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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).

Logs
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  • 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],...")
  • 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...")
  • 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...")
  • 16:12, 17 September 2021 Lila talk contribs created page Finding Roots of an Equation (Created page with "==Resources== In mathematics, the roots of a function are the x-values that make y = 0. For example, the roots of the polynomial <math> y = x^2 - 4 </math> are 2 and -2, since...")
  • 16:02, 17 September 2021 Lila talk contribs created page Implicit and explicit equations (Created page with "In mathematics, an implicit equation is a relation of the form {{math|1=''R''(''x''<sub>1</sub>, …, ''x<sub>n</sub>'') = 0}}, where {{mvar|R}} is a function of several varia...")
  • 11:23, 17 September 2021 Lila talk contribs created page Matrix Algebra and Matrix Multiplication (Created page with "==Matrix Operations== ===Adding and subtracting matrices=== In order to add or subtract two matrices, they must be of the same dimension; that is, the two matrices must have t...")
  • 19:45, 16 September 2021 Lila talk contribs created page Gauss-Jordan Elimination (Created page with "Now that we can write systems of equations in augmented matrix form, we will examine the various row operations that can be performed on a matrix, such as addition, multiplica...")
  • 19:38, 16 September 2021 Lila talk contribs created page Vectors and Matrices (Created page with "==Resources== * [https://www.unf.edu/~mzhan/chapter3.pdf Brief Introduction to Vectors and Matrices], University of North Florida * [https://www.usna.edu/Users/math/uhan/sm286...")
  • 18:48, 16 September 2021 Lila talk contribs created page Algebraic Expressions (Created page with "==Introduction== To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we s...")
  • 16:09, 16 September 2021 Lila talk contribs created page Differential Equations Applications (Created page with "==Applications== The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the...")
  • 13:43, 16 September 2021 Lila talk contribs created page Multiple Transformations of Functions (Created page with "See Single Transformations of Functions ==Resources== * [https://online.math.uh.edu/Math1330-unpaid/ch1/s13/CombTransf/Combining_Transformations_Math1330_s13.pdf Combining...")
  • 11:44, 16 September 2021 Lila talk contribs created page Exponential Properties (Created page with "==Introduction== Exponential properties can be used to manipulate equations involving exponential expressions and/or functions. Here are some important exponential properties:...")
  • 17:09, 15 September 2021 Lila talk contribs created page Single Transformations of Functions (Created page with "==Introduction== One kind of transformation involves shifting the entire graph of a function up, down, right, or left. The simplest shift is a vertical shift, moving the graph...")
  • 15:43, 15 September 2021 Lila talk contribs created page Order of Differential Equations (Created page with "==Introduction== The order of a differential equation is determined by the highest-order derivative. The higher the order of the differential equation, the more arbitrary cons...")
  • 12:45, 15 September 2021 Lila talk contribs created page Volume of a cylinder (Created page with "thumb|Cylinder geometry The volume of a cylinder is <math> V = \pi r^2h </math>, where <math> r </math> is the radius of the circular base of th...")
  • 12:37, 15 September 2021 Lila talk contribs created page Areas of basic shapes (Created page with "Shape terminology Basic area formulas ==Resources== * [https://www.mathsisfun.com/area.html Area of Basic Shap...")
  • 11:43, 15 September 2021 Lila talk contribs created page Absolute Value Functions (Created page with "In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, |x| = x if x is positive, and...")
  • 09:21, 15 September 2021 Lila talk contribs created page Zeros of Polynomials (Created page with "==Resources== * [https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/evaluate-a-polynomial-using-the-remainder-theorem/ Finding Zeros with Remainder Theorem], Lum...")
  • 17:51, 14 September 2021 Lila talk contribs created page Dividing Polynomials (Created page with "* [https://courses.lumenlearning.com/waymakercollegealgebra/chapter/polynomial-long-division/ Polynomial Long Division], Lumen Learning * [https://www.purplemath.com/modules/p...")
  • 16:47, 14 September 2021 Lila talk contribs created page Range of a Function (Created page with "==Definition== In mathematics, the range of a function may refer to either of two closely related concepts: * The codomain of the function * The image of the function Given tw...")
  • 16:20, 14 September 2021 Lila talk contribs created page Graphs (Created page with "==Resources and Examples== * [https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/plotting-ordered-pairs-in-the-cartesian-coordinate-system/ Plotting Points on a...")
  • 13:37, 14 September 2021 Lila talk contribs created page Solving Equations and Inequalities (Created page with "==Resources and Examples== ===General Resources=== * [https://tutorial.math.lamar.edu/classes/alg/Solving.aspx Solving Equations and Inequalities], Paul's Online Notes * [http...")
  • 12:25, 14 September 2021 Lila talk contribs created page Simplifying Radicals (Created page with "==Resources and Examples== * [https://courses.lumenlearning.com/boundless-algebra/chapter/radicals/ Introduction to Radicals], Lumen Learning: Boundless Algebra * [https://www...")
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