Teaching Calculus
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The pleasure lies not in discovering the truth, but in searching for it. This is a blog for high school calculus teachers and students. After many years of teaching, I have been fortunate enough to spend the last 30 some years working with calculus teachers around the country. If you are a calculus teacher or student, I hope the things I've learned and shared will be of use to you and..
Teaching Calculus
3w ago
For several years now, I’ve been posting a series of notes on reviewing for the AP Calculus Exams. The questions on the AP Calculus exams, both multiple-choice and free response, fall into ten types. I’ve published posts on each. The ..read more
Teaching Calculus
1M ago
The reason you review is TO MAKE MISTAKES! When you’re reviewing for the AP Calculus exams your goal is to make mistakes. Why make mistakes? Easy: to find out what you’re doing wrong so you can fix it. And to ..read more
Teaching Calculus
1M ago
A large amount of time in Unit 10 is devoted to convergence tests. These tests tell you under what conditions a series will converge, when the infinite sum will approach a finite number. The tests are really theorems. As with ..read more
Teaching Calculus
2M ago
The polynomial function approximates the value of correct to 5 decimal places: This is not a fluke! Now, approximating the value of a sine function is easier with a calculator. But sines are not the only functions in Math World ..read more
Teaching Calculus
2M ago
The Cartesian coordinate system, the one you’ve been using up to now, is not the only way to find your way around the plane. In the Cartesian system, every point has two coordinates representing its distance and direction from the ..read more
Teaching Calculus
3M ago
I guess the obvious answer is so you will have something to use your new knowledge of the definite integral on. This unit is a collection of the first applications. There are many more. The whole idea is based on ..read more
Teaching Calculus
3M ago
Differential equations are equations that include derivatives. Their solution is not a number, but rather a function which along with its derivative(s) satisfies the equation. That is, when the function and its derivative(s) are substituted into the differential equation the ..read more
Teaching Calculus
4M ago
Antiderivatives are needed to evaluate definite integrals. The next thing to consider is how to find antiderivatives. Each of the formulas you learned for finding a derivative may be reversed to find antiderivatives. For example, since , it follows that ..read more
Teaching Calculus
4M ago
The Fundamental Theorem of Calculus is, well, fundamental. It relates the derivative and the integral. Writing a Riemann sum with all that fancy notation is tedious. To speed things up a special notation is used to replace it. The limit ..read more
Teaching Calculus
4M ago
You are now ready to move into the study of integration, the other “half” of calculus. To integrate is defined as “to bring together or incorporate parts into a whole” (Dictionary.com). The initial problem in integral calculus is to find ..read more