Dr Thompson's AP Calculus University High School

By Dr Kevin Thompson

Education K-12

What's Dr Thompson's AP Calculus University High School about?

AP Calculus lessons University High School Normal,IL

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Dr Thompson's AP Calculus University High School episodes:

09.20.2017
2.4 day 2
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 found here http://www.uhigh.ilstu.edu/math/thompson/sketchpad/apcalc/2.4_The%20Leaning%20Tower%20of%20Pisa.doc
04.16.2014
Euler's Method (BC only)
Euler's method to approximate the value of a function given a differential equation and initial point is explored.
04.09.2014
10.5 (BC only) Integral Test for Convergence
We explore the integral test to determine convergence. The harmonic series is revisited.
04.07.2014
10.4 (BC only) Convergence and Polar functions
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.
03.26.2014
10.3 (BC only) Taylor Polynomials and error bound
We explore the error bound for Taylor polynomials.
03.20.2014
10.2 (BC only) Taylor Polynomials day 2
We explore creating Taylor polynomials. We also center them at other values and create new polynomials from given ones.
03.19.2014
10.2 (BC only) Taylor Polynomials
We explore creating Taylor polynomials. We also center them at other values and create new polynomials from given ones.
03.18.2014
8.5 day 2 Work from pumping
Work done pumping milk shake
03.17.2014
8.5 day 1 Work done lifting a leaky bucket
Some example problems involving force and work. Lifting a leaky bucket and pumping to fill a tank.
03.05.2014
10.1 (BC only) Power Series
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...
03.04.2014
8.3 day 3 volumes of revolution
An example of the shell method
03.04.2014
8.3 day 2 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.
02.28.2014
9.4 (BC only) Day 2 Improper Integrals
This lesson focuses upon evaluating improper integrals using limits. 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
02.27.2014
8.3 day 1 volumes of revolution
Methods of disks and washers are explored in calculating the volume of a solid.
02.26.2014
9.4 (BC only) Improper Integrals
This lesson focuses upon evaluating improper integrals using limits. Includes a discussion of L'Hospital's rule
02.25.2014
8.2 area between 2 curves Day 2
Several problems are explored finding the area between two curves. Integrating with respect to y is explored as well. In the last 5 seconds, the black parabola is opening the wrong direction/. The idea being described is...
02.24.2014
8.2 area between 2 curves Day 1
Several problems are explored finding the area between two curves.
02.21.2014
9.1 (BC only) Sequences
This lesson focuses upon sequences. It looks at a formal definition for the limit of a sequence.
02.19.2014
8.1 integral as net change
Focus upon real life problems and the integral as the net change. Force, Work, Acceleration, Velocity are tied together. Units are discussed. A problem with electricity and Hooke's Law
02.19.2014
8.4 (BC only) Length of a curve
This lesson focuses upon finding the length of a curve as a function of x and a function of y.
02.14.2014
11.1 and 11.2 (BC only) Partial Fraction Decomposition
This lesson focuses upon parametric functions and their first and second derivatives.
02.11.2014
7.5 (BC only) Partial Fraction Decomposition
This lesson focuses upon looking at several examples of partial fraction decomposition.
02.10.2014
7.4 Newton's law of cooling and solving a separable differential equation.
This lesson focuses upon developing the exponential function A=Pe^(rt) from a separable differential equation. Next Newton's Law of cooling is explored.
02.07.2014
7.4 Intro
Introduction to separable differential equations
02.07.2014
7.3 Integration by parts
Using integration by parts. Investigate problems using this specific method. An "unknown integral" type problem is explored.
02.06.2014
7.2 Using u substitution for indefinite integrals day 2
Using u-substitution to determine the antiderivative of tangent
02.04.2014
7.2 Using u substitution for indefinite integrals
2 examples of using a method of u substitution for indefinite integrals.
01.31.2014
7.1 differential equations and slope fields (day2)
An introduction to first order differential equations and slope fields. A slope field is graphed using Geometer's Sketchpad. Strategies to investigate slope fields are given.
01.29.2014
7.1 differential equations and slope fields
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.
01.24.2014
6.5 Approximations with trapezoids
Using approximations, the volume of a pool is approximated using trapezoids.
01.22.2014
6.4 Fundamental Theorem of Calculus Day 2
Investigates the second half of the Thm. Time is spent looking at examples as well as finding anti derivatives with specific conditions
01.17.2014
6.4 Fundamental Theorem of Calculus-- an introduction
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...
01.15.2014
6.3 day 3
Exploring through Sketchpad, the connection between a function and a function representing the signed area from a to x is explored. The function [F(x)] that is the signed area from a to x for the function f(x) is revealed...
01.14.2014
6.3 day 2
Exploring through Sketchpad, the connection between a function and a function representing the signed area from a to x is explored. The function [F(x)] that is the signed area from a to x for the function f(x) is revealed...
01.13.2014
6.3 definite integral day 1
Rules for the definite integral are explored.
01.13.2014
6.2 the definite integral and reimann sums
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.
01.08.2014
6.1 Rectangle approximation methods
Explore how the area under a curve can connect to a real life situation involving velocity and time. Rectangle methods are explored to approximate the area.
12.09.2013
5 .6 Related Rates Day 2
Examine a more complicated related rate question
12.09.2013
5 .6 Related Rates
Examine two related rate questions
12.04.2013
5.5 Day 2 Differentals
Using Differentials to approximate changes in the function
12.03.2013
5.5 Linearization and Newton's Method
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.
12.03.2013
5.4 day 3 Proof of minimum distance
When light reflects off a surface, to another point. This is the shortest distance of any reflection (when the triangles are similar) We consider a calculus proof of the topic.
12.03.2013
5.4 day 2 maximize profit and minimize average cost.
Examples of optimization of profit and average cost
12.03.2013
5.4 Optimization
Using the derivative to maximize or minimize. 2 geometric examples are explored.
12.03.2013
5.3 day 2 connecting the graphs to concavity and points of inflection
Examines the graphical connections between concavity and the first and second derivative
12.03.2013
5.3 intro-derivatives and the connection to graphs
analyzing the connection between pos/neg derivatives and if f' exists or is zero at a specific value
12.03.2013
5.2 The Antiderivative Day 2
Investigation of the antiderivative of a function. We look at how there are multiple functions that can satisfy a specific derivative.
12.03.2013
5.2 The Antiderivative
Investigation of the antiderivative of a function. We look at how there are multiple functions that can satisfy a specific derivative.
12.03.2013
5.1 day 1 Critical points and extrema
Investigate the definition of a critical point. Examine various functions and their extrema.
12.03.2013
4.4 day 2. Application involving the derivative of an exponential
How fast is a rumor spreading? This question is explored.

What's Dr Thompson's AP Calculus University High School about?

Download our free app to listen on your phone

Dr Thompson's AP Calculus University High School episodes:

2.4 day 2

Euler's Method (BC only)

10.5 (BC only) Integral Test for Convergence

10.4 (BC only) Convergence and Polar functions

10.3 (BC only) Taylor Polynomials and error bound

10.2 (BC only) Taylor Polynomials day 2

10.2 (BC only) Taylor Polynomials

8.5 day 2 Work from pumping

8.5 day 1 Work done lifting a leaky bucket

10.1 (BC only) Power Series

8.3 day 3 volumes of revolution

8.3 day 2 volumes of revolution

9.4 (BC only) Day 2 Improper Integrals

8.3 day 1 volumes of revolution

9.4 (BC only) Improper Integrals

8.2 area between 2 curves Day 2

8.2 area between 2 curves Day 1

9.1 (BC only) Sequences

8.1 integral as net change

8.4 (BC only) Length of a curve

11.1 and 11.2 (BC only) Partial Fraction Decomposition

7.5 (BC only) Partial Fraction Decomposition

7.4 Newton's law of cooling and solving a separable differential equation.

7.4 Intro

7.3 Integration by parts

7.2 Using u substitution for indefinite integrals day 2

7.2 Using u substitution for indefinite integrals

7.1 differential equations and slope fields (day2)

7.1 differential equations and slope fields

6.5 Approximations with trapezoids

6.4 Fundamental Theorem of Calculus Day 2

6.4 Fundamental Theorem of Calculus-- an introduction

6.3 day 3

6.3 day 2

6.3 definite integral day 1

6.2 the definite integral and reimann sums

6.1 Rectangle approximation methods

5 .6 Related Rates Day 2

5 .6 Related Rates

5.5 Day 2 Differentals

5.5 Linearization and Newton's Method

5.4 day 3 Proof of minimum distance

5.4 day 2 maximize profit and minimize average cost.

5.4 Optimization

5.3 day 2 connecting the graphs to concavity and points of inflection

5.3 intro-derivatives and the connection to graphs

5.2 The Antiderivative Day 2

5.2 The Antiderivative

5.1 day 1 Critical points and extrema

4.4 day 2. Application involving the derivative of an exponential