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Calculus 3: Vector Functions

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All Calculus 33D SpaceVector FunctionsDot and cross productEquations of lines and planesParametric curves, conic sectionsTangent vectors and arc lengthCylinders and quadric surfacesIntegrals of vector functionsArc length and curvatureMultivariable functionsSurface parameterizationPartial derivativesLinearization, chain rule, gradientTangent planes and linear approximationsOptimizationLagrange multipliersDouble integralsTriple integralsChanging coordinates for integrationSurface areaVector fields, divergence, and curlLine integralsGreen's TheoremFluxStokes' TheoremDivergence TheoremComplex numbers
Trig Substitution with Initial Condition Problem

dy/dt = 125+9t2\frac{1}{25 + 9t^2}, with initial condition y(53)=π30y\left(\frac{5}{3}\right) = \frac{\pi}{30}.

Vector FunctionsEasyVideo
Square of Vector Magnitude

Calculate the square of the magnitude of vector a=(2,3)\mathbf{a} = (2, 3).

Vector FunctionsEasyVideo
Magnitude Squared of a Vector

Find the magnitude squared of vector v=(−4,3)\mathbf{v} = (-4, 3).

Vector FunctionsEasyVideo
Derivative of a VectorValued Function

Find the derivative of the vector-valued function R(t)=(f(t),g(t),h(t))\mathbf{R}(t) = (f(t), g(t), h(t)) where ff, gg, and hh are scalar functions.

Vector FunctionsEasyVideoNeeds Attention