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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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• 16:53, 25 October 2021 Lila talk contribs created page Exact Differential Equations (Created page with "==Definition== Given a simply connected and open subset ''D'' of '''R'''² and two functions ''I'' and ''J'' which are continuous on ''D'', an implicit first-order o...")
• 14:28, 25 October 2021 Lila talk contribs created page Metric Spaces (Created page with "In mathematics, a '''metric space''' is a set together with a metric on the set. The metric is a function (math...")
• 14:26, 25 October 2021 Lila talk contribs created page Distance Functions, Metrics (Created page with "thumb|200px|An illustration comparing the [[Taxicab geometry|taxicab metric to the Euclidean metric on the plane: According to the taxicab metr...")
• 14:22, 25 October 2021 Lila talk contribs created page Topological Spaces (Created page with "In mathematics, a '''topological space''' is, roughly speaking, a geometrical space in which ''closeness'' is defined but cannot n...")
• 14:19, 25 October 2021 Lila talk contribs created page Heine-Borel Theorem (Created page with "In real analysis the '''Heine–Borel theorem''', named after Eduard Heine and Émile Borel, states: For a subset ''S'' of Euclidean space '''R'''<sup>''n...")
• 14:05, 25 October 2021 Lila talk contribs created page Algebraic Structure of the Real Numbers (Created page with "In mathematics, a '''real number''' is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity th...")
• 13:58, 25 October 2021 Lila talk contribs created page Closed Subsets in Higher Dimensions (Created page with "In geometry, topology, and related branches of mathematics, a '''closed set''' is a set whose complement is an ...")
• 13:56, 25 October 2021 Lila talk contribs moved page Open Subsets in Higher Dimensions to Open Subsets
• 13:54, 25 October 2021 Lila talk contribs created page Open Subsets in Higher Dimensions (Created page with "right|thumb|Example: The blue [[circle represents the set of points (''x'', ''y'') satisfying {{math|1=''x''² + ''y''² = ''r...")
• 13:52, 25 October 2021 Lila talk contribs created page Limit Points (or Cluster Points) in Higher Dimensions (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...")
• 13:49, 25 October 2021 Lila talk contribs moved page Distance Between Two Points in the Real Numbers to Distance Between Two Points
• 13:47, 25 October 2021 Lila talk contribs created page The Nested Interval Theorem for the Real Numbers (Created page with "thumb|400px|4 members of a sequence of nested intervals In mathematics, a sequence of '''nested intervals''' is understood as a...")
• 13:41, 25 October 2021 Lila talk contribs created page Limit of a sequence in the Real Numbers (Created page with "File:Archimedes pi.svg|350px|right|thumb|alt=diagram of a hexagon and pentagon circumscribed outside a circle|The sequence given by the perimeters of regular ''n''-sided [[p...")
• 13:38, 25 October 2021 Lila talk contribs created page Distance Between Two Points in the Real Numbers (Created page with "thumb|upright=1.35|Using the Pythagorean theorem to compute two-dimensional Euclidean distance In mathematics, the '''Euclidean distance...")
• 13:34, 25 October 2021 Lila talk contribs created page Cauchy-Schwarz Formula (Created page with "The '''Cauchy–Schwarz inequality''' (also called '''Cauchy–Bunyakovsky-Schwarz inequality''')<ref>{{cite web|url=https://mathshistory.st-andrews.ac.uk/Biographies/Schwarz/...")
• 12:19, 25 October 2021 Lila talk contribs created page The Fundamental Theorem (Created page with "The '''fundamental theorem of calculus''' is a theorem that links the concept of differentiating a function (calculating the grad...")
• 11:27, 25 October 2021 Lila talk contribs created page The Darboux Integral (Created page with "In real analysis, a branch of mathematics, the '''Darboux integral''' is constructed using '''Darboux sums''' and is one possible definition of the integral of a [...")
• 11:23, 25 October 2021 Lila talk contribs created page The Riemann Integral (Created page with "== Licensing == Content obtained and/or adapted from: * [http://mathonline.wikidot.com/riemann-stieltjes-integrals Riemann-Stieltjes Integrals from mathonline.wikidot.com] un...")
• 13:07, 22 October 2021 Lila talk contribs created page Relative Extrema and Convex Functions (Created page with " http://mathonline.wikidot.com/convex-and-concave-functions")
• 13:06, 22 October 2021 Lila talk contribs created page Newton's Method (Created page with "In numerical analysis, '''Newton's method''', also known as the '''Newton–Raphson method''', named after Isaac Newton and Joseph Raphson, is a root-finding alg...")
• 09:29, 22 October 2021 Lila talk contribs created page Linear Differential Equations (Created page with "In mathematics, a '''linear differential equation''' is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives,...")
• 09:08, 22 October 2021 Lila talk contribs created page Homogeneous Differential Equations (Created page with "A differential equation can be '''homogeneous''' in either of two respects. A first order differential equation is said to be homogeneous if it may be written :<math...")
• 16:11, 21 October 2021 Khanh talk contribs created page Variation Of Parameters (2nd Order) (Created page with "In mathematics, '''variation of parameters''', also known as '''variation of constants''', is a general method to solve inhomogeneous linear ordinary differential equations....")
• 15:11, 21 October 2021 Lila talk contribs created page The Limit Theorems for Functions (Created page with "<h1 id="toc0">The Uniqueness of Limits of a Function Theorem</h1> <p>Recall from <a href="/the-limit-of-a-function">The Limit of a Function</a> page that for a function <math>...")
• 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...")

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