{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='3.1 Linearization PROOF | Nonlinear Dynamics' data-url='/boclips/videos/648911b8367b025363a6c127' data-video-url='/boclips/videos/648911b8367b025363a6c127' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\n3.1 Linearization PROOF | Nonlinear Dynamics\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30360345\" href=\"/search?publisher_ids%5B%5D=30360345\"\u003eVirtually Passed\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eNonlinear Dynamics mini-series Part 1: • 1.0 A better way ... Part 2: • 2.0 A better way ... Part 3: • 3.0 A better way ... This video shows a formal proof behind linearization for 2D flows: dx/dt = f(x,y) dy/dt = g(x,y) Step 1: Find...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eNonlinear Dynamics mini-series Part 1: • 1.0 A better way ... Part 2: • 2.0 A better way ... Part 3: • 3.0 A better way ... This video shows a formal proof behind linearization for 2D flows: dx/dt = f(x,y) dy/dt = g(x,y) Step 1: Find fixed points. This involves solving for where dx/dt and dy/dt both are equal to 0. Step 2: Approximate f(x,y) and g(x,y) as linear functions at these fixed points. This results in the matrix equation: d/dt X = [A] X. The matrix [A] will contain partial derivatives of f and g. The matrix [A] is also known as the jacobian matrix. 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