Surface_integrals_Sec_9-13

Surface_integrals_Sec_9-13 - Surface Integrals and Stokes...

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1 Surface Integrals and Stokes’ Theorem ± This unit is based on Sections 9.13 and 9.14 , Chapter 9. ± All assigned readings and exercises are from the textbook ± Objectives : Make certain that you can define, and use in context, the terms, concepts and formulas listed below: evaluate integrals over a surface. find the surface area and mass of a surface. calculate the flux of a vector across a surface. verify Stokes’ theorem for particular examples of smooth surfaces with smooth bounding curves. solve line integral problems using Stokes’ theorem. ± Reading : Read Section 9.13 - 9.14, pages 524-538. ± Exercises : Complete problems
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2 Surface Integrals S surface a of area the integral double = = ∫∫ S dS curve a of length the = C ds ± The main difficulty is in expressing dS becomes ± When we go from curves to surfaces, the basic integral (length of a curve)
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3 Surface Integrals (Cont.) ± When the surface has only one z for each (x, y), it is the graph of a function z(x, y). In other cases S can twist and close up: a sphere
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Surface_integrals_Sec_9-13 - Surface Integrals and Stokes...

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