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# MA 242 - Analytic Geometry and Calculus III

North Carolina State University,, Fall 2004 , Prof. Larry K. Norris

Updated On 02 Feb, 19

##### Overview

Cartesian Coordinates in space - Vectors - The Dot Product - The Cross Product - Equations of Lines and Planes - Vector Functions and Space Curves - Derivatives and Integrals of Vector Functions - Arc Length and Curvature - Motion in Space - Functions and surfaces - Functions of several variables - level curves of f(x,y)and level surfaces of f(x,y,z) - Limits and continuity of f(x,y) and f(x,y,z) - partial derivatives - differentiability of f(x,y) and f(x,y,z) - The Chain Rule - Directional derivatives and the gradient vector - optimization - Double Integrals over Rectangles - Iterated integrals - Double Integrals over general regions - Double integrals in polar coordinates - Applications of double integrals - Triple integrals in Cartesian coordinates - Cylindrical coordinates - Triple integrals in cylindrical coordinates

Spherical coordinates - Triple integrals in spherical coordinates - Vector Fields - Line integrals - Line integrals of functions along parameterized curves - Line integrals of vector fields along parameterized curves; The defintion of the work done by a force - The fundamental theorem for Line Integrals - Greens Theorem - Divergence and Curl - Parametric Surfaces - BEGIN MAPLE ASSIGNMENT - tangent planes to parametrized surfaces - Surface area of Parameterized Surfaces - Surface Integrals - surface integral of a function - surface integral of a vector field - Stokes Theorem - The Divergence Theorem -

## Lecture 49:

4.1 ( 11 )

###### Lecture Details

Continue with Section 13.6. Finish “surface integral of a function”
Begin “surface integral of a vector field”. NOTE A slide with the title “Line integral of Vector Fields” in this lecture. The title of that slide should be “Surface Integral of Vector fields”.

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