  Shell method introduced.

8.3 day 2 volumes of revolution

Several problems are explored finding the area between two curves.

8.2 area between 2 curves Day 1

This lesson focuses upon finding the length of a curve as a function of x and a function of y.

8.4  (BC only) Length of a curve

This lesson focuses upon parametric functions and their first and second derivatives.

11.1 and 11.2  (BC only) Partial Fraction Decomposition

This lesson focuses upon looking at several examples of partial fraction decomposition.

7.5  (BC only) Partial Fraction Decomposition

Using integration by parts. Investigate problems using this specific method.  An  "unknown integral" type problem is explored.

7.3 Integration by parts

2 examples using two methods of u substitution for indefinite integrals.

7.2 Using u substitution for indefinite integrals

An introduction to first order differential equations and slope fields.  A slope field is graphed using Geometer's Sketchpad.  Connections to the fundamental theorem of calculus are made.

7.1 differential equations and slope fields

Using approximations, the volume of a pool is approximated using trapezoids.

6.5 Approximations with trapezoids

The lesson begins with a  connection being illustrated between position and velocity.  This is a review.  However, the area under the velocity graph is calculated and the connection back to position is explored.  This lesson also examined a graph and a function defined as the integral of another function.   The derivative of the integral is examined.

6.4 Fundamental Theorem of Calculus-- an introduction

This section looks at several properties of definite integrals including how to combine or separate them over a given interval, combining functions, and reversing the limits.

6.3 definite integral day 1

A reimann sum is constructed and then developed into the definite integral.  A connection to area is explored.  Definite integrals are evaluated using knowledge of geometry.

6.2 the definite integral and reimann sums

5 .6 Related Rates Day 2

Examines how the slope of the tangent line at a point could aid in the estimation of a function value or in estimation of the x intercepts.

5.5 Linearization and Newton's Method

Investigation of the antiderivative of a function.  We look at how there are multiple functions that can satisfy a specific derivative.

5.2 The Antiderivative

Investigate the definition of a critical point.  Examine various functions and their extrema.

5.1  day 1 Critical points and extrema

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