Search for episodes from Dr Thompson's AP Calculus University High School with a specific topic:

Latest episodes from Dr Thompson's AP Calculus University High School

2.4 day 2

Play Episode Listen Later Sep 20, 2017 40:25


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:

Euler's Method (BC only)

Play Episode Listen Later Apr 16, 2014 35:44


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

10.5 (BC only) Integral Test for Convergence

Play Episode Listen Later Apr 9, 2014 26:41


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

10.4 (BC only) Convergence and Polar functions

Play Episode Listen Later Apr 7, 2014 57:50


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.

10.3 (BC only) Taylor Polynomials and error bound

Play Episode Listen Later Mar 26, 2014 52:34


We explore the error bound for Taylor polynomials.

10.2 (BC only) Taylor Polynomials day 2

Play Episode Listen Later Mar 20, 2014 15:57


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

Play Episode Listen Later Mar 19, 2014 44:21


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

8.5 day 2 Work from pumping

Play Episode Listen Later Mar 18, 2014 16:39


Work done drinking a milk shake

8.5 day 1 Work done lifting a leaky bucket

Play Episode Listen Later Mar 17, 2014 44:54


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

10.1 (BC only) Power Series

Play Episode Listen Later Mar 5, 2014 45:35


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.

8.3 day 3 volumes of revolution

Play Episode Listen Later Mar 4, 2014 20:33


8.3 day 2 volumes of revolution

Play Episode Listen Later Mar 4, 2014 35:09


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.

9.4 (BC only) Day 2 Improper Integrals

Play Episode Listen Later Feb 28, 2014 53:13


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

8.3 day 1 volumes of revolution

Play Episode Listen Later Feb 27, 2014 45:01


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

9.4 (BC only) Improper Integrals

Play Episode Listen Later Feb 26, 2014 53:13


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

8.2 area between 2 curves Day 2

Play Episode Listen Later Feb 25, 2014 33:22


Several problems are explored finding the area between two curves. Integrating with respect to y is explored as well.

8.2 area between 2 curves Day 1

Play Episode Listen Later Feb 24, 2014 21:31


Several problems are explored finding the area between two curves.

9.1 (BC only) Sequences

Play Episode Listen Later Feb 21, 2014 32:57


This lesson focuses upon sequences. It looks at a formal definition for the limit of a sequence.

8.1 integral as net change

Play Episode Listen Later Feb 19, 2014 41:51


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

8.4 (BC only) Length of a curve

Play Episode Listen Later Feb 19, 2014 42:18


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

11.1 and 11.2 (BC only) Partial Fraction Decomposition

Play Episode Listen Later Feb 14, 2014 34:02


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

7.5 (BC only) Partial Fraction Decomposition

Play Episode Listen Later Feb 11, 2014 43:08


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

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

Play Episode Listen Later Feb 10, 2014 40:34


This lesson focuses upon developing the exponential function A=Pe^(rt) from a separable differential equation. Next Newton's Law of cooling is explored.

7.4 Intro

Play Episode Listen Later Feb 7, 2014 42:18


Introduction to separable differential equations

7.3 Integration by parts

Play Episode Listen Later Feb 7, 2014 38:21


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

7.2 Using u substitution for indefinite integrals day 2

Play Episode Listen Later Feb 6, 2014 23:13


Using u-substitution to determine the antiderivative of tangent

7.2 Using u substitution for indefinite integrals

Play Episode Listen Later Feb 4, 2014 39:10


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

7.1 differential equations and slope fields (day2)

Play Episode Listen Later Jan 31, 2014 40:42


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.

7.1 differential equations and slope fields

Play Episode Listen Later Jan 29, 2014 32:04


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.

6.5 Approximations with trapezoids

Play Episode Listen Later Jan 24, 2014 12:13


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

6.4 Fundamental Theorem of Calculus Day 2

Play Episode Listen Later Jan 22, 2014 43:22


Investigates the second half of the theorem. Time is spent looking at examples as well as finding anti derivatives with specific conditions

6.4 Fundamental Theorem of Calculus-- an introduction

Play Episode Listen Later Jan 17, 2014 44:24


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.

6.3 day 3

Play Episode Listen Later Jan 15, 2014 33:38


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 to be the anti-derivative. An example using the anti-derivative is completed.

6.3 day 2

Play Episode Listen Later Jan 14, 2014 40:08


Lesson starts with average value of a function. 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 to be the anti-derivative.

6.3 definite integral day 1

Play Episode Listen Later Jan 13, 2014 30:40


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.

6.2 the definite integral and reimann sums

Play Episode Listen Later Jan 13, 2014 33:26


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.

6.1 Rectangle approximation methods

Play Episode Listen Later Jan 8, 2014 35:26


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.

5 .6 Related Rates Day 2

Play Episode Listen Later Dec 9, 2013 44:27


Examine a more complicated example

5 .6 Related Rates

Play Episode Listen Later Dec 9, 2013 35:21


Examine two related rate questions

5.5 Day 2 Differentals

Play Episode Listen Later Dec 4, 2013 46:19


Using Differentials to approximate changes in the function

5.5 Linearization and Newton's Method

Play Episode Listen Later Dec 3, 2013 46:19


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.

5.4 day 3 Proof of minimum distance

Play Episode Listen Later Dec 3, 2013 22:28


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.

5.4 day 2 maximize profit and minimize average cost.

Play Episode Listen Later Dec 3, 2013 15:54


5.4 Optimization

Play Episode Listen Later Dec 3, 2013 26:26


Using the derivative to maximize or minimize. 2 geometric examples are explored.

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

Play Episode Listen Later Dec 3, 2013 27:03


Examines the graphical connections between concavity and the first and second derivative

5.3 intro-derivatives and the connection to graphs

Play Episode Listen Later Dec 3, 2013 51:56


analyzing the connection between pos/neg derivatives and if f' exists or is zero at a specific value

5.2 The Antiderivative Day 2

Play Episode Listen Later Dec 3, 2013 36:47


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

Play Episode Listen Later Dec 3, 2013 18:03


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

5.1 day 1 Critical points and extrema

Play Episode Listen Later Dec 3, 2013 46:57


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

4.4 day 2. Application involving the derivative of an exponential

Play Episode Listen Later Dec 3, 2013 22:46


How fast is a rumor spreading? This question is explored.

4.4 day 1 Derivatives of exponentials and logarithms

Play Episode Listen Later Dec 3, 2013 42:43


Determines the general formula for exponential and natural logarithms. the derivative of e^x is explored. Sketchpad is used to show the connection of slope for e^x.

Claim Dr Thompson's AP Calculus University High School

In order to claim this podcast we'll send an email to with a verification link. Simply click the link and you will be able to edit tags, request a refresh, and other features to take control of your podcast page!

Claim Cancel