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Hi! START HERE: Course overview
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Plotting points in three dimensions
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Distance between points in three dimensions
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Center, radius, and equation of the sphere
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Describing a region in three-dimensional space
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Using inequalities to describe the region
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Sketching level curves of multivariable functions
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Vector and parametric equations of a line
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Parametric and symmetric equations of a line
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Symmetric equations of a line
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Parallel, intersecting, skew, and perpendicular lines
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Equation of a plane
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Intersection of a line and a plane
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Parallel, perpendicular and angle between planes
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Parametric equations for the line of intersection of two planes
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Symmetric equations for the line of intersection of two planes
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Distance between a point and a line
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Distance between a point and a plane
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Distance between parallel planes
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Reducing equations to standard form
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Sketching the surface
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Domain of a multivariable function
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Domain of a multivariable function, example 2
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Limit of a multivariable function
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Precise definition of the limit for multivariable functions
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Discontinuities of multivariable functions
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Compositions of multivariable functions
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Partial derivatives in two variables
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Partial derivatives in three or more variables
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Higher order partial derivatives
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Differential of a multivariable function
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Chain rule for multivariable functions
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Chain rule for multivariable functions, tree diagram
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Implicit differentiation for multivariable functions
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Directional derivatives in the direction of the vector
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Directional derivatives in the direction of the angle
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Linear approximation in two variables
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Linearization of a multivariable function
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Gradient vectors and the tangent plane
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Maximum rate of change and its direction
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Equation of the tangent plane
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Normal line to the surface
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Critical points
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Second derivative test
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Global extrema
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Extreme value theorem
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Extreme value theorem, example 2
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Maximum product of three real numbers
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Maximum volume of a rectangular box inscribed in a sphere
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Minimum distance from the point to the plane
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Points on the cone closest to the given point
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Two dimensions, one constraint
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Two dimensions, one constraint, example 2
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Three dimensions, one constraint
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Three dimensions, two constraints
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Approximating double integrals with rectangles
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Midpoint rule for double integrals
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Riemann sums for double integrals
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Average value
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Iterated integrals
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Double integrals
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Type I and II regions
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Finding surface area
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Finding volume
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Changing the order of integration
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Changing iterated integrals to polar coordinates
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Changing double integrals to polar coordinates
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Sketching area
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Finding area
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Finding volume
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Double integrals to find mass and center of mass
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Midpoint rule for triple integrals
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Iterated integrals
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Triple integrals
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Average value
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Finding volume
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Expressing the integral six ways
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Cylindrical coordinates
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Changing triple integrals to cylindrical coordinates
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Finding volume
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Spherical coordinates
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Changing triple integrals to spherical coordinates
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Finding volume
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Jacobian for two variables
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Jacobian for three variables
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Triple integrals to find mass and center of mass
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Moments of inertia
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Vector from two points
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Combinations of vectors
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Sum of two vectors
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Copying vectors and using them to find combinations
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Unit vector in the direction of the given vector
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Angle between a vector and the x-axis
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Magnitude and angle of the resultant force
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Dot product of two vectors
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Angle between two vectors
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Orthogonal, parallel or neither
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Acute angle between the lines
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Acute angles between the curves
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Direction cosines and direction angles
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Scalar equation of a line
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Scalar equation of a plane
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Scalar and vector projections
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Cross product of two vectors
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Vector orthogonal to the plane
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Volume of the parallelepiped from vectors
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Volume of the parallelepiped from adjacent edges
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Scalar triple product to prove vectors are coplanar
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Domain of a vector function
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Limit of a vector function
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Sketching the vector equation
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Projections of the curve
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Vector and parametric equations of a line segment
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Vector function for the curve of intersection of two surfaces
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Derivative of a vector function
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Unit tangent vector
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Parametric equations of the tangent line
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Integral of a vector function
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Arc length of a vector function
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Reparametrizing the curve
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Unit tangent and unit normal vectors
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Curvature
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Maximum curvature
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Normal and osculating planes
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Velocity and acceleration vectors
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Velocity, acceleration and speed, given position
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Velocity and position given acceleration and initial conditions
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Tangential and normal components of acceleration
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Line integral of a curve
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Line integral of a vector function
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Potential function of a conservative vector field
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Potential function of a conservative vector field to evaluate a line integral
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Independence of path
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Work done by the force field
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Open, connected, and simply-connected
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Green's theorem for one region
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Green's theorem for two regions
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Curl and divergence of a vector field
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Potential function of a conservative vector field, three dimensions
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Points on the surface
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Surface of the vector equation
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Parametric representation of the surface
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Tangent plane to the parametric surface
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Area of a surface
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Surface integrals
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Surface integrals, example 2
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Stokes' theorem
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Divergence theorem
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Separable differential equations
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Change of variable for separable differential equations
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Separable differential equations initial value problems
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Population growth
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Predator-prey systems
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Exact differential equations
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Linear differential equations
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Linear differential equations initial value problems
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Homogeneous distinct real roots
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Homogeneous equal real roots
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Homogeneous complex conjugate roots
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Homogeneous initial value problems
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Homogeneous initial value problems, example 2
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Homogeneous initial value problems, example 3
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Homogeneous initial value problems, example 4
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Undetermined coefficients
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Variation of parameters, system of equations
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Nonhomogeneous initial value problems
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Laplace transforms using the table
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Laplace transforms using the definition
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Laplace transforms and initial value problems
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Inverse Laplace transforms
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Wrap-up
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