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### Slide_15

Course: MATH 1104, Spring 2008
School: National University of...
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Multivariable MA1104 Calculus Lecture 15 Dr KU Cheng Yeaw Monday March 16, 2009 Recap Last Lecture ... we finished our study on multiple integrations! Overview In this lecture, we begin a study on vector calculus. We first introduce vector fields. Unlike (scalar) functions of several variables, a vector field assigns a vector to a point in plane/space. we introduce line integrals over a curve in plane/space...

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National University of Singapore - MATH - 1104
MA1104 Multivariable Calculus Lecture 16Dr KU Cheng Yeaw Thursday March 19, 2009RecapLast Lecture . We introduced vector fields. An important examples is gradient vector field. We say that F is a conservative vector field if F is the gradient vector fi
National University of Singapore - MATH - 1104
MA1104 Multivariable Calculus Lecture 17Dr KU Cheng Yeaw Monday March 23, 2009RecapLast Lecture . we considered integral of a vector field. This type of line integrals appear frequently in physics. It turns out that the computation of this line integra
National University of Singapore - MATH - 1104
MA1104 Multivariable Calculus Lecture 18Dr KU Cheng Yeaw Thursday March 26, 2009RecapLast Lecture . we study Green's Theorem and see how to apply it to compute line integrals. Green's Theorem can be regarded as the counterpart of the Fundamental Theore
National University of Singapore - MATH - 1104
MA1104 Multivariable Calculus Lecture 19Dr KU Cheng Yeaw Monday March 30, 2009RecapLast lecture . we defined two operations (curl and divergence) that can be performed on vector fields. They have physical significance. We appreciate this physical inter
National University of Singapore - MATH - 1104
MA1104 Multivariable Calculus Lecture 20Dr KU Cheng Yeaw Thursday April 2, 2009RecapLast lecture . we defined the surface area of a general parametric surface we introduced surface integral of scalar field over a smooth curve. The main idea is to use p
National University of Singapore - MATH - 1104
MA1104 Multivariable Calculus Lecture 21Dr KU Cheng Yeaw Monday April 6, 2009RecapLast lecture . we defined surface integrals (flux) of vector fields F dS =S SF n dS. We can evaluate these integrals usingparametrization r(u, v) of the surface S we s
National University of Singapore - MATH - 1104
MA1104 Multivariable Calculus Lecture 22Dr KU Cheng Yeaw Thursday April 9, 2009RecapLast lecture . we proved the Divergence Theorem. we proved Stoke's TheoremOverviewIn this lecture . we shall see some examples using Stoke's Theorem.Stoke's Theorem
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