Calculus Three Lecture Notes

about calculus three
calculus three homework
vector functions
operations with vector functions
limits and continuity of vector functions
graphs of vector functions
vector differentiation
tangent vectors
smooth curves
derivative rules
vector integration
motion of an object
unit tangent and unit normal vectors
arc length function
curvature
functions of several variables
graphs of functions
polynomial functions
rational functions
level curves
level surfaces
limits of multivariate functions
continuity of multivariate functions
partial derivatives
higher order partial derivatives
tangent planes
total differential
linear approximation with multivariate functions
differentiability
chain rule with one independent parameter
chain rule with two independent parameters
chain rule with several independent parameters
directional derivatives
the gradient
the gradient and directional derivatives
steepest ascent and steepest descent
normal property of the gradient
tangent planes and normal lines
relative extrema
critical points
second partials test
absolute extrema
lagrange multipliers with one parameter
lagrange multipliers with two parameters
double integral over a rectanglular region
iterated integrals
volume interpretation
double integral over a more general region
area and volume as a double integral
double integrals in polar coordinates
surface area
surface area with parametrizations
triple integrals
triple integrals over z-simple regions
planar lamina
moments and center of mass
moments of inertia
probability density functions
triple integrals in cylinderical coordinates
triple integrals in spherical coordinates
jacobians
change of variables in double integrals
change of variables in triple integrals
vector fields
divergence and curl
conservative vector fields
line integrals
line integral of a vector field
work as a line integral
fundamental theorem of line integrals
independence of path
greens theorem
line integrals for areas
greens theorem for doubly-connected regions
vector functions quiz
differentiation and integration of vector functions quiz
tangent vectors - arc length - curvature quiz
functions of several variables quiz
limits and continuity quiz
partial derivatives quiz
tangent planes approximations and differentiability quiz
chain rules quiz
directional derivatives and the gradient quiz
extrema of functions of several variables quiz
lagrange multipliers quiz
double integrals over rectangular regions quiz
double integrals over more general regions quiz
double integrals in polar coordinates quiz
surface area quiz
triple integrals quiz
change of variables in multiple integrals quiz
vector fields quiz
line integrals quiz
fundamental theorem of line integrals quiz
greens theorem quiz
calculus 3 review 1
calculus 3 review 2
calculus 3 review 3
calculus 3 review 4
calculus 3 practice test 1
calculus 3 practice test 2
calculus 3 practice test 3
calculus 3 practice test 4
calculus 3 practice test 5

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Cite this as:
Calculus Three Lecture Notes
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/calculus-three-lecture-notes.html