These notes are written for a one-semester calculus path which meets thrice per week and is, ideally, supported via a working laptop or computer lab. The path is designed for all times technology majors who've a precalculus history, and whose basic curiosity lies within the purposes of calculus. we attempt to target these themes that are of maximum value to them and use existence technological know-how examples to demonstrate them. whilst, we attempt of remain mathematically coherent with no changing into technical. To make this possible, we're prepared to sacrifice generality. there's much less of an emphasis on through hand calculations. as an alternative, extra advanced and critical difficulties locate their position in a working laptop or computer lab. during this feel, we're attempting to undertake a number of principles from calculus reform. between them is a extra visible and no more analytic process. We commonly discover new rules in examples sooner than we supply formal definitions.
In yet one more approach we go away extensively from the normal method of calculus. We introduce differentiability as an area estate with out utilizing limits. The philosophy in the back of this concept is that limits are the an enormous stumbling block for many scholars who see calculus for the 1st time, they usually take in a considerable a part of the 1st semester. notwithstanding mathematically rigorous, our method of the spinoff makes no need of limits, permitting the scholars to get fast and with no unresolved difficulties to this idea. it really is real that our definition is extra restrictive than the standard one, and less features are differentiable during this manuscript than in a regular textual content. however the capabilities which we don't realize as being differentiable aren't rather very important for college students who will take just one semester of calculus. moreover, in our opinion the underlying geometric notion of the spinoff is no less than as transparent in our procedure because it is within the one utilizing limits.
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Calculus Without Limits