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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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• 12:50, 13 November 2021 Khanh talk contribs created page Iterated Integrals and Fubini's Theorem (Created page with "==Resources== * [https://tutorial.math.lamar.edu/classes/calciii/IteratedIntegrals.aspx Iterated Integrals, Paul's Online Notes] == Licensing == Content obtained and/or adap...")
• 12:29, 13 November 2021 Khanh talk contribs created page Lebesque Theorem for Riemann Integrability on the Real Line (Created page with "In mathematics, the '''Lebesgue differentiation theorem''' is a theorem of real analysis, which states that for almost every point, the value of an integrable function is the...")
• 15:52, 12 November 2021 Khanh talk contribs created page The Inverse Function Theorem and the Implicit Function Theorem (Created page with "In this chapter, we want to prove the inverse function theorem (which asserts that if a function has invertible differential at a point, then it is locally invertible itself)...")
• 15:40, 12 November 2021 Khanh talk contribs created page Taylor's Formula in Several Variables (Created page with "Let <math>S \subseteq \mathbb{R}^n</math> be open, <math>\mathbf{x} \in S</math>, and <math>f : S \to \mathbb{R}</math>. If <math>\mathbf{t} \in \mathbb{R}^n</math> then we kn...")
• 14:27, 12 November 2021 Khanh talk contribs created page Mean-Value Theorems for Vector Valued Functions (Created page with "==The Mean Value Theorem for Differentiable Functions from Rn to Rm== Recall that if <math>f</math> is a continuous function on the closed interval <math>[x, y]</math> and di...")
• 20:04, 11 November 2021 Khanh talk contribs created page Rules for Differentiation and Tangent Planes (Created page with "We will now look at a bunch of rules for differentiating vector-valued function, all of which are analogous to that of differentiating real-valued functions. We will not prove...")
• 17:07, 11 November 2021 Khanh talk contribs created page Limits of Sequences in the Euclidean space and the Bolzano-Weierstrass Theorem (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 pol...")
• 12:42, 11 November 2021 Khanh talk contribs created page Laplace Transform to Systems of ODEs (Created page with "This is an example to illustrate how Laplace transforms can be used to solve systems of differential equations. Solve the following system. <div style=...")
• 15:05, 10 November 2021 Lila talk contribs created page Divergence Theorem (Created page with "The '''divergence theorem''', also known as '''Gauss's theorem''' or '''Ostrogradsky's theorem''', is a theorem which relates the flux of a vector field through a closed surfa...")
• 14:13, 10 November 2021 Lila talk contribs created page The Hilbert Space L2 and the Hilbert Cube (Created page with "==Definition and illustration of Hilbert Space== ===Motivating example: Euclidean vector space=== One of the most familiar examples of a Hilbert space is the Euclidean vect...")
• 12:51, 10 November 2021 Lila talk contribs created page Surface Integrals (Created page with "A '''surface integral''' is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. G...")
• 12:17, 10 November 2021 Lila talk contribs created page Partial Derivatives and Integrals (Created page with "===Partial Derivatives of Functions from Rn to Rm=== <p>One of the core concepts of multivariable calculus involves the various differentiations of functions from <span class=...")
• 16:07, 9 November 2021 Lila talk contribs created page The Substitution and Composition Theorems (Created page with "== Substitution Theorem e == === Definite integrals === Let {{math|''φ'' : [''a'', ''b''] → ''I''}} be a differentiable function with a continuous derivative, where {{math...")
• 15:44, 9 November 2021 Lila talk contribs created page The Additivity Theorem (Created page with "<blockquote style="background: white; border: 1px solid black; padding: 1em;"> Let <span class="math-inline"><math> f </math></span> be a real-valued function on the interval...")
• 15:08, 9 November 2021 Lila talk contribs created page Riemann Integrable Functions (Created page with "== Overview == Let {{mvar|f}} be a non-negative real-valued function on the interval {{math|[''a'', ''b'']}}, and let :<math>S = \left \{ (x, y) \, : \ a \leq x \leq b, 0 <...")
• 14:18, 9 November 2021 Lila talk contribs created page The Topology of Higher Dimensions: interior, closure and boundary (Created page with "We are now going to discuss some important classifications of points regarding a subset <span class="math-inline"><math>S</math></span> of <span class="math-inline"><math>\mat...")
• 14:03, 9 November 2021 Lila talk contribs created page Bounded Sets and Bounded Functions in a Metric Space (Created page with "<blockquote style="background: white; border: 1px solid black; padding: 1em;"> <td><strong>Definition:</strong> Let <span class="math-inline"><math>(M, d)</math></span> be a m...")
• 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 ...")

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