PPT-Taylor Polynomials & Approximations

Section 87 AP Calculus Taylor Polynomials are used to show that polynomial functions can be used as approximations for other elementary functions To find P to approximate f choose c st Pcfc. Taylor January 2005 Taylor diagrams Taylor 2001 provide a way of graphically summarizing how closely a pattern or a set of patterns matches observations The similarity between two patterns is quantified in terms of their Polynomials are attractive because they are well understood and they have signi64257cant simplicity and structure in that they are vector spaces and rings Additionally degreetwo polynomials conic sections that are also known as quadrics show up in m 1 This relation is the socalled binomial expansion It certainly is an improvement over multiplying out ababab by hand The series in eq 1 can be used for any value of n integer or not but when n is an integer the series terminates or ends after n1 te Polynomials are attractive because they are well understood and they have signi64257cant simplicity and structure in that they are vector spaces and rings Additionally degreetwo polynomials conic sections that are also known as quadrics show up in m Local algebraic approximations. Variants on Taylor series. Local-Global approximations. Variants on “fudge factor”. Local algebraic approximations. Linear Taylor series. Intervening variables. Transformed approximation. Goal: To simplify polynomial expressions by adding or subtracting. Standard: . 9.2.3.2 – Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.. Guiding Question: How do I simplify polynomials expressions? AND how do I add or subtract polynomials expressions?. Local algebraic approximations. Variants on Taylor series. Local-Global approximations. Variants on “fudge factor”. Local algebraic approximations. Linear Taylor series. Intervening variables. Transformed approximation. Classify polynomials and write polynomials in standard form. . Evaluate . polynomial expressions. .. Add and subtract polynomials. . Objectives. monomial. degree of a monomial. polynomial. degree of a polynomial. Section 8.7 AP Calculus. Taylor Polynomials are used to show that polynomial functions can be used as approximations for other elementary functions.. To find P to approximate f, choose #c . s.t. . P(c)=f(c).. Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems. Students will know the terms for polynomials.. Students will know how to arrange polynomials in ascending and descending order.. Definitions. Coefficient. : the numerical factor of each term.. Constant. : the term without a variable.. Term. : a number or a product of a number and variables raised . to a power.. Polynomial. : a finite sum of terms of the form . Georgina . Hall. Princeton, . ORFE. Joint work with . Amir Ali Ahmadi. Princeton, ORFE. 1. 5/4/2016. IBM May 2016. Nonnegative and convex polynomials. A polynomial . is nonnegative if . How does . nonnegativity. SOL A.2b. REVIEW. Represent . Polynomials Using Algebra . Tiles. Represent x. 2. 3. 2) Represent x. 2. 4x – 2. . REVIEW. Represent . Polynomials Using Algebra . Tiles. 3) Represent 3x. HW ANS: Day 3 . pg. 170-171 #’s 3,9,11,15,17,19,27,29,35,37,41 . . SWBAT: Divide Polynomials using Long Division Page 13. Do by hand. Factor First. SWBAT: Divide Polynomials using Long Division .