Multivariable calculus

Multivariable calculus

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Course Description

Thinking about multivariable function

Introduction to multivariable calculus

vector and matrices

visualizing scalar-valued function

visualizing multivariable function(articles)

Derivatives of multivariable functions

Partial derivatives
Gradient and directional derivatives
Partial derivative and gradient (articles)
Differentiating parametric curve
Multivariable chain rule
Partial derivative of vector -valued function
differentiating vector valued function (articles)
Divergence and  curl (article)

Applications of multivariable derivative

Tangent planes and local linearization
Quadratic approximations
Optimizing multivariable  function
Optimizing multivariable  function (article)
Lagrange multipliers and constrained Optimizing
Constrained Optimizing (article)

Integrating multivariable functions

Line integral for scalar function
Line integral in vector field
Line integral in vector field (article)
Double integral
Double integral (article)
Triple integral
change of variables
Polar ,spherical and cylindrical coordinate
Surface integral preliminaries
Surface integral
Surface integral (article)
Flux in 3D
Flux in 3D(article)

Green’s, Stokes’, and the divergence theorems

Formal definition of div and curl (optional reading)
Green ‘s theorem
Green ‘s theorem (articles)
2D  divergence theorem
Stokes’ theorem
Stokes’ theorem (article)
3D Divergence  theorem
Divergence  theorem (article)
Proof of Strokes’ theorem
Types of region in three dimensions
Divergence theorem proof


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