This is a BC topic Good Question 16 (11-30-2018) What you get when you substitute. Geometric Series – Far Out (2-14-2017) A very interesting and instructive mistake Synthetic Summer Fun (7-10-2017) Finding the Taylor series coefficients without differentiating Error Bounds (2-22-2013) The alternating series error bound, and the Lagrange error bound The Lagrange Highway (5-20-15)…
This is a BC topic POWER SERIES (Maclaurin series and Taylor series) Introducing Power Series 1 (2-8-2013) Making better approximations Introducing Power Series 2 (2-11-2013) Graphing and seeing the interval of convergence Introducing Power Series 3 (2-13-2013) Questions pointing the way to power series Graphing Taylor Polynomials (2-7-2017) Using a graphing calculator to graphs Taylor…
This is a BC topic. SEQUENCES Everyday series (1-17-2017) The most familiar series: Numbers Amortization (2-9-2015) An important use of a (finite) series – Find you mortgage payment without calculus. Convergence Test List A summary of the tests. Download and copy for your students (and yourself) Which Convergence Test Should I Use? Part 1 (2-9-2018)…
In BC calculus the only application parametric equations and vectors is motion in a plane. Polar equations concern area and the meaning of derivatives. See the review notes for more detail and an outline of the topics. (only 3 items here) Motion Problems: Same Thing Different Context (11-16-2012) Implicit Differentiation of Parametric Equations (5-17-2014) A…
Past posts on differential equations Differential Equations (1-5-2015) The basics and definitions. Domain of a Differential Equation (4-7-2017) notes and examples on finding the domain of the solution of a differential equation. (Updated thru the 2018 exam.) Slope Fields (1-9-2015) Graphical solutions: The solution is lurking in the slope field. Euler’s Method (1-12-2015) Numerical solutions (BC…
It will soon be time to start reviewing for the AP Calculus Exams. So, it’s time to start planning your review. For the next weeks through the beginning of April I will be posting notes for reviewing. There are not new; versions have been posted for the last few years and these are only slightly…
This is an exploration based on the AP Calculus question 2018 AB 6. I originally posed it for teachers last summer. This will make, I hope, a good review of many of the concepts and techniques students have learned during the year. The exploration, which will take an hour or more, includes these topics: Finding…
More posts on differential equations Good Question 2: 2002 BC 5 (2-17-2015) A differential equation that cannot be solved by separating the variables is investigated anyway. Most of this question is AB material. A Family of Functions (2-21-2015) Further investigation of the general solution of the equation discussed above in Good Question 2. Most of…
Happy New Year ! A few more links to posts on accumulation. Painting a Point (2-4-2013) Paint often and the paint accumulates. Good Question 6: 2000 AB 4 (8-25-2015) Accumulation Good Question 8 – or not? (1-5-2016) Accumulation Density (1-10-2017) Accumulation and Differential Equations (2-1-2013) Solving differential equations without the “+C“ Review Notes: Type 1 Questions:…
The idea that the definite integral is an “accumulator” means that integrating a rate of change over an integral gives the net amount of change over the interval.Many of the application of integration are based on this idea. Here are some past posts on this idea. Accumulation An introductory activity to explore accumulation and the relationship…
One of the major applications of integration is to find the volumes of various solid figures. Volume of Solids with Regular Cross-sections This is where to start with volume problems. After all, solids of revolution are just a special case of solids with regular cross-sections. Volumes of Revolution Subtract the Hole from the Whole and…
So, you’ve finally proven the Fundamental Theorem of Calculus and have written on the board: And the students ask, “What good is that?” and “When are we ever going to use that?” Here’s your answer. There are two very important uses of this theorem. First, in words the theorem says that “the integral of a…
