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

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• 14:52, 20 October 2021 Lila talk contribs created page VariationOfParameters2Ord (Created page with "In mathematics, '''variation of parameters''', also known as '''variation of constants''', is a general method to solve inhomogeneous differential equation|inhomogeneous...")
• 14:35, 20 October 2021 Lila talk contribs created page Extrema of a Function (Created page with "thumb|Local and global maxima and minima for cos(3π''x'')/''x'', 0.1≤'' x ''≤1.1 In mathematical analysis, the '''maxima''' and...")
• 14:24, 20 October 2021 Lila talk contribs created page Derivatives of Functions with Inverses (Created page with "File:Umkehrregel 2.png|thumb|right|250px|Rule:<br><math>{\color{CornflowerBlue}{f'}}(x) = \frac{1}{{\color{Salmon}{(f^{-1})'}}({\color{Blue}{f}}(x))}</math><br><br>Example f...")
• 14:22, 20 October 2021 Lila talk contribs created page The Derivative (Created page with "thumb|The [[graph of a function, drawn in black, and a tangent line to that graph, drawn in red. The slope of the tangent line is equa...")
• 14:04, 20 October 2021 Lila talk contribs created page Neighborhoods in 𝐑 (Created page with "<h1 id="toc0">The Real Number Line</h1> <p>One way to represent the real numbers <math>\mathbb{R}</math> is on the real number line as depicted below.</p> <div class="image-co...")
• 13:25, 20 October 2021 Lila talk contribs created page Real Function Limits:Infinite (Created page with "==Informal Infinite Limits== Another kind of limit involves looking at what happens to <math>f(x)</math> as <math>x</math> gets very big. For example, consider the function <m...")
• 13:19, 20 October 2021 Lila talk contribs created page Real Function Limits:One-Sided (Created page with "In calculus, a '''one-sided limit''' is either of the two limits of a function ''f''(''x'') of a real v...")
• 13:07, 20 October 2021 Lila talk contribs created page Divergence Criteria (Created page with "<h1 id="toc0">The Divergence Criteria for Sequences</h1> <p>Thus far we have looked at criteria for sequences to be convergent. We will now begin to look at some criteria whic...")
• 12:55, 20 October 2021 Lila talk contribs created page Monotone Functions (Created page with "right|thumb|Figure 1. A monotonically non-decreasing function. Image:Monotonicity example2.svg|right|thumb|Figure 2. A monotonically non-...")
• 12:24, 20 October 2021 Lila talk contribs created page The Continuous Extension Theorem (Created page with " ==Resources== * [http://mathonline.wikidot.com/the-continuous-extension-theorem The Continuous Extension Theorem], mathonline.wikidot.com")
• 11:22, 20 October 2021 Lila talk contribs created page Uniform Continuity (Created page with "File:Continuity and uniform continuity 2.gif|thumb|upright=1.5|The graph of <math>f(x)=\tfrac1x</math> escapes the top and/or bottom of the <math>\text{height}\times \text{w...")
• 11:20, 20 October 2021 Lila talk contribs created page Lipschitz Functions (Created page with "File:Lipschitz Visualisierung.gif|thumb|right|For a Lipschitz continuous function, there exists a double cone (white) whose origin can be moved along the graph so that the w...")
• 10:35, 20 October 2021 Lila talk contribs created page Sequences:Tails (Created page with "<h1 id="toc0">The Tail of a Sequence of Real Numbers</h1> <p>We will now look at an important aspect of a sequence known as the tail of a sequence.</p> <table class="wiki-cont...")
• 09:56, 20 October 2021 Lila talk contribs created page Sequences:Limits (Created page with "In mathematics, the '''limit of a sequence''' is the value that the terms of a sequence "tend to", and is often denoted using the <math>\lim</math> symbol (e.g., <math...")
• 09:16, 20 October 2021 Lila talk contribs created page Real Function Limits:Sequential Criterion (Created page with "The Sequential Criterion for a Limit of a Function We will now look at a very important theorem known as The Sequential Criterion for a Limit which merges the concept of the l...")
• 19:09, 19 October 2021 Lila talk contribs created page Cluster Points in 𝐑 (Created page with "In mathematics, a '''limit point''' (or '''cluster point''' or '''accumulation point''') of a set <math>S</math> in a topological space <math>X</math...")
• 18:55, 19 October 2021 Lila talk contribs created page Real Numbers:Bounded Subsets (Created page with "Image:Bounded unbounded.svg|right|thumb|An artist's impression of a bounded set (top) and of an unbounded set (bottom). The set at the bottom continues forever towards the r...")
• 18:28, 19 October 2021 Lila talk contribs created page Functions:Operations (Created page with "===Operations=== Functions obey many of the same operations as normal numbers. However, one key difference is the domain of the function, which may change depending on the ope...")
• 15:43, 19 October 2021 Khanh talk contribs created page Inverse Laplace Transform (Created page with " In mathematics, the '''inverse Laplace transform''' of a function ''F''(''s'') is the piecewise-continuous and exponentially-restricted real function ''f''(''t'') which has t...")
• 15:26, 19 October 2021 Lila talk contribs created page Real Numbers:Irrational (Created page with "right|thumb|240px|The number [[Square root of 2|{{radic|2}} is irrational.]] In mathematics, the '''irrational numbers''' (from in-...")
• 15:13, 19 October 2021 Lila talk contribs created page Real Numbers:Rational (Created page with "thumb|The rational numbers (<math>\mathbb{Q}</math>) are included in the [[real numbers (<math>\mathbb{R}</math>), while themselves including the [...")
• 14:50, 19 October 2021 Lila talk contribs created page Real Numbers:Suprema and Infima (Created page with "Image:Infimum illustration.svg|thumb|right|250px|A set <math>P</math> of real numbers (hollow and filled circles), a subset <math>S</math> of <math>P</math> (filled circles)...")
• 13:12, 19 October 2021 Lila talk contribs created page Real Numbers:Absolute Value (Created page with "== Absolute Values == ''Absolute Values'' represented using two vertical bars, <math>\vert</math>, are common in Algebra. They are meant to signify the number's distance from...")
• 13:01, 19 October 2021 Lila talk contribs created page Real Numbers:Inequalities (Created page with "== Definition of Inequalities == As opposed to an equation, an '''inequality''' is an expression that states that two quantities are unequal or not equivalent to one another....")
• 12:42, 19 October 2021 Lila talk contribs created page Sigma Notation (Created page with "Summation notation allows an expression that contains a sum to be expressed in a simple, compact manner. The uppercase Greek letter sigma, Σ, is used to denote the sum o...")
• 11:40, 19 October 2021 Lila talk contribs created page Extreme values on closed and bounded domains (Created page with "<blockquote style="background: white; border: 1px solid black; padding: 1em;"> '''Extreme Value Theorem:''' If ''f'' is a continuous function and closed on the interval [<mat...")
• 09:49, 19 October 2021 Lila talk contribs created page Gradients (Created page with "File:Gradient2.svg|thumb|300px|The gradient, represented by the blue arrows, denotes the direction of greatest change of a scalar function. The values of the function are re...")
• 13:17, 18 October 2021 Lila talk contribs moved page Intro to Polynomial Functions to Polynomial Functions
• 10:20, 18 October 2021 Lila talk contribs moved page Algebraic graphing technics to Algebraic graphing techniques (Misspelled title)
• 16:38, 17 October 2021 Khanh talk contribs created page Taylor's Theorem (Created page with "File:Taylorspolynomialexbig.svg|thumb|right|300px|The exponential function ''y'' = ''e''^''x'' (red) and the corresponding Taylor polynomial of degree fo...")
• 15:56, 17 October 2021 Khanh talk contribs created page L'Hospital's Rules (Created page with " File:Hopital sin x by -0.5x.png|thumb|upright=1.5|Example application of l'Hôpital's rule to f(x) = sin(x) and g(x) = −0.5x: the function h(x) = f(x)/g(x) is undefined a...")
• 14:50, 17 October 2021 Khanh talk contribs created page Abel’s Theorem (Created page with "In mathematics, '''Abel's theorem''' for power series relates a limit of a power series to the sum of its coefficients. It is named after Norwegian mathematician Niels Henrik...")
• 22:34, 16 October 2021 Khanh talk contribs created page Real Numbers:Intervals (Created page with " thumb|400px|The addition ''x'' + ''a'' on the number line. All numbers greater than ''x'' and less than ''x'' + ''a'' fall within that open interval....")
• 21:55, 16 October 2021 Khanh talk contribs created page Real Numbers:Archimedean Property (Created page with "thumb|250px|Illustration of the Archimedean property. In abstract algebra and analysis, the '''Archimedean property''', named after the anci...")
• 21:17, 16 October 2021 Khanh talk contribs created page Adjusting claims and hypothesis (Created page with "=='''Line Graphs'''== {| style="padding:2px; text-align:center; float:right;" | thumb|An example of a comparative line graph. |} Line grap...")
• 20:49, 16 October 2021 Khanh talk contribs created page Weighted moving average graphs continued (Created page with "== Calculating the Mean == The mean, or more precisely the arithmetic mean, is simply the arithmetic average of a group of numbers (or '''data set''') and is shown using -bar...")
• 15:59, 16 October 2021 Khanh talk contribs created page Part-to-part ratios & Part-to-whole ratios (Created page with "thumb|right|Pie chart of populations of English native speakers A '''pie chart''' (or a '''circle chart''') is a circular statistical graph...")
• 15:35, 16 October 2021 Khanh talk contribs created page Weighted moving average graphs (Created page with "thumb|Smoothing of a noisy sine (blue curve) with a moving average (red curve). In statistics, a '''moving average''' ('''...")
• 15:00, 16 October 2021 Khanh talk contribs created page Index numbers (Created page with "thumb|The ratio of width to height of standard-definition television In mathematics, a '''ratio''' indicates how many times one number contains a...")
• 17:46, 15 October 2021 Khanh talk contribs created page Time series model of exponential growth (Created page with "thumb|250px|Time series: random data plus trend, with best-fit line and different applied filters|alt=|right In mathematics, a '''time s...")
• 16:21, 15 October 2021 Khanh talk contribs created page Euler's Number (Created page with " File:hyperbola E.svg|thumb|237px|right|Graph of the equation {{Math|1=''y'' = 1/''x''}}. Here, {{mvar|e}} is the unique number larger than 1 that makes the shaded area equa...")
• 14:19, 15 October 2021 Lila talk contribs created page The Mean Value Theorem (Created page with "== Formal statement == File:Mittelwertsatz3.svg|thumb|The function <math>f</math> attains the slope of the secant between <math>a</math> and <math>b</math> as the derivative...")
• 13:34, 15 October 2021 Lila talk contribs created page Techniques for Finding Derivatives (Created page with "== Techniques of Differentiation == <p> The definition of a derivative, <math>f'(x)=\lim_{{\Delta}x\rightarrow 0} \frac{f(x+{\Delta}x)-f(x)}{{\Delta}x}</math> is not the only...")
• 12:42, 15 October 2021 Khanh talk contribs created page Proportionality vs. Linearity (Created page with " thumb|300x300px|The variable ''y'' is directly proportional to the variable ''x'' with proportionality constant ~0.6. File:Inverse propo...")
• 09:34, 15 October 2021 Lila talk contribs created page Multiple Integrals (Created page with "thumb|right|Integral as area between two curves. File:Volume under surface.png|right|thumb|Double integral as volume under a surface {{math...")
• 19:42, 14 October 2021 Khanh talk contribs created page Optimization Applications (Created page with " ==Introduction== Optimization is one of the uses of calculus in the real world. Perhaps we are a pizza parlor and wish to maximize profit. Perhaps we have a flat piece of car...")
• 16:10, 14 October 2021 Khanh talk contribs created page Absolute change (additive reasoning) & Relative change (multiplicative reasoning) (Created page with "=Measuring Errors= In this lesson we will learn how to quantify errors. Learning objectives * identify true and relative true errors * identify approximate and relative appro...")
• 15:57, 14 October 2021 Lila talk contribs created page Cauchy Problem (Created page with "A '''Cauchy problem''' in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain...")
• 15:20, 14 October 2021 Khanh talk contribs created page Continuous Growth (Created page with "File:Exponential.svg|thumb|300px|right|The graph illustrates how exponential growth (green) surpasses both linear (red) and cubic (blue) growth. {{legend|green|Exponential g...")
• 15:11, 14 October 2021 Lila talk contribs created page Theorem:Bolzano-Weierstrass (Created page with "===Theorem (Bolzano—Weierstrass)=== <blockquote style="background: white; border: 1px solid black; padding: 1em;">Every bounded sequence of real numbers contains a conve...")

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