Orthogonal polynomials

begun a new unit that involves unpacking polynomial expressions. The common core standards that apply are; Expressions A-SSE.1 Interpret parts of an expression, such as terms, factors and coefficients. Arithmetic with polynomials and Rational Expression A-APR.1 Understand that polynomials form a system analogous to the integers, namely that they are closed under the operations of addition, subtraction and multiplication; add, subtract, and multiply polynomials. This particular unit is important because

In Logit and Probit models, a dependent variable takes only two values that represent the occurrence of an event (yes or no) or a choice between two alternatives. In the current case, to model choice status of each individual WTP for improved solid waste management respondents differed in age, educational attainment, income, sex and other observable characteristics. These are denoted by S. In the dichotomous choice method, individuals are assumed to have utility function, U, income (I), and a set

Programmatically Computing Mathematical Constants Many mathematical constants are useful for programming. For instance, if you need to use the transcendental number pi, you need to calculate it somehow. I set out to create a “library” of sorts to calculate as many mathematical constants as I could. Constant Explanation and Code Alladi-Grinstead constant The Alladi-Grinstead constant is defined as ec-1, where ck=21kln(kk-1). To do summation (), one has to use a for-loop with precision-limiting behavior

No Reasoning Without Algebra I am a math major, I love and excel at math, and I failed my first algebra test. I know of many people who hate math, who struggled with math, who could not get past algebra, no matter how hard they tried. Yet we cannot blame them—and we cannot blame algebra either. I got past that test and I passed the class, and algebra has helped me in countless ways, and it has made me a better student. It is the responsibility of schools to prepare students for the working

Problem 4. Prove that (y^3+z^3 ) x^2+yz^4 is irreducible over C[x,y,z]. Also prove that (y^3+z^3 ) x^2+y^2 z^3 is irreducible. Assume that (y^3+z^3 ) x^2+yz^4=a*b. Then one of a or b is linear in x^2 and the other doesn’t have x^2 at all because the degree of the product is the sum of the two degrees. Now we write 〖a=cx〗^2+d, so c and d have only y’s and z’s. Then (y^3+z^3 ) x^2+yz^4=(〖cx〗^2+d)*b But now b*d=yz^4, and since C[y,z] is a unique factorization domain, b and d must be monomials.

This is my personal favorite chapter. You can factor polynomials in a few different ways: by GCF, through the form X2+BX+C, through the form AX2+ BX+C, and by graphing. There is a way that Mrs. Ladner teaches to factor called “Big X Bottoms Up” that uses either the X2+BX+C or AX2+BX+C. To do this method

Sketch a graph of the polynomial f(x) = (x-2)3Compute the results of the following operations involving polynomials: 4.(5k4+2k3+8)-(k2+4) 5.(x+2)(x2 + 4x +2) 6.Rewrite the polynomial expression T = (-0.01897V + 25.41881 V2 - 0.42456 V3 + 0.04365 V4)/V Student does not recognize quadratic function Student does not infer from graph intersections in creating equation How can you recognize a graph from each of the function families? Which function family does this graph belong to? What is the general

The shape of the basis parabola y=x2 changes for different forms of the parabolic function causing it to translate, reflect or dilate. Dilation (widening or narrowing) of the parabola occurs when the basis parabola y=x2 is multiplied or divided (m) therefore changing the equation to either y=mx2 or y=x^2/m. For instance, if the parabola is multiplied by two the parabola becomes narrower whereas if the parabola is divided by two the parabola becomes wider. This is evident in the graph in question

exact answer. A problem of great importance in science and engineering is that of determining the roots/zeros of an equation of the form f(x) =0 A polynomial equation(algebraic equation) f(x)= Pn(x) = a0xn + a1xn-1 +a2xn-2 + - - - - - - - - - - - - - - - - - - - + an-1x + an An equation that contains polynomials, exponential functions, trigonometric functions etc.

IB Mathematics SL I IA Lab: Infinite Summation Kristen Rodríguez Mr. Zivkovich May 2010 1 When one considers the concept of infinite summation, there are many observable patterns between the exponent on the numerator and both the result and the sum of the series. This investigation aims to explore this concept of infinite summation and finally arrive at a general statement to determine the sum of the infinite sequence tn. The analysis will also discuss the scope and limitations of the general