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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 50:

4.1 ( 11 )

###### Lecture Details

Review day for Test #4. Contains a number of worked examples.
Test #4 will cover the material in all sections of chapter 13 except sections 13.7 and 13.8 (which will be covered later). Morever, the test includes the materials in section 10.5 (Parameterized surfaces), pg. 787-788 (tangent planes to parameterized surfaces) and secton 12.6 (surface area of paramterized surfaces). This material is covered in DVD Lectures #37 - #49 (exclude #40). Lecture #50 is the Review day for Test #4.

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