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Calculus 3

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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
Describing Particle Path with Vector Valued Functions

Describe the path of a particle in three-dimensional space using vector valued functions.

Vector FunctionsMediumVideoNeeds Attention
Vector Valued Functions in R3

Give an example of a vector-valued function r(t) and determine its domain and range in R3R^3.

Vector FunctionsMediumVideoNeeds Attention
Calculating Volume with Double integrals

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Double integralsMediumVideoNeeds Attention
Calculating Volume with Double integrals2

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Double integralsMediumVideoNeeds Attention
Reversing Order of Integration with Rational Functions

Given an iterated integral with a function having y5+1y^5 + 1 in the denominator, reverse the order of integration to simplify the integral.

Double integralsMediumVideoNeeds Attention
Solving Double integrals Using the Fundamental Theorem of Calculus

Solve a double integral problem using the Fundamental Theorem of Calculus.

Double integralsMediumVideoNeeds Attention
Calculating Volume with Double integrals23

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Double integralsMediumVideoNeeds Attention
Reversing Order of Integration with Rational Functions2

Given an iterated integral with a function having y5+1y^5 + 1 in the denominator, reverse the order of integration to simplify the integral.

Double integralsMediumVideoNeeds Attention
Solving Double integrals Using the Fundamental Theorem of Calculus2

Solve a double integral problem using the Fundamental Theorem of Calculus.

Double integralsMediumVideoNeeds Attention
Calculating Volume with Double integrals234

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Double integralsMediumVideoNeeds Attention
Reversing Order of Integration with Rational Functions23

Given an iterated integral with a function having y5+1y^5 + 1 in the denominator, reverse the order of integration to simplify the integral.

Double integralsMediumVideoNeeds Attention
Solving Double integrals Using the Fundamental Theorem of Calculus23

Solve a double integral problem using the Fundamental Theorem of Calculus.

Double integralsMediumVideoNeeds Attention
Calculating Volume with Double integrals2345

Using the double integral method, find the volume of the given surface projected onto the xy-plane over a specified rectangular region.

Double integralsMediumVideoNeeds Attention
Reversing Order of Integration with Rational Functions234

Given an iterated integral with a function having y5+1y^5 + 1 in the denominator, reverse the order of integration to simplify the integral.

Double integralsMediumVideoNeeds Attention
Solving Double integrals Using the Fundamental Theorem of Calculus234

Solve a double integral problem using the Fundamental Theorem of Calculus.

Double integralsMediumVideoNeeds Attention
Solving Double integrals Over Specified Domains

Solve a double integral problem involving a function of two variables over a specified domain.

Double integralsMediumVideoNeeds Attention
Transforming Integrals via Change of Variables and Jacobians

Perform a change of variables to transform the integral of a function over a region into an integral over a new coordinate system, using the Jacobian for a scaling factor.

Changing coordinates for integrationMediumVideoNeeds Attention
Triple Integral in Spherical Coordinates

Calculate the triple integral of the given region using spherical coordinates, where the region is bounded by a cone and a sphere.

Triple integralsMediumVideoNeeds Attention
Compute the Curl of a Vector Field

Compute the curl of a given vector field F⃗\vec{F}.

Vector fields, divergence, and curlMediumVideoNeeds Attention
Solving Vector Field Problems with Div Grad and Curl

Using the div, grad, and curl operators, solve a problem involving vector fields and partial differential equations.

Vector fields, divergence, and curlMediumVideoNeeds Attention