1057 15 Vector Analysis In Chapter 15, you will combine your knowledge of vectors with your knowledge of integral calculus. Section 15.1 introduces vector fields, such as those shown above. Examples of vector fields include velocity fields, electromagnetic...
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1057 15 Vector Analysis In Chapter 15, you will combine your knowledge of vectors with your knowledge of integral calculus. Section 15.1 introduces vector fields, such as those shown above. Examples of vector fields include velocity fields, electromagnetic fields, and gravitational fields. NASA In this chapter, you will study vector fields, line integrals, and surface integrals. You will learn to use these to determine real-life quantities such as surface area, mass, flux, work, and energy. In this chapter, you should learn the following. ■ How to sketch a vector field, determine whether a vector field is conservative, find a potential function, find curl, and find divergence. (15.1) ■ How to find a piecewise smooth parametrization, write and evaluate a line integral, and use Green’s Theorem. (15.2, 15.4) ■ How to use the Fundamental Theorem of Line Integrals, independence of path, and conservation of energy. (15.3) ■ How to sketch a parametric surface, find a set of parametric equatio
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