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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).

• 21:00, 11 April 2022 Wikiadmin talk contribs uploaded File:Radian.png
• 17:39, 11 April 2022 Wikiadmin talk contribs created page Radians (Created page with "One radian is the angle at which the arc's length of the circle is equal to its own radius. How many times does the radius fit into the circle's perimeter? Ans: <math>2\pi</math> times for a radius of one. That is ~6.28.... a real number. This ratio is the same for circles of any radius, it's a constant. If the perimeter of the circle with a radius of one is <math>2\pi</math> and one full turn is 360°, there is our conversion formula between radians and degrees. 180°,...")
• 23:59, 10 April 2022 Wikiadmin talk contribs uploaded a new version of File:Parametric line.png
• 23:05, 10 April 2022 Wikiadmin talk contribs deleted page File:Parametric circle.png (Deleted old revision 20220410230503!Parametric_circle.png)
• 23:05, 10 April 2022 Wikiadmin talk contribs uploaded a new version of File:Parametric circle.png
• 23:02, 10 April 2022 Wikiadmin talk contribs created page File:Parametric line.png
• 23:02, 10 April 2022 Wikiadmin talk contribs uploaded File:Parametric line.png
• 22:58, 10 April 2022 Wikiadmin talk contribs created page File:Parametric circle.png
• 22:58, 10 April 2022 Wikiadmin talk contribs uploaded File:Parametric circle.png
• 22:58, 10 April 2022 Wikiadmin talk contribs deleted page File:Parametric parabola.png (Deleted old revision 20220410212416!Parametric_parabola.png)
• 21:24, 10 April 2022 Wikiadmin talk contribs uploaded a new version of File:Parametric parabola.png
• 19:43, 10 April 2022 Wikiadmin talk contribs created page File:Parametric parabola.png
• 19:43, 10 April 2022 Wikiadmin talk contribs uploaded File:Parametric parabola.png
• 16:56, 8 April 2022 Wikiadmin talk contribs created page Derivative of inverse functions (Created page with "When we do a composition of a function and its inverse the result is that we do some operation, undo it with the reversed operation, which results in the output and the input being equal to each other. In mathematical notation: <math>f(f^{-1}(x)) = x</math>. For now we skip the conditions for which a function is invertible. To make the proof easier to read let's write <math>f^{-1}(x) = g(x)</math>: The rate of change of <math>x</math> is trivial, it's 1. If <math>\frac{...")
• 21:16, 7 April 2022 Wikiadmin talk contribs created page Change the base of a logarithm (Created page with "Logarithms are pretty natural when it comes to powers of two, powers of three and other common powers. If we have <math>2^x = 5</math> we know that <math>2^2 = 4</math> and that <math>2^3 = 8</math>. For <math>2 < x < 3</math> there must be some number such that raising 2 to that number yields exactly 5. The interesting property here is that we can also write <math>3^y = 5</math>, which means that the number 5 can be written as many different logs with different bases ea...")
• 23:06, 6 April 2022 Wikiadmin talk contribs created page File:Euler constant graph.png
• 23:06, 6 April 2022 Wikiadmin talk contribs uploaded File:Euler constant graph.png
• 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