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Introduction to Points in 3 Dimensional Space

Distance Formula and Equation of a Sphere in 3D With Examples

Distance from a Point to the y-axis in 3D Space.

Find a Unit Vector in the Same Direction as the Given Vector

Are the two Vectors Parallel? :: How to Determine if Vectors are Parallel

Magnitude and Angle of the Resultant Force :: Cartesian Components of Vectors

Find the Tension in Cables Attached to a Hanging Mass:: Vectors :: Static Equillibrium

Dot Product of Two Vectors

How to Find the Angle Between Two Vectors :: Why Cosine and Dot Product Explained

Find Unit Vector Perpendicular to Two Vectors :: Using Dot Product!

Find Force Needed to Supply 100 Nm of Torque

Acute Angle Between a Line and a Plane

Angle Between two Intersecting Lines :: 3D Vectors :: First Show Intersection

Planes Parallel, Orthogonal, or Neither, Angle Between Planes Approach

Find the Limit of a Vector Function

Vector Function for the Curve of Intersection of Two Surfaces

Derivative of a Vector Function

Derivative of the Vector Function :: r(t) = ta x (tb +t^2 c)

Find the Unit Tangent and Unit Normal Vectors

Integral of a Vector Function

Arc Length of the Curve :: Two Examples :: Calculus 3

Both Curvature Formulas Derivation :: Vector Calculus

Contour Plots || Contour Maps || Multivariable Functions || Calculus 3

Domain of Multivariable Functions || Two Examples!

Multivariable Limits Polar Coordinates

Multivariable Limits :: Show the Limit Does Not Exist :: TWO WAYS! :: Polar Coordinates

What The Heck are Partial Derivatives?? With Visualization, Examples and Clairaut's Theorem!!

Partial Derivative Examples Advanced (Including Derivative of an Integral)

Find the Linear Approximation of f(x,y) = 1-xycos(pi y) at the Point (1,1)

Use Differentials to Estimate the Amount of Metal in a Cylindrical Can

Use the Chain Rule to find the Partial Derivatives

Use the Chain Rule to Find the Partial Derivatives of z = tan(u/v), u-2s+3t, v=3s-2t

Find the Directional Derivative of f(x,y,z) = xy+yz+xz at (1,-1,3) in the direction of (2,4,5)

Find all points at which the direction of fastest change of the function is i+j

Local Extrema and Saddle Points of a Multivariable Function. 2nd Derivative Test

Use Lagrange Multipliers to Find the Maximum and Minimum Values of f(x,y) = x^3y^5

Midpoint Rule Double Integrals Using Level Curves!

Evaluate by Reversing the Order of Integration :: integral bounds include ln(x)!!

Double Integrals in Polar Coordinates

Graphing Polar Curves by Changing the Parameter

Double Integral to find Area Enclosed by a Cardioid r=2-2cos(t)

Find the Centroid of the Triangular Region Given the Vertices :: Double Integrals

Moments of Inertia :: Double Integrals :: Polar Coordinates

Evaluate by Changing to Cylindrical Coordinates :: 2 Ways!!!

Triple Integral to find Volume Cylindrical and Spherical Coordinates :: Inside Sphere Outside Cone

Evaluate By Changing to Spherical Coordinates :: Above Cone Between Two Spheres

Triple Integral in Spherical Coordinates to find Volume :: Under Sphere Between Two Cones.

Change of Variables in Multiple Integrals (Find the Jacobian)

Line Integrals of Scalar Functions: Evaluate Line Integrals : Contour Integrals

Line Integral of a Vector Field :: F(x,y,z) = sin(x) i + cos(y) j + xz k

Fundamental Theorem for Line Integrals :: Conservative Vector Field Line Integral

Green's Theorem Examples

Scalar Surface Integral ∫∫ x^2yz dS where S is part of the plane z=1+2x+3y

Scalar Surface Integral ∫∫xy dS, S is the triangular region (1,0,0), (0,2,0), (0,0,2)

Evaluate the Surface Integral over the Helicoid r(u,v) = ucos v i + usin v j + v k

Find the Flux of the Vector Field F = x i + y j + z^4 k Through the Cone with Downward Orientation

Use Stokes' Theorem to Evaluate the Surface Integral

Divergence Theorem:: Find the flux of F = ( cos(z) + xy^2, xexp(-z), sin(y)+x^2z )

Multivariable Limit Using the Definition

What Angle Equalizes Horiz. Range and Vertical Distance? || Projectile Motion

Description:

Explore advanced calculus concepts in this comprehensive 7-hour course covering multivariable functions, vector calculus, and integration techniques. Delve into 3D geometry, vector operations, partial derivatives, and multiple integrals. Master topics such as contour plots, directional derivatives, Lagrange multipliers, and line integrals. Learn to apply Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Gain practical skills in solving complex problems involving scalar and vector fields, surface integrals, and flux calculations. Enhance your understanding of mathematical concepts with real-world applications in physics and engineering.

Calculus 3

Jonathan Walters

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#Mathematics #Calculus #Algebra #Linear Algebra #Vectors #Partial Derivatives #Multivariable Calculus #Double Integrals #Surface Integrals #Multivariable Functions #Line Integrals #Triple Integrals

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