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MATH 230

COURSE DESCRIPTION: Calculus and Vector Analysis (4:4:0) Three-
dimentional analytic geometry; vectors in space; partial
differention; double and triple integrals; integral vector
calculus.  Students who have passed either MATH 231 or 232 may
not schedule MATH 230 for credit.

PREREQUISITES: MATH 141.

TOPICS

THREE-DIMENSIONAL ANALYTIC GEOMETRY AND VECTORS
Three-Dimensional Coordinate Systems
Vectors
The Dot Product
The Cross Product
Equations of Lines and Planes
Vector Functions and Space Curves
Arc Length and Curvature
Motion in Space: Velocity and Acceleration
Cylindrical and Spherical Coordinates

PARTIAL DERIVATIVES
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes and Differentials
The Chain Rule
Directional Derivatives and the Gradient Vector
Maximum and Minimum Values
Lagrange Multipliers

MULTIPLE INTEGRALS
Double Integrals over Rectangles
Iterated Integrals
Double Integrals over General Regions
Double Integrals in Polar Coordinates
Applications of Double Integrals
Surface Area
Triple Integrals
Triple Integrals in Cylindrical and Spherical Coordinates
Change of Variables in Multiple Integrals

VECTOR CALCULUS
Vector Fields
Line Integrals
The Fundamental Theorem for Line Integrals
Green's Theorem
Curl and Divergence
Parametric Surfaces and Their Areas

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