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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'''<sup>2</sup> 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''<sup>2</sup> + ''y''<sup>2</sup> = ''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...")
  • 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''<sup>''x''</sup> (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...")
  • 14:52, 14 October 2021 Lila talk contribs created page Continuous Functions (Created page with "'''Continuity''' marks a new classification of functions, especially prominent when the theorems explained later on in this page will be put to use. However, if one is reading...")
  • 14:14, 14 October 2021 Lila talk contribs moved page Cardinality:𝐍 to Cardinality of important sets (Too specific)
  • 13:59, 14 October 2021 Lila talk contribs created page Cardinality:𝐍 (Created page with "Two important generalizations of natural numbers arise from the two uses of counting and ordering: cardinal numbers and ordinal numbers. * A natural number can be used to expr...")
  • 13:19, 13 October 2021 Lila talk contribs created page Sets:Uncountable (Created page with "In mathematics, an '''uncountable set''' (or '''uncountably infinite set''')<ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=Uncountably Infinite|url=https://m...")
  • 13:01, 13 October 2021 Lila talk contribs created page Sets:Countable (Created page with "In mathematics, a '''countable set''' is a set with the same cardinality (number of elements) as some subset of the set of natural numbers. A countable set is either a finite...")
  • 09:59, 13 October 2021 Lila talk contribs created page Real Numbers:Sequences (Created page with "==Definition== Sequences occur frequently in analysis, and they appear in many contexts. While we are all familiar with sequences, it is useful to have a formal definition....")
  • 09:35, 13 October 2021 Lila talk contribs created page Functions:Restriction (Created page with "thumb|The function ''x''<sup>2</sup> with domain '''R''' does not have an [[inverse function. If we restrict ''x''<sup>2</sup> to the non-neg...")
  • 14:49, 12 October 2021 Lila talk contribs created page The Least-squares Solution (Created page with "'''Ordinary least squares''' ('''OLS''') is a type of linear least squares method for estimating the unknown parameters in a linear regression model. OLS chooses the parameter...")
  • 13:51, 12 October 2021 Lila talk contribs created page Recursion (Created page with "==Recursion in mathematics== thumb|250px|The [[Sierpinski triangle—a confined recursion of triangles that form a fractal]] ===Recursively d...")
  • 13:03, 12 October 2021 Lila talk contribs created page Natural Numbers:Well-Ordering (Created page with "In mathematics, the well-ordering principle states that every non-empty set of positive integers contains a least element.[1] In other words, the set of positive integers is w...")
  • 09:08, 12 October 2021 Lila talk contribs created page Functions:Forward Image (Created page with "File:Codomain2.SVG|thumb|upright=1.5|<math>f</math> is a function from domain <math>X</math> to codomain <math>Y.</math> The yellow oval inside <math>Y</math> is the image o...")
  • 08:48, 12 October 2021 Lila talk contribs created page Real Numbers:Algebraic Properties (Created page with "===Some simple results=== At this point there are a large number of very simple results we can deduce about these operations from the axioms. Some of these follow, and some o...")
  • 08:44, 12 October 2021 Lila talk contribs created page Real Numbers (Created page with "==Why we need the real numbers== This is a good juncture to justify the subject of real analysis, which essentially reduces to justifying the necessity of studying <math>\R</m...")
  • 00:36, 12 October 2021 Khanh talk contribs created page Univariate, Bivariate, Correlation and Causation (Created page with "==Univariate Data== In mathematics, a '''univariate''' object is an expression, equation, function or polynomial involving only one variable. Objects involving more than one...")
  • 00:26, 12 October 2021 Khanh talk contribs created page Geometric interpretation of interpolation (Created page with "In the mathematical field of numerical analysis, '''interpolation''' is a type of estimation, a method of constructing (finding) new data points based on the range of a discre...")
  • 22:26, 10 October 2021 Khanh talk contribs created page Depreciation (Created page with "thumb|380px|An asset depreciation at 15% per year over 20 years In accountancy, '''depreciation''' refers to two aspects of the same concept: fir...")
  • 21:41, 10 October 2021 Khanh talk contribs created page Regression (Created page with "==Regression== Regression analysis is the process of building a model of the relationship between variables in the form of mathematical equations. The general purpose is to e...")
  • 21:24, 10 October 2021 Khanh talk contribs created page Simple and Compound Interest (Linear and Exponential Models) (Created page with "'''Interest''', in finance and economics, is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the princ...")
  • 01:17, 9 October 2021 Khanh talk contribs created page Proportional reasoning (Created page with "== Vocabulary == '''Ratio:''' The comparison of two numbers. '''Reciprocal:''' The multiplicative inverse of a number -- when the numerator and denominator of a fraction are...")
  • 14:11, 8 October 2021 Lila talk contribs created page The Geometric Interpretation of the Determinant (Created page with "This parallelogram picture <center> x200px </center> is familiar from the construction of the sum of the two vectors. One way to compute the...")
  • 14:02, 8 October 2021 Lila talk contribs created page Diagonalization of Matrices (Created page with "The prior subsection defines the relation of similarity and shows that, although similar matrices are necessarily matrix equivalent, the converse does not hold. Some matrix-eq...")
  • 13:40, 8 October 2021 Lila talk contribs created page Orthonormal Bases and the Gram-Schmidt Process (Created page with "The prior subsection suggests that projecting onto the line spanned by <math> \vec{s} </math> decomposes a vector <math>\vec{v}</math> into two parts <center> <TABLE border=0p...")
  • 13:12, 8 October 2021 Lila talk contribs created page The Dimension of a Vector Space (Created page with "In the prior subsection we defined the basis of a vector space, and we saw that a space can have many different bases. For example, following the definition of a basis, we saw...")
  • 12:39, 8 October 2021 Lila talk contribs created page The Column Space and Nullspace of a Linear Transformation (Created page with "Isomorphisms and homomorphisms both preserve structure. The difference is that homomorphisms needn't be onto and needn't be one-to-one. This means that homomorphisms are a mor...")
  • 16:37, 7 October 2021 Lila talk contribs created page Applications of Derivatives (Created page with " ==Resources== * [https://mathresearch.utsa.edu/wikiFiles/MAT1193/Derivative%20Formulas/Presentation3b,4,5_Limits%20&%20Derivative%20Formulas.pptx Limits & Derivative Formulas...")
  • 17:10, 6 October 2021 Khanh talk contribs created page Debt-to-income (DTI) ratios (Created page with "In the consumer mortgage industry, '''debt-to-income ratio''' (often abbreviated '''DTI''') is the percentage of a consumer's monthly gross income that goes toward paying debt...")
  • 20:20, 3 October 2021 Khanh talk contribs created page Sets:Finite (Created page with "In mathematics (particularly set theory), a '''finite set''' is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle cou...")
  • 19:48, 3 October 2021 Khanh talk contribs created page Functions:Composition (Created page with "In mathematics, '''function composition''' is an operation that takes two functions {{math|''f''}} and {{math|''g''}} and produces a function {{math|''h''}} such that {{math|1...")
  • 16:50, 3 October 2021 Khanh talk contribs created page Functions:Inverse Image (Created page with "The '''inverse image''' (or '''preimage''') of a given subset <math>B</math> of the codomain of <math>f,</math> is the set of all elements of the domain that map to the member...")
  • 16:44, 3 October 2021 Khanh talk contribs created page Functions:Inverses (Created page with " Image:Inverse Function.png|thumb|right|A function {{mvar|f}} and its inverse {{math|''f''<sup> −1</sup>}}. Because {{mvar|f}} maps {{mvar|a}} to 3, the inverse {{math|'...")
  • 15:01, 3 October 2021 Khanh talk contribs created page Introduction to Determinants (Created page with "The determinant is a function which associates to a square matrix an element of the field on which it is defined (commonly the real or complex numbers). The determinant is req...")
  • 14:49, 3 October 2021 Khanh talk contribs created page Dot Products and Orthogonality (Created page with "We first consider orthogonal projection onto a line. To orthogonally project a vector <math> \vec{v} </math> onto a line <math>\ell</math>, mark the point on the line at which...")
  • 14:27, 3 October 2021 Khanh talk contribs created page Mathematical (Linear) relationships (Created page with "==Linear Relationship== We are going to start by looking at simple functions called '''linear equations'''. When none of the instances of x and y in the algebraic expressio...")
  • 14:16, 3 October 2021 Khanh talk contribs created page The Sine Function (Created page with "==Sine and Cosine Graphs== And here in this graph, the colors we've chosen to draw the waves in have no relation to the frequency. Both waves have the same frequency, but we'v...")
  • 13:52, 3 October 2021 Khanh talk contribs created page Ratios and percentages (Created page with "==Ratio== In mathematics, a '''ratio''' indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then t...")
  • 13:29, 3 October 2021 Khanh talk contribs created page Graphical Display (Created page with "thumb|A pie chart showing the composition of the 38th Parliament of Canada. A '''chart''' is a graphical representation for data v...")
  • 16:13, 2 October 2021 Lila talk contribs created page Piecewise Linear Function (Created page with "rightA piecewise function is a function that is given by different expressions on different intervals. The graph of <math>f(x) = \begin{cases} x^2, &...")
  • 15:51, 2 October 2021 Lila talk contribs created page Sets:Cardinality (Created page with "==Infinite Sets and Cardinality== '''The Size of a Finite Set''' When deciding how large finite sets are, we generally count the number of elements in the set, and say two se...")
  • 13:10, 1 October 2021 Lila talk contribs created page Two-dimensional coordinate systems (Created page with "==Two-Dimensional Vectors== ===Introduction=== In most mathematics courses up until this point, we deal with '''scalars'''. These are quantities which only need one number to...")
  • 11:33, 1 October 2021 Lila talk contribs created page Proofs:Induction (Created page with "The beauty of induction is that it allows a theorem to be proven true where an infinite number of cases exist without exploring each case individually. Induction is analogous...")
  • 11:21, 1 October 2021 Lila talk contribs created page Natural Numbers:Postulates (Created page with "==Peano's Axioms for the Natural Numbers== # 1 is a natural number. # For every natural number <math> n </math>, the successor to <math> n </math> (<math> n + 1 </math>) is al...")
  • 10:51, 1 October 2021 Lila talk contribs created page Sets:Families (Created page with "A set of sets is usually referred to as a ''family'' or ''collection'' of sets. Often, families of sets are written with either a script or [http://en.wikipedia.org/wiki/Frakt...")
  • 10:41, 1 October 2021 Lila talk contribs created page The First Derivative Test (Created page with "== The First Derivative Test == <p> The definition of a derivatives tells us that a derivative is the slope of the tangent line at a point on the function. </p> <p> Derivative...")
  • 15:59, 30 September 2021 Lila talk contribs created page Mathematical Error (Created page with "At the time of writing this, the 'population clock' run by the USA states that there are 316,356,429 people living in the USA. However, many sources will say that the populati...")
  • 16:52, 29 September 2021 Lila talk contribs created page Functions as Relations (Created page with "== Introduction == This article examines the concepts of a ''function'' and a ''relation''. A '''''relation''''' is any association or link between elements of one set, call...")
  • 13:37, 29 September 2021 Lila talk contribs created page Subspaces of Rⁿ and Linear Independence (Created page with "One of the examples that led us to introduce the idea of a vector space was the solution set of a homogeneous system. For instance, we've seen in Linear Algebra/Definition a...")
  • 12:59, 29 September 2021 Lila talk contribs created page Introduction to Linear Transformations (Created page with "A '''linear transformation''' is an important concept in mathematics because many real world phenomena can be approximated by linear models. Unlike a linear function, a line...")
  • 12:58, 29 September 2021 Lila talk contribs created page The Inverse of a Linear Transformation (Created page with "A '''linear transformation''' is an important concept in mathematics because many real world phenomena can be approximated by linear models. Unlike a linear function, a line...")
  • 12:36, 29 September 2021 Lila talk contribs created page Introduction to Vector Spaces (Created page with "A '''vector space''' (over <math>\R</math>) consists of a set <math>V</math> along with two operations "<math>+</math>" and "<math>\cdot</math>" subject to these conditions....")
  • 16:54, 28 September 2021 Juan.gutierrez3 talk contribs created page Metric spaces (Created page with "<noinclude>{{navigation|Book=Topology |current=Metric Spaces |previous=Basic Concepts Set Theory |next=Topological Spaces}}</noinclude> ==Before we begin== {{TOC right}} Befo...")
  • 14:31, 28 September 2021 Lila talk contribs created page Proofs:Quantifiers (Created page with "==Proving a statement with a universal quantifier== To prove a statement of the form :For all <math>x</math>, <math>P(x)</math> first ask the reader to pick an arbitrary const...")
  • 14:11, 28 September 2021 Lila talk contribs created page Series (Created page with "Frequently in analysis it is useful to consider the sum of infinitely many numbers. So for some sequence of numbers (''a''<sub>''n''</sub>) we may want to consider expression...")
  • 09:54, 28 September 2021 Lila talk contribs created page Writing Mathematics (Created page with "== Parts of a Theorem == A [https://en.wikipedia.org/wiki/Theorem theorem] is a ''proven statement'' that was constructed using previously proven statements, such as theorems,...")
  • 15:28, 27 September 2021 Lila talk contribs created page Equivalence Relations (Created page with "We have seen that certain common relations such as "=", and congruence (which we will deal with in the next section) obey some of these rules above. The relations we will deal...")
  • 15:24, 27 September 2021 Lila talk contribs created page Relations (Created page with "== Introduction == This article examines the concepts of a ''function'' and a ''relation''. A '''''relation''''' is any association or link between elements of one set, call...")
  • 14:44, 27 September 2021 Lila talk contribs created page Functions:Bijective (Created page with "A function is bijective if it is both injective and surjective. That is, a bijective function maps each element of the domain to a distinct element in the codomain, and every...")
  • 14:37, 27 September 2021 Lila talk contribs created page Functions:Surjective (Created page with "A function is surjective, or "onto", if for all <math> b\in B </math>, there exists at least one <math> a\in A </math> such that <math> f(a) = b </math>; that is, every elemen...")
  • 13:57, 27 September 2021 Lila talk contribs created page Functions:Injective (Created page with "A function <math> f: A\to B </math> is injective, or "one-to-one", if for all <math> a_1, a_2\in A </math>, <math> a_1 \neq a_2 </math> implies that <math> f(a_1) \neq f(a_2)...")
  • 13:09, 27 September 2021 Juan.gutierrez3 talk contribs created page Test (Created page with "{{{{BOOKTEMPLATE}}/Page}} <noinclude>{{navigation|Book=Algebra |current=Order of Operations |previous=Arithmetic |next=Real_Numbers }}</noinclude> The '''''Order of Operation...")
  • 12:01, 27 September 2021 Lila talk contribs created page Functions:Definition (Created page with "A function (or "mapping") is a relationship between two sets <math> A </math> and <math> B </math> that maps each input <math> a\in A </math> to exactly one output <math> b\in...")
  • 22:54, 26 September 2021 Khanh talk contribs created page Periodic Function (Created page with "A '''periodic function''' is a function that repeats its values at regular intervals, for example, the trigonometric functions, which repeat at intervals of 2π radians. Peri...")
  • 22:25, 26 September 2021 Khanh talk contribs created page Linear and Exponential Models (Created page with "* [https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-vs-linear-growth/v/linear-exponential-models Exponential v...")
  • 22:20, 26 September 2021 Khanh talk contribs created page Logistic Growth Model (Created page with "thumb|320px|right|Standard logistic sigmoid function where <math>L=1,k=1,x_0=0</math> A '''logistic function''' or '''logistic curve''' is a commo...")
  • 22:14, 26 September 2021 Khanh talk contribs created page Carrying Capacity and Logistic Growth Rate (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/08%3A_Introduction_to_Differential_Equations/8.4%3A_The_Logistic_Equation The Logistic Equation...")
  • 22:04, 26 September 2021 Khanh talk contribs created page Weighted averages (Created page with "The '''weighted arithmetic mean''' is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equ...")
  • 21:50, 26 September 2021 Khanh talk contribs created page Conversions (Created page with "* [https://www.khanacademy.org/math/geometry-home/geometry-volume-surface-area/geometry-volume-rect-prism/v/conversion-between-metric-units Conversion Between Metric Units], K...")
  • 21:39, 26 September 2021 Khanh talk contribs created page Probability (Created page with "thumb|250px|The probabilities of rolling several numbers using two dice. '''Probability''' is the branch of mathematics concerning numeri...")
  • 21:14, 26 September 2021 Khanh talk contribs created page Standard Deviation (Created page with "* [https://www.youtube.com/watch?v=IaTFpp-uzp0 How To Calculate The Standard Deviation], The Organic Chemistry Tutor * [https://www.youtube.com/watch?v=Uk98hiMQgN0 Standard De...")
  • 21:05, 26 September 2021 Khanh talk contribs created page Mean and Central Limit Theorem (Created page with "In probability theory, the '''central limit theorem''' ('''CLT''') establishes that, in many situations, when independent random variables are summed up, their properly normal...")
  • 20:58, 26 September 2021 Khanh talk contribs created page Sampling (Created page with "* [https://courses.lumenlearning.com/math4libarts/chapter/sampling-methods/ Sampling Methods], Lumen Learning * [https://www.khanacademy.org/math/statistics-probability/design...")
  • 20:46, 26 September 2021 Khanh talk contribs created page First-degree equation involving percentages (Created page with "* [https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-percent-problems/v/solving-percent-problems Solving Percent Problems], Khan Academy * [...")
  • 20:35, 26 September 2021 Khanh talk contribs created page Data (Created page with "Data are individual facts, statistics, or items of information, often numeric, that are collected through observation. In a more technical sense, data are a set of values of q...")
  • 20:12, 26 September 2021 Khanh talk contribs created page Inverse functions and the identity function (Created page with "* [https://www.youtube.com/watch?v=kWorj5BBy9k Inverse Matrices and Their Properties], video by Professor Dave Explains * [https://www.khanacademy.org/math/algebra-home/alg-ma...")
  • 16:35, 26 September 2021 Khanh talk contribs created page Critical Points of a Function (Created page with "400px|thumb|right|The abscissae ("x-coordinates") of the red circles are stationary points; the blue squares are inflection points. '...")
  • 16:17, 26 September 2021 Khanh talk contribs created page Continuity of functions with two variables (Created page with "https://openstax.org/books/calculus-volume-3/pages/4-2-limits-and-continuity Limits and Continuity], OpenStax")
  • 16:15, 26 September 2021 Khanh talk contribs created page Continuity of a function (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/2%3A_Vector-Valued_Functions_and_Motion_in_Space/2.1%3A_Vector_Valued_Funct...")
  • 16:11, 26 September 2021 Khanh talk contribs created page Maxima, Minima and Critical Points of a Function (Created page with "* [https://openstax.org/books/calculus-volume-3/pages/4-7-maxima-minima-problems Maxima and Minima], OpenStax * [https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analyt...")
  • 16:08, 26 September 2021 Khanh talk contribs created page Limit and Continuity for a Function of several variables (Created page with "* [https://math.libretexts.org/Courses/University_of_California_Davis/UCD_Mat_21A%3A_Differential_Calculus/4%3A_Applications_of_Definite_Integrals/4.1%3A_Extreme_Values_of_Fun...")
  • 16:00, 26 September 2021 Khanh talk contribs created page Dot Product (Created page with "* [https://www.youtube.com/watch?v=0iNrGpwZwog The Vector Dot Product ] Video by Professor Dave Explains 2018")
  • 12:44, 26 September 2021 Lila talk contribs created page Sets:Operations (Created page with "==Definitions== The two main set operations that we deal with are union and intersection. The union of two sets <math> A </math> and <math> B </math> is defined as <math> A \c...")
  • 10:20, 26 September 2021 Lila talk contribs created page Sets:Definitions (Created page with "==Definitions== A set is any collection of objects. The objects in a set are called elements. For example, <math> \N = {1, 2, 3, ....} </math> is the set of all natural number...")
  • 23:57, 25 September 2021 Khanh talk contribs created page Path Independence and Conservation Fields (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/4%3A_Integration_in_Vector_Fields/4.5%3A_Path_Independence%2C_Conservative_...")
  • 23:53, 25 September 2021 Khanh talk contribs created page Vector Fields and Line Integrals (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/LineIntegralsVectorFields.aspx Line Integrals of Vector Fields], Paul's Online Notes * [https://www.khanacademy.org/math/mul...")
  • 23:45, 25 September 2021 Khanh talk contribs created page Arc Lengths (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/LineIntegralsPtI.aspx Line Integral with Respect to Arc Length], Paul's Online Notes * [https://www.youtube.com/watch?v=wcNU...")
  • 23:41, 25 September 2021 Khanh talk contribs created page Line Integrals (Created page with "In mathematics, a '''line integral''' is an integral where the function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''cur...")
  • 23:31, 25 September 2021 Khanh talk contribs created page Vector Fields (Created page with "In vector calculus and physics, a '''vector field''' is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualis...")
  • 23:26, 25 September 2021 Khanh talk contribs created page Change of Variables in Multiple Integrals (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/15%3A_Multiple_Integration/15.7%3A_Change_of_Variables_in_Multiple_Integrals Change of Variable...")
  • 23:22, 25 September 2021 Khanh talk contribs created page Triple Integrals (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/tripleintegrals.aspx Triple Integrals], Paul's Online Notes * [https://www.youtube.com/watch?v=7iy83x8bv6o Triple Integrals...")
  • 23:20, 25 September 2021 Khanh talk contribs created page Double Integral (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/DoubleIntegrals.aspx Double Integrals] Paul's Online Notes * [https://www.youtube.com/watch?v=BJ_0FURo9RE Double Integrals],...")
  • 23:19, 25 September 2021 Khanh talk contribs created page Double Integrals in Polar Form (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/dipolarcoords.aspx Double Integrals in Polar Coordinates], Paul's Online Notes * [https://math.libretexts.org/Bookshelves/Ca...")
  • 23:13, 25 September 2021 Khanh talk contribs created page Area by Double Integration (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/DIGeneralRegion.aspx Double Integrals Over General Regions], Paul's Online Notes * [https://math.libretexts.org/Bookshelves/...")
  • 23:10, 25 September 2021 Khanh talk contribs created page Double Integrals (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/DoubleIntegrals.aspx Double Integrals] Paul's Online Notes * [https://www.youtube.com/watch?v=BJ_0FURo9RE Double Integrals],...")
  • 23:02, 25 September 2021 Khanh talk contribs created page Triple Integrals in Rectangular Coordinates (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Map%3A_University_Calculus_(Hass_et_al)/14%3A_Multiple_Integrals/14.5%3A_Triple_Integrals_in_Rectangular_Coordinates Triple...")
  • 22:59, 25 September 2021 Khanh talk contribs created page Double and Iterated Integrals over Rectangular regions (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/15%3A_Multiple_Integration/15.1%3A_Double_Integrals_over_Rectangular_Regions Double Integrals o...")
  • 22:54, 25 September 2021 Khanh talk contribs created page Curves in Space and Vector Functions (Created page with "A '''vector-valued function''', also referred to as a '''vector function''', is a mathematical function of one or more variables whose range is a set of multidimensional vecto...")
  • 22:50, 25 September 2021 Khanh talk contribs created page Differentiability (Created page with "*[https://math.libretexts.org/Courses/University_of_California_Davis/UCD_Mat_21C%3A_Multivariate_Calculus/13%3A_Partial_Derivatives/13.6%3A_Tangent_Planes_and_Differentials#:~...")
  • 22:41, 25 September 2021 Khanh talk contribs created page Determinants (Created page with "In mathematics, the '''determinant''' is a scalar value that is a function of the entries of a square matrix. It allows characterizing some properties of the matrix and the li...")
  • 22:10, 25 September 2021 Khanh talk contribs created page Equations of Planes (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/eqnsofplanes.aspx Equations of Planes], Paul's Online Notes * [https://www.youtube.com/watch?v=2sZKZHyaQJ8 How To Find The E...")
  • 22:08, 25 September 2021 Khanh talk contribs created page Parametric Equations of Lines (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/eqnsoflines.aspx Equations of Lines], Paul's Online Notes * [https://www.khanacademy.org/math/linear-algebra/vectors-and-spa...")
  • 21:45, 25 September 2021 Khanh talk contribs created page Vectors, Unit Vectors (Created page with "In mathematics, a '''unit vector''' in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a...")
  • 21:32, 25 September 2021 Khanh talk contribs created page The limit and continuity for a function of several variables (Created page with "* [https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivatives/v/partial-derivatives-introduction Introduction to Partial Derivatives...")
  • 21:12, 25 September 2021 Khanh talk contribs created page Partial Derivatives (Created page with "In mathematics, a '''partial derivative''' of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as oppos...")
  • 20:39, 25 September 2021 Khanh talk contribs created page The Limit and Continuity of a Function (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus__Early_Transcendentals_(Stewart)/14%3A_Partial_Derivatives/14.02%3A_Limits_and_Continuity Limits and Contin...")
  • 20:36, 25 September 2021 Khanh talk contribs created page Limit and Continuity of Function of Several Variables (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(Apex)/12%3A_Functions_of_Several_Variables/12.02%3A_Limits_and_Continuity_of_Multivariable_Functions Limi...")
  • 20:23, 25 September 2021 Khanh talk contribs created page Functions of Several Variables (Created page with "* [https://tutorial.math.lamar.edu/classes/calciii/multivrblefcns.aspx Functions of Several Variables], Paul's Online Notes * [https://math.libretexts.org/Bookshelves/Calculus...")
  • 20:20, 25 September 2021 Khanh talk contribs created page Distance Formula (Created page with "* [https://openstax.org/books/calculus-volume-3/pages/3-3-arc-length-and-curvature Arc Length], OpenStax")
  • 20:18, 25 September 2021 Khanh talk contribs created page Arc Length (Created page with "* [https://openstax.org/books/calculus-volume-3/pages/3-3-arc-length-and-curvature Arc Length and Curvature], OpenStax")
  • 20:17, 25 September 2021 Khanh talk contribs created page Derivatives of Vector Functions (Created page with "* [https://openstax.org/books/calculus-volume-3/pages/3-2-calculus-of-vector-valued-functions Calculus of Vector-Valued Functions], OpenStax")
  • 20:14, 25 September 2021 Khanh talk contribs created page Integrals of Vector Functions (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus__Early_Transcendentals_(Stewart)/13%3A_Vector_Functions/13.02%3A_Derivatives_and_Integrals_of_Vector_Functi...")
  • 20:09, 25 September 2021 Khanh talk contribs created page Vectors (Created page with "* [https://www.khanacademy.org/math/algebra-home/alg-vectors Vectors], Khan Academy")
  • 15:56, 25 September 2021 Khanh talk contribs created page Curves in Space and Vector-Valued Functions (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/13%3A_Vector-Valued_Functions/13.1%3A_Vector-Valued_Functions_and_Space_Curves Vector-Valued Fu...")
  • 15:48, 25 September 2021 Khanh talk contribs created page Equations of Lines, Planes and Surfaces in Space (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/12%3A_Vectors_in_Space/12.5%3A_Equations_of_Lines_and_Planes_in_Space Equations of Lines and Pl...")
  • 15:41, 25 September 2021 Khanh talk contribs created page Vectors in The Plane, Space (Created page with "* [https://math.libretexts.org/Courses/Monroe_Community_College/MTH_212_Calculus_III/Chapter_11%3A_Vectors_and_the_Geometry_of_Space/11.1%3A_Vectors_in_the_Plane Vectors in th...")
  • 15:32, 25 September 2021 Khanh talk contribs created page Conics (Created page with "* [https://courses.lumenlearning.com/boundless-algebra/chapter/introduction-to-conic-sections/ Introduction to Conic Sections], Lumen Learning")
  • 15:31, 25 September 2021 Khanh talk contribs created page Cylinders and Quadratic Surfaces (Created page with "* [https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/12%3A_Vectors_in_Space/12.6%3A_Quadric_Surfaces Quadric Surfaces], Mathematics LibreTexts")
  • 15:27, 25 September 2021 Khanh talk contribs created page Motion in Space (Created page with "* [https://openstax.org/books/calculus-volume-3/pages/3-4-motion-in-space Motion in Space], openstax")
  • 14:24, 25 September 2021 Khanh talk contribs created page Transformations of Functions (Created page with "In linear algebra, linear transformations can be represented by matrices. If <math>T</math> is a linear transformation mapping <math>\mathbb{R}^n</math> to <math>\mathbb{R}^m...")
  • 13:51, 25 September 2021 Khanh talk contribs created page Systems of Inequalities (Created page with "In mathematics a '''linear inequality''' is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: It shows the data w...")
  • 23:59, 24 September 2021 Khanh talk contribs created page Polynomial Functions and Their Graphs (Created page with "* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Intro_to_Polynomial_and_Power_Functions/MAT1053_M2.1Intro_to_Power_Functions_and_Polynomial_Functions.pdf Intro to Power Fun...")
  • 23:53, 24 September 2021 Khanh talk contribs created page Combinations of Functions/Composite Functions (Created page with "* [https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:composing/v/function-composition Intro to Composing Functions], Khan Academy * [h...")
  • 23:47, 24 September 2021 Khanh talk contribs created page Other Types of Equations (Created page with "* [https://courses.lumenlearning.com/waymakercollegealgebra/chapter/writing-formulas-for-polynomial-functions/ Polynomial Equations], Lumen Learning * [https://courses.lumenl...")
  • 23:34, 24 September 2021 Khanh talk contribs created page Models and Applications (Created page with "* [https://courses.lumenlearning.com/wmopen-collegealgebra/chapter/introduction-models-and-applications/ Models and Applications], Lumen Learning")
  • 23:28, 24 September 2021 Khanh talk contribs created page Applications of Integrals (Created page with " * Average value of a function * Area between curves * Distance, velocity, acceleration * Volume * Work * Arc length * Surface area * Center of mass * Hydrostatic pressure and...")
  • 23:13, 24 September 2021 Khanh talk contribs created page Second Derivative Test (Created page with "After establishing the critical points of a function, the ''second-derivative test'' uses the value of the second derivative at those points to determine whether such points a...")
  • 23:05, 24 September 2021 Khanh talk contribs created page First Derivative Test (Created page with "The first-derivative test examines a function's monotonic properties (where the function is increasing or decreasing), focusing on a particular point in its domain. If the fun...")
  • 22:49, 24 September 2021 Khanh talk contribs created page The Second Derivative (Created page with "right|thumb|200px|The second derivative of a quadratic function is constant. In calculus, the '''second derivative''', or the '''sec...")
  • 22:32, 24 September 2021 Khanh talk contribs created page Derivatives and Graphs (Created page with "* [https://www.khanacademy.org/math/old-ap-calculus-ab/ab-derivatives-analyze-functions/ab-connecting-func-and-derivatives/v/intuitively-drawing-the-derivative-of-a-function T...")
  • 22:29, 24 September 2021 Khanh talk contribs created page Derivatives of Logarithmic Functions (Created page with "* [https://www.khanacademy.org/math/in-in-grade-12-ncert/xd340c21e718214c5:continuity-differentiability/xd340c21e718214c5:logarithmic-functions-differentiation/v/derivative-lo...")
  • 22:23, 24 September 2021 Khanh talk contribs created page Derivatives of Exponential Functions (Created page with "* [https://www.youtube.com/watch?v=fqYds-feWcw Exponential Functions Differentiation], Khan Academy * [https://www.khanacademy.org/math/in-in-grade-12-ncert/xd340c21e718214c5:...")
  • 22:19, 24 September 2021 Khanh talk contribs created page 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. In...")
  • 22:14, 24 September 2021 Khanh talk contribs created page Function Evaluation (Created page with "* [https://www.youtube.com/watch?v=E9YEUQR9NAU Evaluating Functions], Khan Academy * [https://courses.lumenlearning.com/waymakercollegealgebra/chapter/evaluate-and-solve-funct...")
  • 18:55, 24 September 2021 Khanh talk contribs created page Composite Functions (Created page with "In mathematics, '''function composition''' is an operation that takes two functions {{math|''f''}} and {{math|''g''}} and produces a function {{math|''h''}} such that {{math|1...")
  • 14:21, 24 September 2021 Lila talk contribs created page Eigenvalues and Eigenvectors (Created page with "In linear algebra, an eigenvector of a matrix is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding e...")
  • 14:03, 24 September 2021 Lila talk contribs created page MAT3223 (Created page with "MAT 3223. Complex Variables. (3-0) 3 Credit Hours. Prerequisites: MAT 2214 and MAT 3213. An introduction to complex variables, including elementary functions, line integrals,...")
  • 13:51, 24 September 2021 Lila talk contribs created page Logical Implication (Created page with "A logical implication is a relationship between two statements. If a statement Q is always true when another statement P is true, then we say that "P implies Q", which is deno...")
  • 11:58, 24 September 2021 Lila talk contribs created page Logical Equivalence (Created page with "In mathematics, two statements are logically equivalent if they produce the same truth value in every case. For example, "x is greater than 7" and "x is not less than or equal...")
  • 11:06, 24 September 2021 Lila talk contribs created page Proofs:Biconditionals (Created page with "A biconditional of two propositions P and Q takes the form "<math> P </math> if and only if <math> Q </math>". This can also be written as "<math> P \iff Q </math>, which is e...")
  • 10:59, 24 September 2021 Lila talk contribs created page Deductive Rules (Created page with "In mathematics, deductive reasoning is the process of making conclusions using axioms and previously proven theorems and statements. ==Resources== * [https://en.wikipedia.org...")
  • 10:47, 24 September 2021 Lila talk contribs created page Proofs:Cases (Created page with "Some proofs are easier to do if we split them up into two or more cases. Example: Proof that <math> x^2 \ge 0 </math> for all real numbers. We can break this up into three ca...")
  • 10:28, 24 September 2021 Lila talk contribs created page Proofs:Contradiction (Created page with "A proof by contradiction is a proof in which we assume the negation of the conclusion of our proposition/theorem, and show that this assumption leads to a contradiction. If th...")
  • 09:39, 24 September 2021 Lila talk contribs created page Proofs:Contraposition (Created page with "Let <math> P </math> and <math> Q </math> be propositions such that <math> P \implies Q </math>. Then, the contrapositive of the conditional statement "<math> P \implies Q </m...")
  • 09:13, 24 September 2021 Lila talk contribs created page Counting Rules (Created page with "==Resources== * [https://www.hamilton.ie/ollie/EE304/Counting.pdf Some Simple Counting Rules], Hamilton Institute * [https://www.stat.purdue.edu/~huang251/slides4.pdf Basic Co...")
  • 20:28, 23 September 2021 Lila talk contribs created page Quantifiers (Created page with "Quantifiers are words, expressions, or phrases that indicate the number of elements that a statement pertains to. In mathematical logic, there are two quantifiers: the univers...")
  • 17:02, 23 September 2021 Lila talk contribs created page Linear and Absolute Value Inequalities (Created page with "==Resources== * [https://openstax.org/books/college-algebra/pages/2-7-linear-inequalities-and-absolute-value-inequalities Linear Inequalities and Absolute Value Inequalities],...")
  • 17:30, 22 September 2021 Khanh talk contribs created page Tangent Lines and Derivatives (Created page with "220px|right|thumb|Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. In geometry, the '''tangent li...")
  • 17:13, 22 September 2021 Khanh talk contribs created page Average (Created page with "* [https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:average-rate-of-change-word-problems/a/average-rate-of-change-review Average rate of...")
  • 17:10, 22 September 2021 Khanh talk contribs created page Equation of a Line (Created page with "* [https://www.youtube.com/watch?v=gvwKv6F69F0 Equation of a Line], Khan Academy * [https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8bb...")
  • 17:06, 22 September 2021 Khanh talk contribs created page Rates of Change (Created page with "In mathematics, a '''rate''' is the ratio between two related quantities in different units.[1] If the denominator of the ratio is expressed as a single unit of one of these q...")
  • 16:25, 22 September 2021 Khanh talk contribs created page Conditional Probability (Created page with " In probability theory, '''conditional probability''' is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or...")
  • 15:14, 22 September 2021 Khanh talk contribs created page Payout Annuities (Created page with "==Resources== * [https://courses.lumenlearning.com/math4libarts/chapter/payout-annuities/ Payout Annuities], Lumen Learning")
  • 13:17, 22 September 2021 Lila talk contribs created page Remainder and Factor Theorem (Created page with "The polynomial division algorithm is as follows: suppose d(x) and p(x) are nonzero polynomials where the degree of p(x) is greater than or equal to the degree of d(x). Then th...")
  • 11:34, 22 September 2021 Lila talk contribs created page Integrating Factor (Created page with "When solving first order linear differential equations of the form <math> \frac{dy}{dx} + p(x)y = g(x) </math>, we can utilize the "integrating factor" <math> \mu\(x\)</math>...")
  • 10:42, 22 September 2021 Lila talk contribs created page Rational Equations (Created page with "Rational equations are equations containing rational expressions (or expressions with fractions that contain real numbers and/or variables). Some examples of rational equation...")
  • 10:14, 22 September 2021 Lila talk contribs created page Graph of equations (Created page with "==Resources== * [https://math.libretexts.org/Courses/Lumen_Learning/Book%3A_Beginning_Algebra_(Lumen)/02%3A_Graphing/2.02%3A_The_Coordinate_Plane The Coordinate Plane], Lumen...")
  • 10:07, 22 September 2021 Lila talk contribs created page Proofs:Direct (Created page with "==Resources== * [https://link-springer-com.libweb.lib.utsa.edu/content/pdf/10.1007%2F978-1-4419-7127-2.pdf Course Textbook], pages 53-57")
  • 10:07, 22 September 2021 Lila talk contribs created page Mathematical Proofs (Created page with "==Resources== * [https://link-springer-com.libweb.lib.utsa.edu/content/pdf/10.1007%2F978-1-4419-7127-2.pdf Course Textbook], pages 47-53")
  • 16:55, 21 September 2021 Lila talk contribs created page Systems of Inequalities in Two Variables (Created page with "A system of inequalities in two variables consists of two or more inequalities with the same two variables, typically x and y. These systems can have zero solutions, one solut...")
  • 16:30, 21 September 2021 Lila talk contribs created page Radical & Rational Exponent (Created page with "The principal nth root of a is written as <math> \sqrt[n]{a} </math>, where n is a positive integer greater than or equal to 2. In the radical expression, n is called the inde...")
  • 16:17, 21 September 2021 Lila talk contribs created page Sentential Logic (Created page with "==Resources== * [https://link-springer-com.libweb.lib.utsa.edu/book/10.1007%2F978-1-4419-7127-2 Course Textbook], pages 15-45 * [http://discrete.openmathbooks.org/dmoi2/sec_pr...")
  • 13:57, 21 September 2021 Lila talk contribs created page Statements (Created page with "==Resources== * [https://link-springer-com.libweb.lib.utsa.edu/content/pdf/10.1007%2F978-1-4419-7127-2.pdf Course Textbook], pages 4-25")
  • 17:56, 20 September 2021 Lila talk contribs created page Derivatives of Products and Quotients (Created page with "===Product Rule=== Let <math> f(x) </math> and <math> g(x) </math> be differentiable functions. Then, the derivative of their product, <math> f(x)g(x) </math>, is <math> \fra...")
  • 17:04, 20 September 2021 Lila talk contribs created page The Cross Product (Created page with "The cross product is an operation between two 3-dimensional vectors that returns a third vector orthogonal (i.e., perpendicular) to the first two. For vectors <math> u = \lang...")
  • 13:33, 20 September 2021 Lila talk contribs created page Laplace Transform (Created page with "==Resources== * [https://tutorial.math.lamar.edu/classes/de/LaplaceIntro.aspx Laplace Transforms], Paul's Online Notes")
  • 12:59, 20 September 2021 Lila talk contribs created page Complex Numbers (Created page with "A complex number is a number of the form <math> a + bi </math> where <math> a </math> is the real part of the complex number, and <math> bi </math> is the imaginary part of th...")
  • 12:23, 20 September 2021 Lila talk contribs created page Slope (Created page with "===Slope Between Two Points=== Given two points <math> (x_1, y_1) </math> and <math> (x_2, y_2) </math>, the slope m between these two points is <math> m = \frac{y_2 - y_1}{x...")
  • 12:08, 20 September 2021 Lila talk contribs created page Scientific Notation (Created page with "Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form...")
  • 22:57, 17 September 2021 Khanh talk contribs created page Limits Involving Infinity (Created page with "==Limits involving infinity== ===Limits at infinity=== thumb|300px|The limit of this function at infinity exists. Let <math>S\subseteq\mathbb...")
  • 22:44, 17 September 2021 Khanh talk contribs created page One-Sided Limits (Created page with "File:X^2+sign(x).svg|thumb|350px|The function ''f''(''x'') = ''x''<sup>2</sup> + sign(''x'') has a left limit of -1, a right limit of +1, and a function value of 0 at the po...")
  • 22:37, 17 September 2021 Khanh talk contribs created page Linear Functions (Created page with "Solving Linear Equations Examples: * [https://www.youtube.com/watch?v=bsGyJ0GeRy8 Example 1]. Produced by TA Catherine Sporer, UTSA * [https://www.youtube.com/watch?v=nGZcfHQ...")
  • 22:33, 17 September 2021 Khanh talk contribs created page Quadratic Equations (Created page with "==Resources== * [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Quadratic_Functions/MAT1053_M2.2Quadratic_Functions.pdf Quadratic Functions], Book Chapters * [https://mathres...")
  • 22:24, 17 September 2021 Khanh talk contribs created page Graphs of Functions (Created page with "right|thumb|250px| Graph of the function <math>f(x) = x^3 - 9x.</math> In mathematics, the '''graph''' of a function <math>f</math> is the set...")
  • 20:22, 17 September 2021 Lila talk contribs created page Linear Homogeneous Equations (Created page with "Homogeneous linear differential equations take the form <math> P_{n}(x)y^{(n)} + P_{n-1}(x)y^{(n-1)} + ... + P_{2}(x)y^{(2)} + P_{1}(x)y^{(1)} </math> ==Resources== * [https:/...")
  • 20:06, 17 September 2021 Lila talk contribs created page Initial Value Problem (Created page with "With initial value problems, we are given a differential equation, and one or more points (depending on the order of the equation) to solve the constants in the general soluti...")
  • 19:20, 17 September 2021 Lila talk contribs created page Solutions of Differential Equations (Created page with "A solution of a differential equation is an expression of the dependent variable that satisfies the relation established in the differential equation. For example, the solutio...")
  • 17:24, 17 September 2021 Lila talk contribs created page Exponential and Logarithmic Equations (Created page with "==Resources== * [https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/a/solving-exponential-equations-with-logarithms Solving Exponent...")
  • 16:36, 17 September 2021 Lila talk contribs created page The inverse sine, cosine and tangent functions (Created page with "<math> sin(x) = \theta \to arcsin(\theta) = x</math> ==Resources== * [https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-an-angle/a/inverse-trig-functions...")
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