[PDF] Mordell’s Equation

FUNCTIONAL EQUATIONS

Example 2 1 Let a , 1 Solve the equation af(x) + f(1 x) = ax; where the domain of f is the set of all non-zero real numbers Date: November 7, 2016 Lecture notes for the Math Circle, Irvine Partially supported by the NSF grant DMS-1510232 1

Equation Vocabulary; Patterns, Functions, and Algebra; 6

equation, using a different color for each word Also, have students write definitions of each vocabulary word without referring to the organizer Then, display the Equation Vocabulary Example Key, and have students correct their handout, as needed 3 Distribute copies of the Equation Vocabulary handout, and have students work in pairs to

Equation Editor and MathType: Top Tips from an Expert

equations, equation numbers, or chapter/section breaks This is similar to the way you can click an icon in Word and go to the next page – Equation Browse – Clicking the right arrow will take you to either the next equation in the document, and the left arrow will take you to the previous equation

Mordell’s Equation

The Equation y2 = x3 + k; k 2Z f 0g Called Mordell’s equation because of Mordell’s (1888-1972) lifelong interest in it Earlier named after Bachet (1581{1638) y2 = x3 + 1 Outline Examples without integral solutions Examples with integral solutions Connection to the abc-conjecture

Solving the Quartic Equation

Solving the Quartic Equation Our goal is to learn how to nd the roots of ax4+bx3+cx2+dx+e = 0, where a 6= 0 The rst person to discover how to do this was Lodovico de Ferrari (who lived 1522-1565), but we will follow Descartes’ Method (Descartes lived 1596-1650, and published his method in 1637) Stage 1

Algebra Worksheet -- Determining the Equation from a Linear

LinearEquationGraphs(A)Answers Name: Date: Determinetheequationofeachlinefromitsgraph x y-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10-10

Math 456 Lecture Notes: Bessel Functions and their

1 The Transport Equation

1 The Transport Equation The transport equation models the concentration of a substance owing in a uid at a constant rate De nition 1 For parameters c2R, the transport equation on R R+ is u t+ cu x= 0: (1) The corresponding IVP for the transport equation is (u t+ cu x= 0 x2R;t>0 uj t=0 = f(x) x2R: (2)