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. 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. 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).. Pawlak’s. Rough Sets. Section 2.4. Properties of Approximations. Proposition 2.2. Proof (1). Proof (2). Proof (3). Proof (4). Proof (5). Proof (6). Proof (7). Proof (8). Proof (9). Proof (10). Proof (11). Section 9.3a. While it is beautiful that certain functions can be. r. epresented exactly by infinite Taylor series, it is the. inexact Taylor series that do all the work…. In practical terms, we would like to be able to use. Local algebraic approximations. Variants on Taylor series. Local-Global approximations. Variants on “fudge factor”. Local algebraic approximations. Linear Taylor series. Intervening variables. Transformed approximation.  . in Various Civilizations. Rachel Barnett.  . BC. Babylon. ∏. = . 3 ⅛ = 3.125. A. B. C. D. E. Egypt. ∏ . = 4(8/9)² = 3.16049…. Problem number 50 . Rhind Papyrus. m. otivation, capabilities. 1D theory .  1D-solver for waves. i. mplementation (without and with Lorentz transformation). e. xcitation of waves (single particle). w. ithout self effects. one and few particles with self effects. Insu. Yu. 27 May 2010. ACM Transactions on Applied Perception . (Presented at APGV 2009). Introduction. Can you see difference ? . Traditionally GI (Path tracing, photon mapping, ray-tracing) uses . 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 . 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 . Plot both x & y intercepts to graph.. A-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, multiplication and division..