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17 VECTOR CALCULUS VECTOR CALCULUS The main results of this chapter are all higher-dimensional versions of the Fundamental Theorem of Calculus (FTC). To help you remember them, we collect them here (without hypotheses) so that you can see more easily their essential similarity. VECTOR CALCULUS 17.10 Summary In this section, we will: Summarize the key theorems learned in this chapter. SUMMARY In each case, notice that: On the left side, we have an integral of a “derivative” over a region. The right side involves the values of the original function only on the boundary of the region. FTC b a F ' x dx F b F a FT FOR LINE INTEGRALS C f dr f r b f r a GREEN’S THEOREM Q P dA P dx Q dy D x y C STOKES’ THEOREM curl F d S F d r C S DIVERGENCE THEOREM div F dV F d S E S