https://williewong.wordpress.com/2019/05/24/migration/2019-09-05T20:15:33+00:00monthlyhttps://williewong.wordpress.com/2019-09-05T20:12:59+00:00weekly0.6https://williewong.wordpress.com/2018/12/03/chromebook-adventure/2018-12-04T04:20:50+00:00monthlyhttps://williewong.wordpress.com/2017/09/27/heat-ball/https://williewong.files.wordpress.com/2017/09/heat-ball1.pngheat-ball1-dimensional heat balls centered at (0,5) for various radii. (Made using Desmos)2017-09-28T13:57:57+00:00monthlyhttps://williewong.wordpress.com/2017/06/30/texlive-on-android/2020-01-04T13:58:01+00:00monthlyhttps://williewong.wordpress.com/2017/06/07/workflow/2017-06-08T03:21:26+00:00monthlyhttps://williewong.wordpress.com/2017/05/02/in-defense-of-integration-by-parts/2017-07-02T03:33:42+00:00monthlyhttps://williewong.wordpress.com/2016/06/29/abusing-jabref-to-manage-snipplets-of-tex/2016-06-29T20:56:44+00:00monthlyhttps://williewong.wordpress.com/2016/02/05/gingko-and-proof-writing/2016-02-05T18:34:10+00:00monthlyhttps://williewong.wordpress.com/2015/06/05/riemann-generalized-riemann-and-darboux-stieltjes-integrals/2016-01-12T00:00:15+00:00monthlyhttps://williewong.wordpress.com/2012/07/24/using-ipython-notebook-for-manual-computations/https://williewong.files.wordpress.com/2012/07/screenshot-from-2012-07-24-150905.pngScreenshot from 2012-07-24 15:09:05Next we do some computations (manipulations of the expression). https://williewong.files.wordpress.com/2012/07/screenshot-from-2012-07-24-150545.pngScreenshot 1After loading the preamble in cell 1, we insert a math expression and display it. 2017-05-03T02:12:54+00:00monthlyhttps://williewong.wordpress.com/2012/07/27/ipython-notebook-take-2/2015-04-30T09:08:56+00:00monthlyhttps://williewong.wordpress.com/2015/04/08/an-optimization-problem-theme/https://williewong.files.wordpress.com/2015/04/optimization-rotation2.pngoptimization-rotation2The variation in the cost function for the blue and green lines, which differ by a a change of slope (rotation around the intersection point) is the signed area of the shaded region, where the sign is determined by whether the red curve is above or below it. https://williewong.files.wordpress.com/2015/04/optimization-translation2.pngoptimization-translation2The difference in cost function is the signed area of the shaded region, where the sign is whether the point is above or below the red curve. https://williewong.files.wordpress.com/2015/04/optimization-translation.pngoptimization-translationA zero-crossing approximant (solid green and blue) can always be improved (dashed green and blue) by changing the intercept. https://williewong.files.wordpress.com/2015/04/optimization-rotation.pngoptimization-rotationA single crossing approximant (solid blue) can always be improved (dashed blue) by changing the slope. 2015-04-10T08:24:42+00:00monthlyhttps://williewong.wordpress.com/2015/04/08/an-optimization-problem-variation/2015-04-08T14:39:23+00:00monthlyhttps://williewong.wordpress.com/enzh-math/2015-03-21T09:17:37+00:00weekly0.6https://williewong.wordpress.com/2015/03/21/so-i-will-be-living-in-michigan-for-the-next-few-years/2015-03-30T14:28:32+00:00monthlyhttps://williewong.wordpress.com/blog/2014-09-19T15:20:02+00:00weekly0.6https://williewong.wordpress.com/2013/12/04/automated-annotation-in-latex-using-ocg/2015-08-30T18:58:40+00:00monthlyhttps://williewong.wordpress.com/2013/06/04/products-and-expectation-values/2013-06-04T15:33:37+00:00monthlyhttps://williewong.wordpress.com/2013/02/07/decay-of-waves-iv-numerical-interlude/2013-02-07T10:28:04+00:00monthlyhttps://williewong.wordpress.com/2013/01/30/whats-wrong-with-tests/2013-01-30T12:08:07+00:00monthlyhttps://williewong.wordpress.com/2013/01/14/the-asymptotically-hyperboloidal-is-not-asymptotically-null/2013-07-18T18:43:10+00:00monthlyhttps://williewong.wordpress.com/2012/10/15/what-is-mathematical-literacy/2012-10-15T16:34:44+00:00monthlyhttps://williewong.wordpress.com/2010/10/28/shock-singularities-in-burgers-equation/https://williewong.files.wordpress.com/2010/10/graphics6.pngNo cusp. Quadratic behaviourhttps://williewong.files.wordpress.com/2010/10/graphics5.pngNegative third derivative cusphttps://williewong.files.wordpress.com/2010/10/graphics4.pngPositive 3rd derivative cusphttps://williewong.files.wordpress.com/2010/10/graphics3.pngClassic fan shapehttps://williewong.files.wordpress.com/2010/10/graphics2.pngShock formationhttps://williewong.files.wordpress.com/2010/10/graphics1.pngDivergent flowPlot of divergent flow. The red curve is the initial velocity distribution. The blue curves are the characterstic lines. 2014-11-20T09:43:00+00:00monthlyhttps://williewong.wordpress.com/2011/11/01/continuity-of-the-infimum/2014-05-07T13:40:19+00:00monthlyhttps://williewong.wordpress.com/2011/09/30/gauge-invariance-geometrically/2011-10-07T07:45:52+00:00monthlyhttps://williewong.wordpress.com/2011/08/30/extensions-of-covector-fields-to-tangent-bundles/2011-08-30T16:44:06+00:00monthlyhttps://williewong.wordpress.com/2011/06/09/decay-of-waves-iiib-tails-for-homogeneous-linear-equation-on-curved-background/https://williewong.files.wordpress.com/2011/06/illustration5.pngIllustration5Figure 52011-06-10T09:51:25+00:00monthlyhttps://williewong.wordpress.com/2011/05/16/decay-of-waves-iiia-nonlinear-tails-in-minkowski-space-redux/2011-05-16T11:27:46+00:00monthlyhttps://williewong.wordpress.com/2011/05/14/decay-of-waves-iib-minkowski-space-with-right-hand-side/https://williewong.files.wordpress.com/2011/05/illustration4.pngIllustration4Figure 4 (again)https://williewong.files.wordpress.com/2011/05/illustration3.pngIllustration3Figure 3https://williewong.files.wordpress.com/2011/05/illustration2.pngIllustration2Figure 22011-12-01T11:21:13+00:00monthlyhttps://williewong.wordpress.com/2011/05/12/decay-of-waves-iia-minkowski-background-homogeneous-case/https://williewong.files.wordpress.com/2011/05/illustration1.pngDomain of dependence 1+1Figure 12011-10-26T13:48:36+00:00monthlyhttps://williewong.wordpress.com/2011/05/05/decay-of-waves-i-introduction/2016-06-23T15:38:08+00:00monthlyhttps://williewong.wordpress.com/2010/11/24/why-do-volvox-spin/2010-11-30T21:58:26+00:00monthlyhttps://williewong.wordpress.com/2010/10/03/what-is-a-function-anyway/2015-02-14T05:55:45+00:00monthlyhttps://williewong.wordpress.com/2010/07/20/conways-base-13-function/2010-09-04T00:50:26+00:00monthlyhttps://williewong.wordpress.com/2010/04/19/why-learn-maths/2010-04-25T04:11:03+00:00monthlyhttps://williewong.wordpress.com/2010/04/02/arrows-impossibility-theorem/2010-04-02T19:21:53+00:00monthlyhttps://williewong.wordpress.com/2009/11/15/healthy-skepticism/2010-03-27T15:22:32+00:00monthlyhttps://williewong.wordpress.com/2010/03/18/compactness-part-1-degrees-of-freedom/2014-11-25T05:42:24+00:00monthlyhttps://williewong.wordpress.com/2010/03/16/minimal-blow-up-solution-to-an-inhomogeneous-nls/2010-03-16T18:09:38+00:00monthlyhttps://williewong.wordpress.com/2010/03/10/trip-to-oxford-a-little-lattice-problem/2010-03-10T11:00:00+00:00monthlyhttps://williewong.wordpress.com/2010/02/12/organizing-references/2011-06-15T21:52:03+00:00monthlyhttps://williewong.wordpress.com/2010/02/08/snowflakes/2010-02-08T15:16:23+00:00monthlyhttps://williewong.wordpress.com/2010/01/28/the-hoop-conjecture-of-kip-thorne-and-spherically-symmetric-space-times/2010-02-04T17:48:26+00:00monthlyhttps://williewong.wordpress.com/2009/11/25/digital-computing-and-catastrophic-failures/2009-11-25T14:16:59+00:00monthlyhttps://williewong.wordpress.com/2009/11/18/aharonov-bohm-effects-analogue-in-water-waves/2009-11-18T15:31:39+00:00monthlyhttps://williewong.wordpress.com/2009/11/17/no-hair-theorems/2010-02-27T11:58:02+00:00monthlyhttps://williewong.wordpress.com/2009/07/01/straightedge-and-compass-constructions/2010-06-13T01:01:51+00:00monthlyhttps://williewong.wordpress.comdaily1.02020-01-04T13:58:01+00:00