MA 242 - Analytic Geometry and Calculus III

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3 STUDENTS

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 – Green’s 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 – Stoke’s Theorem – The Divergence Theorem –

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