{"id":10747,"date":"2020-03-25T11:18:12","date_gmt":"2020-03-25T11:18:12","guid":{"rendered":"http:\/\/blog.bachi.net\/?p=10747"},"modified":"2020-03-25T11:18:12","modified_gmt":"2020-03-25T11:18:12","slug":"khan-academy-youtube","status":"publish","type":"post","link":"https:\/\/blog.bachi.net\/?p=10747","title":{"rendered":"Khan Academy YouTube"},"content":{"rendered":"<h2>Multivariable calculus<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/playlist?list=PLSQl0a2vh4HC5feHa6Rc5c0wbRTx56nF7\">Multivariable calculus<\/a><\/p>\n<ul>\n<li>Multivariable functions | Multivariable calculus | <\/li>\n<li>Representing points in 3d | Multivariable calculus | <\/li>\n<li>Introduction to 3d graphs | Multivariable calculus | <\/li>\n<li>Interpreting graphs with slices | Multivariable calculus | <\/li>\n<li>Contour plots | Multivariable calculus | <\/li>\n<li>Parametric curves | Multivariable calculus | <\/li>\n<li>Parametric surfaces | Multivariable calculus | <\/li>\n<li>Vector fields, introduction | Multivariable calculus | <\/li>\n<li>Fluid flow and vector fields | Multivariable calculus | <\/li>\n<li>3d vector fields, introduction | Multivariable calculus | <\/li>\n<li>3d vector field example | Multivariable calculus | <\/li>\n<li>Transformations, part 1 | Multivariable calculus | <\/li>\n<li>Transformations, part 2 | Multivariable calculus | <\/li>\n<li>Transformations, part 3 | Multivariable calculus | <\/li>\n<li>Partial derivatives, introduction<\/li>\n<li>Partial derivatives and graphs<\/li>\n<li>Formal definition of partial derivatives<\/li>\n<li>Symmetry of second partial derivatives<\/li>\n<li>Gradient<\/li>\n<li>Gradient and graphs<\/li>\n<li>Directional derivative<\/li>\n<li>Directional derivative, formal definition<\/li>\n<li>Directional derivatives and slope<\/li>\n<li>Why the gradient is the direction of steepest ascent<\/li>\n<li>Gradient and contour maps<\/li>\n<li>Position vector valued functions | Multivariable Calculus | <\/li>\n<li>Derivative of a position vector valued function | Multivariable Calculus | <\/li>\n<li>Differential of a vector valued function | Multivariable Calculus | <\/li>\n<li>Vector valued function derivative example | Multivariable Calculus | <\/li>\n<li>Multivariable chain rule<\/li>\n<li>Multivariable chain rule intuition<\/li>\n<li>Vector form of the multivariable chain rule<\/li>\n<li>Multivariable chain rule and directional derivatives<\/li>\n<li>More formal treatment of multivariable chain rule<\/li>\n<li>Curvature intuition<\/li>\n<li>Curvature formula, part 1<\/li>\n<li>Curvature formula, part 2<\/li>\n<li>Curvature formula, part 3<\/li>\n<li>Curvature formula, part 4<\/li>\n<li>Curvature formula, part 5<\/li>\n<li>Curvature of a helix, part 1<\/li>\n<li>Curvature of a helix, part 2<\/li>\n<li>Curvature of a cycloid<\/li>\n<li>Computing the partial derivative of a vector-valued function<\/li>\n<li>Partial derivative of a parametric surface, part 1<\/li>\n<li>Partial derivative of a parametric surface, part 2<\/li>\n<li>Partial derivatives of vector fields<\/li>\n<li>Partial derivatives of vector fields, component by component<\/li>\n<li>Divergence intuition, part 1<\/li>\n<li>Divergence intuition, part 2<\/li>\n<li>Divergence formula, part 1<\/li>\n<li>Divergence formula, part 2<\/li>\n<li>Divergence example<\/li>\n<li>Divergence notation<\/li>\n<li>2d curl intuition<\/li>\n<li>2d curl formula<\/li>\n<li>2d curl example<\/li>\n<li>2d curl nuance<\/li>\n<li>Describing rotation in 3d with a vector<\/li>\n<li>3d curl intuition, part 1<\/li>\n<li>3d curl intuition, part 2<\/li>\n<li>3d curl formula, part 1<\/li>\n<li>3d curl formula, part 2<\/li>\n<li>3d curl computation example<\/li>\n<li>Laplacian intuition<\/li>\n<li>Laplacian computation example<\/li>\n<li>Explicit Laplacian formula<\/li>\n<li>Harmonic Functions<\/li>\n<li>Jacobian prerequisite knowledge<\/li>\n<li>Local linearity for a multivariable function<\/li>\n<li>The Jacobian matrix<\/li>\n<li>Computing a Jacobian matrix<\/li>\n<li>The Jacobian Determinant<\/li>\n<li>What is a tangent plane<\/li>\n<li>Controlling a plane in space<\/li>\n<li>Computing a tangent plane<\/li>\n<li>Local linearization<\/li>\n<li>What do quadratic approximations look like<\/li>\n<li>Quadratic approximation formula, part 1<\/li>\n<li>Quadratic approximation formula, part 2<\/li>\n<li>Quadratic approximation example<\/li>\n<li>The Hessian matrix<\/li>\n<li>Expressing a quadratic form with a matrix<\/li>\n<li>Vector form of multivariable quadratic approximation<\/li>\n<li>Multivariable maxima and minima<\/li>\n<li>Saddle points<\/li>\n<li>Warm up to the second partial derivative test<\/li>\n<li>Second partial derivative test<\/li>\n<li>Second partial derivative test intuition<\/li>\n<li>Second partial derivative test example, part 1<\/li>\n<li>Second partial derivative test example, part 2<\/li>\n<li>Constrained optimization introduction<\/li>\n<li>Lagrange multipliers, using tangency to solve constrained optimization<\/li>\n<li>Finishing the intro lagrange multiplier example<\/li>\n<li>Lagrange multiplier example, part 1<\/li>\n<li>Lagrange multiplier example, part 2<\/li>\n<li>The Lagrangian<\/li>\n<li>Meaning of Lagrange multiplier<\/li>\n<li>Proof for the meaning of Lagrange multipliers | Multivariable Calculus | <\/li>\n<li>Introduction to the line integral | Multivariable Calculus | <\/li>\n<li>Line integral example 1 | Line integrals and Green&#8217;s theorem | Multivariable Calculus | <\/li>\n<li>Line integral example 2 (part 1) | Multivariable Calculus | <\/li>\n<li>Line integral example 2 (part 2) | Multivariable Calculus | <\/li>\n<li>Line integrals and vector fields | Multivariable Calculus | <\/li>\n<li>Using a line integral to find the work done by a vector field example | <\/li>\n<li>Parametrization of a reverse path | <\/li>\n<li>Scalar field line integral independent of path direction | Multivariable Calculus | <\/li>\n<li>Vector field line integrals dependent on path direction | Multivariable Calculus | <\/li>\n<li>Path independence for line integrals | Multivariable Calculus | <\/li>\n<li>Closed curve line integrals of conservative vector fields | Multivariable Calculus | <\/li>\n<li>Example of closed line integral of conservative field | Multivariable Calculus | <\/li>\n<li>Second example of line integral of conservative vector field | Multivariable Calculus | <\/li>\n<li>Double integral 1 | Double and triple integrals | Multivariable Calculus | <\/li>\n<li>Double integrals 2 | Double and triple integrals | Multivariable Calculus | <\/li>\n<li>Double integrals 3 | Double and triple integrals | Multivariable Calculus | <\/li>\n<li>Double integrals 4 | Double and triple integrals | Multivariable Calculus | <\/li>\n<li>Double integrals 5 | Double and triple integrals | Multivariable Calculus | <\/li>\n<li>Double integrals 6 | Double and triple integrals | Multivariable Calculus | <\/li>\n<li>Triple integrals 1 | Double and triple integrals | Multivariable Calculus | <\/li>\n<li>Triple integrals 2 | Double and triple integrals | Multivariable Calculus | <\/li>\n<li>Triple integrals 3 | Double and triple integrals | Multivariable Calculus | <\/li>\n<li>Introduction to parametrizing a surface with two parameters | Multivariable Calculus | <\/li>\n<li>Determining a position vector-valued function for a parametrization of two parameters | <\/li>\n<li>Partial derivatives of vector-valued functions | Multivariable Calculus | <\/li>\n<li>Introduction to the surface integral | Multivariable Calculus | <\/li>\n<li>Example of calculating a surface integral part 1 | Multivariable Calculus | <\/li>\n<li>Example of calculating a surface integral part 2 | Multivariable Calculus | <\/li>\n<li>Example of calculating a surface integral part 3 | Multivariable Calculus | <\/li>\n<li>Surface integral example part 1: Parameterizing the unit sphere | <\/li>\n<li>Surface integral example part 2: Calculating the surface differential | <\/li>\n<li>Surface integral example part 3: The home stretch | Multivariable Calculus | <\/li>\n<li>Surface integral ex2 part 1: Parameterizing the surface | Multivariable Calculus | <\/li>\n<li>Surface integral ex2 part 2: Evaluating integral | Multivariable Calculus | <\/li>\n<li>Surface integral ex3 part 1: Parameterizing the outside surface | <\/li>\n<li>Surface integral ex3 part 2: Evaluating the outside surface | Multivariable Calculus | <\/li>\n<li>Surface integral ex3 part 3: Top surface | Multivariable Calculus | <\/li>\n<li>Surface integral ex3 part 4: Home stretch | Multivariable Calculus | <\/li>\n<li>Conceptual understanding of flux in three dimensions | Multivariable Calculus | <\/li>\n<li>Constructing a unit normal vector to a surface | Multivariable Calculus | <\/li>\n<li>Vector representation of a surface integral | Multivariable Calculus | <\/li>\n<li>Green&#8217;s theorem proof part 1 | Multivariable Calculus | <\/li>\n<li>Green&#8217;s theorem proof (part 2) | Multivariable Calculus | <\/li>\n<li>Green&#8217;s theorem example 1 | Multivariable Calculus | <\/li>\n<li>Green&#8217;s theorem example 2 | Multivariable Calculus | <\/li>\n<li>Constructing a unit normal vector to a curve | Multivariable Calculus | <\/li>\n<li>2D divergence theorem | Line integrals and Green&#8217;s theorem | Multivariable Calculus | <\/li>\n<li>Conceptual clarification for 2D divergence theorem | Multivariable Calculus | <\/li>\n<li>Stokes&#8217; theorem intuition | Multivariable Calculus | <\/li>\n<li>Green&#8217;s and Stokes&#8217; theorem relationship | Multivariable Calculus | <\/li>\n<li>Orienting boundary with surface | Multivariable Calculus | <\/li>\n<li>Orientation and stokes | Multivariable Calculus | <\/li>\n<li>Conditions for stokes theorem | Multivariable Calculus | <\/li>\n<li>Stokes example part 1 | Multivariable Calculus | <\/li>\n<li>Stokes example part 2: Parameterizing the surface | Multivariable Calculus | <\/li>\n<li>Stokes example part 3: Surface to double integral | Multivariable Calculus | <\/li>\n<li>Stokes example part 4: Curl and final answer | Multivariable Calculus | <\/li>\n<li>Evaluating line integral directly &#8211; part 1 | Multivariable Calculus | <\/li>\n<li>Evaluating line integral directly &#8211; part 2 | Multivariable Calculus | <\/li>\n<li>3D divergence theorem intuition | Divergence theorem | Multivariable Calculus | <\/li>\n<li>Divergence theorem example 1 | Divergence theorem | Multivariable Calculus | <\/li>\n<li>Stokes&#8217; theorem proof part 1 | Multivariable Calculus | <\/li>\n<li>Stokes&#8217; theorem proof part 2 | Multivariable Calculus | <\/li>\n<li>Stokes&#8217; theorem proof part 3 | Multivariable Calculus | <\/li>\n<li>Stokes&#8217; theorem proof part 4 | Multivariable Calculus | <\/li>\n<li>Stokes&#8217; theorem proof part 5 | Multivariable Calculus | <\/li>\n<li>Stokes&#8217; theorem proof part 6 | Multivariable Calculus | <\/li>\n<li>Stokes&#8217; theorem proof part 7 | Multivariable Calculus | <\/li>\n<li>Type I regions in three dimensions | Divergence theorem | Multivariable Calculus | <\/li>\n<li>Type II regions in three dimensions | Divergence theorem | Multivariable Calculus | <\/li>\n<li>Type III regions in three dimensions | Divergence theorem | Multivariable Calculus | <\/li>\n<li>Divergence theorem proof (part 1) | Divergence theorem | Multivariable Calculus | <\/li>\n<li>Divergence theorem proof (part 2) | Divergence theorem | Multivariable Calculus | <\/li>\n<li>Divergence theorem proof (part 3) | Divergence theorem | Multivariable Calculus | <\/li>\n<li>Divergence theorem proof (part 4) | Divergence theorem | Multivariable Calculus | <\/li>\n<li>Divergence theorem proof (part 5) | Divergence theorem | Multivariable Calculus | <\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Multivariable calculus Multivariable calculus Multivariable functions | Multivariable calculus | Representing points in 3d | Multivariable calculus | Introduction to 3d graphs | Multivariable calculus | Interpreting graphs with slices | Multivariable calculus | Contour plots | Multivariable calculus | Parametric curves | Multivariable calculus | Parametric surfaces | Multivariable calculus | Vector fields, introduction [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-10747","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/blog.bachi.net\/index.php?rest_route=\/wp\/v2\/posts\/10747","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.bachi.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.bachi.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.bachi.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.bachi.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10747"}],"version-history":[{"count":1,"href":"https:\/\/blog.bachi.net\/index.php?rest_route=\/wp\/v2\/posts\/10747\/revisions"}],"predecessor-version":[{"id":10748,"href":"https:\/\/blog.bachi.net\/index.php?rest_route=\/wp\/v2\/posts\/10747\/revisions\/10748"}],"wp:attachment":[{"href":"https:\/\/blog.bachi.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10747"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.bachi.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10747"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.bachi.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10747"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}