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Combined display of all available logs of Applied Science. You can narrow down the view by selecting a log type, the username (case-sensitive), or the affected page (also case-sensitive).

• 18:00, 6 April 2022 Wikiadmin talk contribs created page Informal discussion of the Euler's constant (Created page with "I'm going to resort to the concept of the '''integral''' without the formalism. If you derive the '''natural log''' the result is the inverse of <math>x</math>. The other direction, if you calculate the '''area under the function's curve''' given by the inverse of <math>x</math> you get the natural log. The reason for this specific function <math>f(x) = 1/x</math> is that deriving logs in any base that isn't <math>e</math> yields <math>1/xb</math>, where <math>b \neq 1</...")
• 01:34, 5 April 2022 Wikiadmin talk contribs created page Derivative of logarithm and exponential (Created page with "<div style="text-align:center;"> <math>f(x) = \ln(x) \iff f'(x) = \frac{1}{x}</math> </div> I'm going to explain some property that is pretty simple and yet often overlooked. Let's write down a short sequence of logarithms in base 2: <math>\log_2{1} = 0</math><br /> <math>\log_2{2} = 1</math><br /> <math>\log_2{4} = 2</math><br /> <math>\log_2{8} = 3</math><br /> <math>\log_2{16} = 4</math><br /> Now the derivative can be defined in terms of a '''tangent''', a ratio '...")
• 17:15, 3 April 2022 Wikiadmin talk contribs deleted page File:Gradient vector graph.png
• 03:02, 2 April 2022 Wikiadmin talk contribs created page File:Gradient vector graph.png
• 03:02, 2 April 2022 Wikiadmin talk contribs uploaded File:Gradient vector graph.png
• 21:34, 1 April 2022 Wikiadmin talk contribs created page Defining the gradient (Created page with "To properly understand the '''gradient''' one is required to know vectors and the '''dot''' '''''(or scalar)''''' '''product'''. When we have color gradients what we see is that one extreme has one color and the other extreme another color, in between a gradient that is the transition between one color to the other. In physics there exists many types of gradients, such as gradients of temperature or pressure. Gradients are important because there are certain phenomena th...")
• 21:29, 1 April 2022 Wikiadmin talk contribs moved page Partial derivatives, directions and gradient to Partial derivatives and direction without leaving a redirect
• 03:16, 1 April 2022 Wikiadmin talk contribs created page File:Level curves nonconstant.png
• 03:16, 1 April 2022 Wikiadmin talk contribs uploaded File:Level curves nonconstant.png
• 02:59, 1 April 2022 Wikiadmin talk contribs created page File:Level curves constant.png
• 02:59, 1 April 2022 Wikiadmin talk contribs uploaded File:Level curves constant.png
• 00:31, 1 April 2022 Wikiadmin talk contribs deleted page File:Levelcurve isotherms.png (Deleted old revision 20220401003123!Levelcurve_isotherms.png)
• 00:31, 1 April 2022 Wikiadmin talk contribs uploaded a new version of File:Levelcurve isotherms.png
• 20:53, 31 March 2022 Wikiadmin talk contribs created page File:Level curves gradient.png
• 20:53, 31 March 2022 Wikiadmin talk contribs uploaded File:Level curves gradient.png
• 18:26, 30 March 2022 Wikiadmin talk contribs deleted page File:Partial derivative graph2.png (Deleted old revision 20220330182551!Partial_derivative_graph2.png)
• 18:25, 30 March 2022 Wikiadmin talk contribs uploaded a new version of File:Partial derivative graph2.png
• 18:22, 30 March 2022 Wikiadmin talk contribs created page File:Partial derivative graph2.png
• 18:22, 30 March 2022 Wikiadmin talk contribs uploaded File:Partial derivative graph2.png
• 03:28, 30 March 2022 Wikiadmin talk contribs moved page Defining the partial derivatives to Partial derivatives, directions and gradient without leaving a redirect
• 16:51, 29 March 2022 Wikiadmin talk contribs created page File:Partial derivative graph.png
• 16:51, 29 March 2022 Wikiadmin talk contribs uploaded File:Partial derivative graph.png
• 02:52, 29 March 2022 Wikiadmin talk contribs moved page Finding critical points of a function to Finding critical points of a single variable function without leaving a redirect
• 02:51, 29 March 2022 Wikiadmin talk contribs moved page Finding extreme values of a function to Finding extreme values of a single variable function without leaving a redirect
• 02:49, 29 March 2022 Wikiadmin talk contribs moved page Conditions for differentiability for many variables to Conditions for differentiability for a single variable without leaving a redirect
• 02:48, 29 March 2022 Wikiadmin talk contribs moved page Conditions for differentiability to Conditions for differentiability for many variables without leaving a redirect
• 02:35, 29 March 2022 Wikiadmin talk contribs created page Defining the partial derivatives (Created page with "The idea of partial derivatives is pretty similar to the regular derivative. The concept of a derivative is that of a rate of change. For multivariable functions we have to look for rates of change on a per variable basis. That's the meaning of ''"partial"''. A multivariable function can increase in one direction and decrease in another. It's impossible for a function to both increase and decrease in the same direction. With the axes being linearly independent from each...")
• 18:23, 28 March 2022 Wikiadmin talk contribs created page Mistakes regarding parametric curves (Created page with "* Sometimes people go on with rules without thinking and do this: <math>y = x^2 \to y(t) = t^2</math> and <math>x = \sqrt{y} \to x(t) = \sqrt{t}</math> which is to randomly do computations without knowing what it means. The graph of <math>(\sqrt{t}, \ t^2)</math> is half a parabola because of the square root and is also a distorted parabola because the horizontal coordinate does not have a constant rate of change.")
• 18:22, 28 March 2022 Wikiadmin talk contribs created page Mistakes regarding polar coordinates (Created page with "* The most common mistake is to confuse Cartesian with polar when plotting a graph. For example: everyone is familiar with '''(x, y)'''. Therefore a common mistake is to think that radius goes along '''x''' and angle is somewhere along '''y'''. Suppose we have (2, 45°). A clueless person thinks x = 2 and y = 45. I have to admit here that I made this mistake and more than once. I think that the origin of this mistake is, ironically, the fact that, a lot of times, polar c...")
• 04:17, 28 March 2022 Wikiadmin talk contribs created page L'Hospital rule (Created page with "One may naturally think that we can extend the rule to multivariable. We cannot do that because with multivariable functions we have partial derivatives, which represent rates of change on a per variable basis. We don't have an equivalent to the L'Hospítal rule for two or more variables.")
• 02:23, 28 March 2022 Wikiadmin talk contribs created page File:Critical points graph2.png
• 02:23, 28 March 2022 Wikiadmin talk contribs uploaded File:Critical points graph2.png
• 15:59, 25 March 2022 Wikiadmin talk contribs created page File:Critical points graph.png
• 15:59, 25 March 2022 Wikiadmin talk contribs uploaded File:Critical points graph.png
• 01:51, 25 March 2022 Wikiadmin talk contribs created page Finding critical points of a function (Created page with "This part continues from where maximum and minimum points of a function left off. Now we deal with the specific case of <math>f''(x) = 0</math>.")
• 16:55, 24 March 2022 Wikiadmin talk contribs created page File:Extreme values graph3.png
• 16:55, 24 March 2022 Wikiadmin talk contribs uploaded File:Extreme values graph3.png
• 19:10, 22 March 2022 Wikiadmin talk contribs created page Finding extreme values of a function (Created page with "If a function is continuous, its rate of change is non-constant and there are intervals in which it's crescent and others where it's decrescent, a natural conclusion is to expect the rate of change to be zero somewhere. <math>f'(x) = 0</math> is a necessary but insufficient condition for a point to be a maximum or a minimum. It's insufficient because there are points where <math>f'(x) = 0</math> and yet that point is neither a maximum nor a minimum. The same concept appl...")
• 04:21, 22 March 2022 Wikiadmin talk contribs created page Parametrization of curves (Created page with "I've never seen this on a textbook, but it's possible to think on the process of parametrization of curves in terms of projected shadows. Suppose you have a moving object describing some curve on the plane. If we could have a projection of its shadow over a wall, one projection for each axis, we could see the shadow moving in one dimension, right or left over a straight line. Now the shadow in each wall would move faster or slower depending on the object's trajectory. Th...")
• 23:07, 21 March 2022 Wikiadmin talk contribs created page File:Extreme values graph2.png
• 23:07, 21 March 2022 Wikiadmin talk contribs uploaded File:Extreme values graph2.png
• 18:27, 21 March 2022 Wikiadmin talk contribs created page File:Extreme values graph.png
• 18:27, 21 March 2022 Wikiadmin talk contribs uploaded File:Extreme values graph.png
• 03:19, 21 March 2022 Wikiadmin talk contribs created page Extreme values of a function (Created page with "If a function is not constant a natural question is whether the function has a maximum value or a minimum value. In calculus we aren't concerned with physical barriers such as temperature going below zero kelvin or speed going beyond the speed of light. The function can have points where the maximum or minimum is local or global. It's important to say that when the limit at a point results in infinity, that point cannot be a maximum or minimum because infinity is not a n...")
• 23:15, 19 March 2022 Wikiadmin talk contribs created page File:Increasing decreasing graph.png
• 23:15, 19 March 2022 Wikiadmin talk contribs uploaded File:Increasing decreasing graph.png
• 18:00, 19 March 2022 Wikiadmin talk contribs created page Increasing and decreasing functions (Created page with "At school we learn to identify crescent and decrescent intervals of functions by inspecting their respective graphs. If the teacher explains the rate of change we can have a better understanding of it. Else we are left with the argument that the graph shows the obvious and no further explanations. What we don't learn is that a derivative is a tool that we need to prove that the function is crescent or decrescent in a certain interval. Case 1 the tangent is positive, wit...")
• 03:29, 18 March 2022 Wikiadmin talk contribs deleted page File:Implicit differentiation folium.png (Deleted old revision 20220318032827!Implicit_differentiation_folium.png)
• 03:28, 18 March 2022 Wikiadmin talk contribs uploaded a new version of File:Implicit differentiation folium.png
• 02:40, 18 March 2022 Wikiadmin talk contribs created page File:Implicit differentiation folium.png