Differentiation and Integration
In this chapter, we examine the mathematical foundations of differentiation and integration. The theorems of this chapter are useful not only to make calculus work but also for studying functions in many other contexts.We do not spend any time on the important applications that typically appear in courses devoted to calculus, such as optimization problems. Rather we will highlight those aspects that either depend on or apply to results in real analysis.
Since we assume that the reader has already seen calculus, we dive right in with key definitions, assuming that the motivating examples are familiar.
KeywordsDifferentiable Function Product Rule Tangent Line Fundamental Theorem Chain Rule
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