VECTOR CALCULUS 17. 2 VECTOR CALCULUS The main results of this chapter are all higher-dimensional versions of the Fundamental Theorem of Calculus (FTC).

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VECTOR CALCULUS 17

2 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.

Summary In this section, we will: Summarize the key theorems learned in this chapter. VECTOR CALCULUS

4 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.

5 FTC p. 1141

6 FT FOR LINE INTEGRALS p. 1141

7 GREEN’S THEOREM p. 1141

8 STOKES’ THEOREM p. 1141

9 DIVERGENCE THEOREM p. 1141