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: 

Dr Thompson's AP Calculus University High School

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

8.3 day 3 volumes of revolution

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

This lesson focuses upon evaluating improper integrals using limits. Using length of the curve, we show that the circumference of a circle of radius pi is 2*pi*r

9.4 (BC only) Day 2 Improper Integrals

Methods of disks and washers are explored in calculating the volume of a solid.

8.3 day 1 volumes of revolution

This lesson focuses upon evaluating improper integrals using limits. L'Hospital's rule is also discussed.

9.4 (BC only) Improper Integrals

AP Calculus lessons University High School Normal,IL

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Dr Thompson's AP Calculus University High School

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