Derivatives can be treated like fractions in solving equations due to their representation as differentials, specifically in the context of the Chain Rule and integration. For example, the equation ##\frac{du}{dx} = 2## simplifies to ##du = 2dx##, illustrating this fractional treatment. However, caution is advised as certain manipulations, such as squaring derivatives, are invalid. The discussion highlights the importance of understanding the foundational concepts of calculus, including limits and differentials, to correctly apply these principles.
PREREQUISITESStudents of calculus, educators teaching calculus concepts, and anyone interested in the foundational principles of mathematical analysis.
I think that would not be wise. Engineers and applied mathematicians would probably be hurt by that.Dale said:In a calculus class I would teach only as much real analysis or sequences as is absolutely necessary to teach calculus. I think that is pretty minimal...
How?FactChecker said:I think that would not be wise. Engineers and applied mathematicians would probably be hurt by that.
Engineers and applied mathematicians need to be very experienced and comfortable with convergent sequences and series of all sorts.Dale said:How?