Peter Saveliev
  • Member for 3 years, 6 months
  • Last seen more than a month ago
What is the best way to intuitively explain the relationship between the derivative and the integral?
34 votes

You start by noticing that the Riemann sums (multiplication followed by addition) and the difference quotients (subtraction followed by division) undo each other. Their limits -- the integral and the ...

View answer
Iconic image to explain the fundamental theorem of calculus?
16 votes

This is about the Riemann sums but the logic is there.

View answer
How shall we teach math online?
3 votes

My home teaching setup. Still to be tested.

View answer
Is Calculus Necessary?
3 votes

The debate seems to be where it was 20 years ago. The reason is that most universities have a "generic" mathematics curriculum, so if the engineers need calculus as it is now, everyone will also get ...

View answer
The use of "$\therefore$" and "$\because$"
2 votes

The context isn't entirely clear so I'll assume this is about teaching. Then, I support Pedro's answer but also want to add that doing both verbal and symbolic versions may be a good idea. For example:...

View answer
Should I go over examples straight from the textbook in Calculus lectures?
2 votes

When I choose to closely follow the book, I use exercises as examples. For me, it's more work but also more freedom. Meanwhile, the students are exposed to both a polished presentation in the book and ...

View answer
The Riemann integral vs Lebesgue integral in several variables for advanced undergraduates
1 votes

The discussion seems to overlook this simple fact: the Lebesgue integral is not a generalization of and cannot serve as a substitute for the Riemann integral.

View answer
How can I motivate the formal definition of continuity?
1 votes

Property (3), i.e., the $\varepsilon-\delta$ definition of continuity, has numerous motivations/interpretations. For example, continuity can be interpreted as accuracy. Suppose we are shooting a ...

View answer
Easy tool to draw stencils
1 votes

Excel comes to mind. This took just a few seconds to make:

View answer
Should I describe the function $x \mapsto f(x_0) + f'(x_0)(x - x_0)$ as "linear" in a freshman calculus class?
1 votes

I think both "the linear approximation of $y=f(x)$ at $x=a$" and "local linear approximation" are fine. Now, it should be made clear that the linear approximation is a function. Next, what kind of ...

View answer
How to help new students accept function notation
0 votes

My answer would be: "What if there is no formula?" Just as $x$ might stand for an unspecified number, $f$ might stand for an unspecified function.

View answer
Vocabulary for giving just numbers, not a full answer
0 votes

"Your goal is to demonstrate that you understand this material."

View answer