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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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• 13:20, 9 November 2021 Lila talk contribs created page The Cartiesian Product (Created page with "File:Cartesian Product qtl1.svg|thumb|Cartesian product <math>\scriptstyle A \times B</math> of the sets <math>\scriptstyle A=\{x,y,z\}</math> and <math>\scriptstyle B=\{1,2...")
• 15:36, 8 November 2021 Lila talk contribs created page Compactness in Metric Spaces (Created page with "=== Compact Sets in a Metric Space === <p> If <span class="math-inline"><math>(M, d)</math></span> is a metric space and <span class="math-inline"><math>S \subseteq M</math></...")
• 15:26, 8 November 2021 Lila talk contribs created page Complete Metric Spaces (Created page with "<h1 id="toc0"><span>Complete Metric Spaces</span></h1> <p>Recall that a sequence <span class="math-inline"><math>(x_n)_{n=1}^{\infty}</math></span> in <span class="math-inline...")
• 14:31, 8 November 2021 Lila talk contribs created page Baire's Theorem and Applications (Created page with "<h1 id="toc0"><span>The Baire Category Theorem</span></h1> <blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td><strong>Lemma 1:</strong> Let <sp...")
• 12:40, 8 November 2021 Lila talk contribs created page Stone-Weierstrass Theorem (Created page with "The '''Weierstrass approximation theorem''' states that every continuous function defined on a closed interval {{math|[''a'', ''b'']}} can be uniformly approximated as closely...")
• 11:53, 8 November 2021 Lila talk contribs created page Separable Metric Spaces (Created page with "===Dense Sets in a Metric Space=== <p>We will now look at a new concept regarding metric spaces known as dense sets which we define below.</p> <blockquote style="background: w...")
• 11:08, 8 November 2021 Lila talk contribs created page Connectedness (Created page with "===Connected and Disconnected Metric Spaces=== <blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td><strong>Definition:</strong> A metric space...")
• 10:40, 8 November 2021 Lila talk contribs created page Convergent Sequences in Metric Spaces (Created page with "===Limits of Sequences in Metric Spaces=== <p>Recall that if a sequence of real numbers <span class="math-inline"><math>(x_n)_{n=1}^{\infty} = (x_1, x_2, ..., x_n, ...)</math>...")
• 10:11, 8 November 2021 Lila talk contribs created page Open Sets and Closed Sets in Metric Spaces (Created page with "<h1 id="toc0"><span>Open and Closed Sets in Metric Spaces</span></h1> A set <span class="math-inline"><math>S \subseteq \mathbb{R}^n</math></span> is said to be open if <span...")
• 09:27, 8 November 2021 Lila talk contribs created page Suprema, Infima, and the Completeness Property (Created page with "<blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td><strong>Definition:</strong> Let <span class="math-inline"><math>S</math></span> be a set th...")
• 08:50, 8 November 2021 Lila talk contribs created page Bounded sets in Higher Dimensions (Created page with "<h1 id="toc0"><span>Bounded Sets</span></h1> <p>Consider the set <span class="math-inline"><math>\mathbb{N} = \{ 1, 2, 3, ... \}</math></span>. As you might imagine, there is...")
• 15:21, 7 November 2021 Khanh talk contribs created page Properly Divergent Sequences (Created page with "Recall that a sequence <math>(a_n)</math> of real numbers is said to be <strong>convergent</strong> to the real number <math>A</math> if <math>\forall \epsilon > 0</math> ther...")
• 14:18, 7 November 2021 Khanh 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> File:Real numbe...")
• 14:47, 6 November 2021 Khanh talk contribs created page Cluster Points (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> is a point <math>x</math...")
• 07:43, 3 November 2021 Lila talk contribs created page Stokes' Theorem (Created page with "thumb|right|An illustration of Stokes' theorem, with surface {{math|Σ}}, its boundary {{math|∂Σ}} and the normal vector {{mvar|n}}. '''Stok...")
• 07:23, 3 November 2021 Lila talk contribs moved page Subspaces of Rⁿ and Linear Independence to Subspaces of Rn and Linear Independence
• 22:59, 30 October 2021 Khanh talk contribs created page Complex Population Growth and Decay Models (Created page with "==Propotionality== thumb|300x300px|The variable ''y'' is directly proportional to the variable ''x'' with proportionality constant ~0.6. ...")
• 10:25, 29 October 2021 Lila talk contribs created page Power Series Solutions (Created page with "In mathematics, the '''power series method''' is used to seek a power series solution to certain differential equations. In general, such a solution assumes a po...")
• 10:20, 29 October 2021 Lila talk contribs created page Laplace Transform to ODEs (Created page with "In mathematics, the Laplace transform is a powerful integral transform used to switch a function from the time domain to the Laplace transform#s-domain equiv...")
• 17:45, 28 October 2021 Lila talk contribs created page Linear Independence of Functions (Created page with "<p>If we have an <math>n^{\mathrm{th}}</math> order linear homogenous differential equation <math>\frac{d^ny}{dt^n} + p_1(t) \frac{d^{n-1}y}{dt^{n-1}} + ... + p_{n-1}(t) \frac...")
• 17:03, 28 October 2021 Lila talk contribs created page Linear Tranformations (Created page with "http://mathonline.wikidot.com/linear-transformations")
• 16:48, 28 October 2021 Lila talk contribs created page Euclidean Spaces: Algebraic Structure and Inner Product (Created page with "==Licensing== Content obtained and/or adapted from: * [http://mathonline.wikidot.com/euclidean-n-space Euclidean n-Space, mathonline.wikidot.com] under a CC BY-SA license * [h...")
• 16:43, 28 October 2021 Lila talk contribs created page Power Series and Analytic Functions (Created page with "==Power Series== http://mathonline.wikidot.com/power-series == Operations on power series == === Addition and subtraction === When two functions ''f'' and ''g'' are decompos...")
• 16:11, 28 October 2021 Lila talk contribs created page Continuous Vector Functions (Created page with "http://mathonline.wikidot.com/continuity-of-vector-valued-functions")
• 16:06, 28 October 2021 Lila talk contribs created page Limits of Vector Functions (Created page with "http://mathonline.wikidot.com/limits-of-vector-valued-functions")
• 12:32, 27 October 2021 Lila talk contribs created page Uniform Convergence of Series of Functions (Created page with "==Pointwise Convergent and Uniformly Convergent Series of Functions== <p>Recall that a sequence of functions <math>(f_n(x))_{n=1}^{\infty}</math> with common domain <math>X</m...")
• 11:08, 27 October 2021 Lila talk contribs created page Uniform Convergence of Sequences of Functions (Created page with "<td><strong>Definition:</strong> An <strong>Infinite Sequence of Functions</strong> <math>(f_n(x))_{n=1}^{\infty} = (f_1(x), f_2(x), ..., f_n(x), ...)</math> is a sequence of...")
• 15:07, 26 October 2021 Lila talk contribs moved page Variation Of Parameters (2nd Order) to Variation Of Parameters
• 14:37, 26 October 2021 Lila talk contribs moved page Method of Undetermined Coefficients (2nd Order) to Method of Undetermined Coefficients
• 14:24, 26 October 2021 Lila talk contribs created page Method of Undetermined Coefficients (2nd Order) (Created page with "In mathematics, the '''method of undetermined coefficients''' is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and...")
• 13:14, 26 October 2021 Lila talk contribs moved page Lindeloff Theorem to Lindelöf Theorem (Misspelled title)
• 12:50, 26 October 2021 Lila talk contribs created page Lindeloff Theorem (Created page with "<h1 id="toc0">Lindelöf and Countably Compact Topological Spaces</h1> <p>Recall from the <a href="/compactness-of-sets-in-a-topological-space">Compactness of Sets in a Topolog...")
• 12:24, 26 October 2021 Lila talk contribs created page Properties of the Integral (Created page with "==Properties== ===Linearity=== The collection of Riemann-integrable functions on a closed interval {{math|[''a'', ''b'']}} forms a vector space under the operations of ...")
• 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 [...")

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