Ppt on polynomials and coordinate geometry practice

ACT and SAT Prep Math Strategies 2013-2014 Hyman.

equations by factoring. What’s on the Test? Intermediate Algebra and Coordinate Geometry Intermediate Algebra (15%). Questions in this content area are based on an understanding of the quadratic formula, rational and radical expressions, absolute value equations and inequalities, sequences and patterns, systems of equations, quadratic inequalities, functions, modeling, matrices, roots of polynomials, and complex numbers. Coordinate Geometry (15%). Questions in this content area are based on graphing/

MODELING MATTER AT NANOSCALES 3. Empirical classical PES and typical procedures of optimization 3.05. Molecular Dynamics.

by a polynomial and the complete solution is obtained after the evaluation of the derivative: with different values of variables obtained by the polynomial in each one/and  the torque (depending on the applied rotational force and the distance between the point of application and the center) acting on the molecule that originates the motion of such coordinate during the simulation. Stages of the Simulation 34 Initialization  Each participating center is initially placed according a trial or guess geometry/

Signal- und Bildverarbeitung, 323

coordinate systems and independence of the choice of coordinates. This is differential geometry, a field designed for the structural description of space and/coordinates This gives Lw= Lww= Lvv= Lvv + Lww = … Lxx+Lyy First order gauge coordinates The gauge coordinates are not defined if & In practice however this is not a problem: we have a finite number of such points, typically just a few, and/differential feature detectors are special (mostly) polynomial combinations of image derivatives, which exhibit /

What is So Spectral? SIGGRAPH 2010 Course Spectral Mesh Processing

Polynomial (e.g., Laplacian): matrix-vector multiplication Rational polynomial (e.g., Butterworth): solving linear systems Spectral compression needs explicit spectral transform Efficient computation to be discussed by Bruno Towards spectral mesh transform Signal representation Vectors of x, y, z vertex coordinates Laplacian operator for meshes Encodes connectivity and geometry Combinatorial: graph Laplacians and/but select first k in practice Example: intrinsic geometry Our first example: correspondence /

The PARCC Institute Middle School and High School Math Preparing for PARCC! NJ’s Next Generation Standardized Assessment System Judith T. Brendel - Spring.

and Expectations of Fluency and Conceptual Understanding UNIT-1 Congruence, Proof, and Constructions UNIT-2 Similarity, Proof, and Trigonometry UNIT-3 Extending to Three Dimensions UNIT-4 Connecting Algebra and Geometry Through Coordinates UNIT-5 Circles With and Without Coordinates UNIT-6 Applications of Probability Focus Areas in Mathematics (CCSS) - HS 46 ALG. - 2 Focus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding UNIT-1 Polynomial, Rational, and/

ALGEBRA 2; AGENDA; DAY 48; MON. Oct. 31, 2011 BENCH WARMER:Find the determinant of the 3 x 3 matrix OBJECTIVE: FINDING THE DETERMINANT AND USING CRAMER’S.

function is U-shaped and is called a parabola. The parabola opens up if a > 0 and opens down if a < 0. The parabola is wider than the graph of and narrower than the graph of The x-coordinate of the vertex is / DAY 77 ; WED. DEC. 14, 2011 BENCH WARMER: Simplify the complex number. OBJECTIVE: Classify polynomials; Using the difference to determine the degree. Graph polynomial functions and describe end behavior. ACTIVITIES: Worksheet Practice 5.1 HOME LEARNING: Pg. 286 # 40 – 46 ALGEBRA 2; AGENDA; DAY 78 ; /

ALGEBRA 2; AGENDA; DAY 48; MON. Oct. 31, 2011 BENCH WARMER:Find the determinant of the 3 x 3 matrix OBJECTIVE: FINDING THE DETERMINANT AND USING CRAMER’S.

and is called a parabola. The parabola opens up if a > 0 and opens down if a < 0. The parabola is wider than the graph of and narrower than the graph of The x-coordinate/ number. OBJECTIVE: Classify polynomials; Using the difference to determine the degree. Graph polynomial functions and describe end behavior. ACTIVITIES: Worksheet Practice 5.1 HOME LEARNING:/GEOMETRY TESTING. NO ALGEBRA 2 CLASS ALGEBRA 2; AGENDA; DAY 89 ; TUE. JAN. 17, 2012 BLOCK SCHEDULE: Periods 1, 3, & 5 BENCH WARMER: Write a polynomial/

Beth Simpson- ELA Assessment Specialist Smarter Balanced Teacher Involvement Coordinator Digital Library State Lead Anton Jackson- Mathematics Assessment.

IABs Algebra and Functions - Linear Functions Algebra and Functions - Quadratic Functions Algebra and Functions - Exponential Functions* Algebra and Functions - Polynomials Functions* Algebra and Functions - Radicals Functions* Algebra and Functions - Rational Functions* Algebra and Functions - Trigonometric Functions* Geometry - Transformations in Geometry* Geometry - Right Triangle Ratios in Geometry Geometry - Three - Dimensional Geometry* Geometry – Proofs* Geometry – Circles* Geometry – Applications/

Enrich Transformations and Polynomials Instruction with Technology Using Geometer’s Sketchpad to Explore Transformational Geometry iLearn Grade 8 Math.

handout “Steps to Modify a Premade GSP Sketch” to complete the Problem Set. Guided Practice Open Reflection.gsp. Create instructions and questions for page 293 of “IMPACT Math” directly in Geometer’s Sketchpad using the text/Coordinate Reflect.gsp 5.5 PS D Coordinate Translate.gsp Whole chapterRooBooGoo.gsp How is the sketch related to the problem set? Share Let’s look at some of the questions and instructions you created. Share How can Geometer’s Sketchpad help develop skills in transformational geometry/

Self-calibration and multi-view geometry Class 10 Read Chapter 6 and 3.2.

practical than the DIAC! Kruppa equations Limit equations to epipolar geometry /geometry Backprojection Represent point as intersection of row and column Useful presentation for deriving and understanding multiple view geometry (notice 3D planes are linear in 2D point coordinates) Condition for solution? Multi-view geometry/and use it for calibration (x,y) 39 Dealing with Wide FOV Camera Two-step linear approach to compute radial distortion Estimates distortion polynomial of arbitrary degree (Thirthala and/

Math with a Twist! Algebra 1 Geometry Algebra 2.

and Equations 3 Graphs 4 Lines 5 Introduction to Functions 6 Exponents and Radicals 7 Polynomials 8 Quadratics Geometry 1 An Informal Introduction to Geometry 2 Congruence and Proof 3 Dissections and Area 4 Similarity 5 Circles 6 Using Similarity 7 Coordinates and/Mathematical Approaches Pedagogical Approaches Implementation Guide Worked out solutions Detailed explanations Clear images and graphs Solutions Manual Additional Practice Lesson Quizzes Chapter Tests Quarter Tests Midyear Test End-of-Year Test /

Lunch and Learn: A Collaborative Time for North Carolina Teachers Your Presenter Information.

previous understandings of multiplication and division to multiply and divide fractions. Measurement and Data  Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Operations and Algebraic Thinking  Write and interpret numerical expressions.  Analyze patterns and relationships. Measurement and Data  Convert like measurement units within a given measurement system.  Represent and interpret data. Geometry  Graph points on the coordinate plane to solve/

CG Architectures, Image Formation, and Models Angel, Chapter 1 CSCI 6360.

and surfaces –Quadrics –Parametric polynomials –All are defined through locations in space or vertices Graphics Library Functionality Preview 1. Primitives –2D and 3D –All about vertices, meshes, and/ approach –Very slow Pipeline Architecture Practical Approach Process objects one at a/Geometry Fragment Display “Application Program” Logic and processes Networking User input events Etc. … GPU CPU Vertex transformations Vertex lighting Clipping Primitive assembly Convert triangles to fragments Tex coordinate/

Collaborative Science: Give us your information, not your conclusions Andy Packard Mechanical Engineering jointly with Michael Frenklach, Ryan Feeley and.

including parameter ρ 34 illustrates the inaccuracy. Key issue: Geometry of feasible set (not a coordinate-aligned cube) is unappreciated. E 66 E 67 ρ /, and N dataset units) The invalidation certificate is a binary tree, with L leaves. At the i’ th leaf –coordinate-aligned cube –Polynomial/rational/and scales Present challenges –Community involvement and participation –Privacy versus Open/Community Analyzing proprietary data –Convenient infrastructure –Math analysis methods Is a rich, large-scale, practical/

Practical parametric geometry for aircraft design

Python programming language J. Philip Barnes www.HowFliesTheAlbatross.com Practical parametric geometry for aircraft design Abstract Practical parametric geometry for aircraft design J. Philip Barnes, Technical Fellow, Pelican Aero Group Theory and application of practical methods for aircraft geometry parameterization and visualization are described. The methods, characterizing the surface geometry of complete aircraft, wings, fuselages, ducts, and new or existing airfoils, include fidelities ranging from/

Spectral Mesh Processing

Polynomial (e.g., Laplacian): matrix-vector multiplication Spectral compression needs explicit spectral transform Spectral mesh transform Signal representation Vectors of x, y, z vertex coordinates Laplacian operator for meshes Encodes connectivity and geometry Combinatorial: graph Laplacians and/ 93, Fouss et al. 06] Full set of eigenvectors used, but select first k in practice Main references Last view: dim reduction Spectral decomposition Full spectral embedding given by scaled eigenvectors (each scaled/

9 th Grade TAKS - Released Tests - by Objective Objective 1 1 Functional relationshipsFunctional relationships 2Properties and attributes of functions.

and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. (A) The student finds specific function values, simplifies polynomial expressions, transforms and solves equations, and/ Abe practices golf /Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to (D) locate and name points on a coordinate plane using ordered pairs of rational numbers. Points K and/

Curriculum Night Thursday, February 23 6:00pm and 7:30pm.

and special segments intersecting circles transformations coordinate geometry surface area and volume of three-dimensional objects proofs Algebra 2 The content of the Algebra 2 course encompasses: functions systems of equations systems of linear inequalities quadratic equations complex numbers algebraic expressions nonlinear relationships including exponential, logarithmic, radical, polynomial, and/Accounting concepts, principles, and practices *Prerequisite Accounting I and teacher approval Student develops/

Of 29 August 4, 2015SIAM AAG: Algebraic Codes and Invariance1 Algebraic Codes and Invariance Madhu Sudan Microsoft Research.

retrieval … PCPs, Small-set expanders, Hardness amplification, Private information retrieval … Maybe even in practice Maybe even in practice Aside: Related to LRCs from Judy Walker’s talk. Aside: Related to LRCs from Judy / … … and a few composition operators preserve it. … and a few composition operators preserve it. Canonical example: Reed-Muller Codes = low- degree polynomials. Canonical example: Reed-Muller Codes = low- degree polynomials. August 4, 2015SIAM AAG: Algebraic Codes and Invariance18 of/

Picking and Curves Week 6 David Breen Department of Computer Science Drexel University Based on material from Ed Angel, University of New Mexico CS 480/680.

and we should be able to determine to which object(s) a position corresponds Practical/at ( x, y ) in the window coordinates within the viewport vp Go to pick.c / © Addison-Wesley 2002 25 Why Polynomials Easy to evaluate Continuous and differentiable everywhere –Must worry about continuity/geometry continuity) The latter gives more flexibility as we have need satisfy only two conditions rather than three at each join point Angel: Interactive Computer Graphics 3E © Addison-Wesley 2002 42 Example Here the p and/

9 th Grade TAKS - Released Tests - by Objective Objective 1 1 Functional relationshipsFunctional relationships 2Properties and attributes of functions.

and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to: (A) find specific function values, simplify polynomial expressions, transform and solve equations, and/2004 #7 The number of hours Abe practices golf each week, g, is 2 more/Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to (D) locate and name points on a coordinate/

© Worboys and Duckham (2004) GIS: A Computing Perspective, Second Edition, CRC Press Chapter 1 Introduction.

Angle and parallelism- translations rotations, and scalings Geometry and invariance © Worboys and Duckham (2004) GIS: A Computing Perspective, Second Edition, CRC Press 3.1 Euclidean space What is a GIS Data and databases Hardware support Functionality © Worboys and Duckham (2004) GIS: A Computing Perspective, Second Edition, CRC Press Euclidean Space Euclidean Space: coordinatized model of space Transforms spatial properties into properties of tuples of real numbers Coordinate frame/

Unstructured Grids. Advancing Front Method. V. Selmin Multidisciplinary Computation and Numerical Simulation.

coordinates u and v with varies on the interval [0,1]. The position r of a node on the surface can then be expressed as a polynomial expansion in u and v on each patch : The total rank of the polynomial is n x m, whereas n and m represent the rank of the polynomial/but it has been found that to be advantageous in practice to consider the smallest faces first. For this purpose, /the list of mesh sides connected to a given node. - Mesh geometry queries: For instance, give all the smallest side contained in a /

Algorithm Design and Analysis (ADA)

zeta function distribution of the primes Birch and Swinnerton-Dyer Conjecture concerns elliptic (~cubic) curves, their rational coordinates, and the zeta function; wide uses (e.g/polynomial equations) and calculus (integration) techniques so only algebra is needed to define them a solution would strongly link topology, analysis and algebraic geometry Yang-Mills Theory (and/1 2 2 2 2 1 1 1 TSPs (and variants) have enormous practical importance Lots of research into good approximation algorithms Recently made/

3D Photography Project An Overview of 3D Photography and The Computational Aspect of Triangle Mesh By Muhammed Santa for 3D photography class, Prof. Ioannis.

coordinates of the object and/Coordinate Recovery: usually involves internal image geometry and camera information.Camera coordinates c(x) and c(y),projector coordinates p(x) and p(y) are needed along with intrinsic parameters c,f,k of the device to determine the 3D coordinates/and/and bilinear and trilinear interpolation could be used for better results. Delaunay triangulation or other surface interpolation methods like polynomial/geometry of the /geometry/and/and/and/and/ center px,py and radius rad of /and/

Multimodal User Authentication: From Theory to Practice

geometry Retina Iris Signature Keystroke dynamics Gait DNA (requires physical sample) Wrist/hand veins Brain activity etc. In theory many of these biometric identifiers should be universal. However, in practice this is not the case. Ideally, a biometric identifier should be universal, unique, permanent and measurable However, in practice/D space Euclidean distances between the K coordinates representing the new face and each of the K-dimensional vectors / 0.54 Linear-SVM 0.07 Polynomial-SVM 0.21 RBF-SVM 0./

GIS Data Preparation and Integration

between features and rules about these relationships --managing data cognizant of shared geometry Implies knowledge /polynomial fitted by least squares between known ground control coords and tic point coords in GIS “Least squares” minimizes the sum of the squared distances between tic/tie pairs derived parameters then applied to all coordinates/and Corrrection Autonomous Hand-held unit provides 10m accuracy (with SA off) $150-$1,500 per unit WAAS (wide area augmentation system) <3 meter accuracy in practice/

CG Architectures, Image Formation, and Models Angel, Chapter 1 CSCI 6360/4360.

at all times Radiosity –Energy based approach –Very slow Pipeline Architecture Practical Approach Process objects one at a time in the order generated by /geometry based on vertices (or, just a bunch of points): MUCH of work in graphics deals with “just points” –E.g., vertex processing and clipping “Effective parallelization” plus several to dozens to hundreds of graphics processors (cores) leads to fast graphics Also, much of the work in pipeline is in converting object representations from one coordinate/

Boundless Lecture Slides Free to share, print, make copies and changes. Get yours at www.boundless.com Available on the Boundless Teaching Platform.

positions of two rows, multiply a row by a nonzero scalar, and add to one row a scalar multiple of another. In practice, one does not usually deal with the systems in terms of equations/polynomial equation of the first degree (such as x = 2y - 7). linear system A mathematical model of a system based on the use of a linear operator. matrix A rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and/

State of the State Mathematics K-12. What’s New? Next Generation Content Standards and Objectives and Standards for Mathematical Practice Smarter Balanced.

I – 6 units Creating equations Function families – linear and exponential Systems Descriptive Statistics Congruence, Proof and Constructions Connecting Algebra and Geometry through Coordinates Math II – 6 units Extending the number system (includes polynomials and complex numbers) Quadratic functions and modeling Expressions and equations Application of Probability Similarity, Right Triangle Trigonometry, and Proof Circles With and Without Coordinates 4 th course options document Learning Progressions A/

LEDAS Solutions for Mechanical System Modeling and Related Problems Egor Ermolin (LEDAS)

all pairs Detects collisions and returns coordinates of a contact points and normal vectors It supports line segments and arcs as geometry primitives and uses direct collision detection /OBB-comparison. This stage can be optimized up-to O(nlogn) comparison (in practice O(n)), but even this is not top of high- performance… * Data / and can be described by “rotating calipers” model 3D case also operates on convex mesh and involves Gaussian sphere structure to test configuration. It requires polynomial /

Collaborative Science: a case study and model Andy Packard, Michael Frenklach Mechanical Engineering jointly with Ryan Feeley and Trent Russi University.

and/and /and/and theory, experiments, analysis and/and assessing uncertainty in outcome measurement Informal description of transport and/  44 and  45 and then reads report/Geometry of feasible set (not a coordinate/and/and/and/and/models and /and/and/coordinate/and 76 assertions, yielding the consistent coordinate/and spread more evenly across data /and/and C 3 H 2 ; I can then discriminate between hypotheses B and/and/and/and/coordinate-aligned cube –collection of polynomial models and error bounds, which/

CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Analytic Geometry B/Advanced Algebra Unit 2: Quadratic Function July 31, 2013 Session will.

Practice What’s the big idea? SMP 1 – Make sense of problems and persevere in solving them SMP 3 – Construct viable arguments and critique the reasoning of others SMP 6 – Attend to precision https://www.teachingchannel.org/videos/class-warm-up-routine Coherence and Focus K-9 th  Algebraic expressions  Properties of operations  Radicals and integer exponents with numerical expressions 11th-12th  Polynomial identities and equations  Polynomial/which the archer stands, and the coordinate pair (2,5) /

Crystallography and Diffraction. Theory and Modern Methods of Analysis Lectures 11-12 Rietveld Analysis Dr. I. Abrahams Queen Mary University of London.

polynomial function. The indices of the polynomial are usually refined as part of the refinement procedure. However increasing the order of the polynomial does not necessarily improve the fit and/and starting model. The key point is to make sure the refinement starts with accurate unit cell and zero point parameters. It is always good practice to refine the unit cell parameters and/, but without the atomic coordinates of the structural model. It uses the space group and unit cell information to calculate/

1 ECG Saarbrücken Robustness issues & CAD André Lieutier Robustness issues in Geometric computations for Computer Aided Design André Lieutier practices.

practices and formalization 2 ECG Saarbrücken Robustness issues & CAD André Lieutier summary 1.Part 1: (practice) –BRep Model and/and Surfaces for Solid Modelling Piecewise Polynomial and rational Trigonometric and primitives Offset surfaces Subdivision Abstract data type Functions 5 ECG Saarbrücken Robustness issues & CAD André Lieutier Piecewise polynomial and rational curves and surfaces Given by the NURBS knots and/ management near discontinuities change of coordinates.. (projective space,...) 21 ECG/

Navigation and Ancillary Information Facility NIF Introduction to the SPICE Ephemeris Subsystem SPK Focused on reading SPK files October 2007.

and velocity) vectors of ephemeris objects from an SPK file one normally needs two kinds of SPICE kernels –Leap seconds kernel (LSK) »Used to convert between Coordinated Universal Time (UTC) and/in other SPICE routines to compute observation geometry of interest. Loop... do as many /polynomials for position, velocity given by differentiation) is used for JPL planetary ephemerides. SPK type 3 (Separate Chebyshev polynomials for position and/ one segment »Maximum: The practical maximum is a few thousand segments/

Geometry lesson 1.1 Sample Warm Up & Test questions 1. What is inductive reasoning? 2. What is a conjecture? 3. Are conjectures always true? 4. A student.

practices many hours a week? 2. How many minutes/hours of Math homework per day do you think is appropriate for this class? Justify your answer. Geometry/1, 0) then AB = ? 5. Find the coordinates of the midpoint of AB using the coordinates above. Analysis lesson 3.2B Warm Up/Reflection 1./polynomial and list the multiplicities. Y = 4x 2 ( x – 2 ) ( x + 7 ) 3 Geometry lesson 4.1 Warm Up 1. Tell which of the following describes deductive reasoning and which describes inductive reasoning. 1) Arguing with “if and/

TASC. Copyright © 2013 CTB/McGraw-Hill LLC. Agenda TASC Overview – TASC Common Core transition – TASC test design and developmental foundation – Subtests.

and adult education centers as they shift from current preparation practices to those required for the full depth and/Polynomials and Rational Expressions Algebra: Reasoning with Equations and Inequalities Algebra: Creating Equations Algebra: Seeing Structure in Expressions Functions: Interpreting Functions Functions: Linear, Quadratic, and Exponential Models Geometry: Geometric Measurement with Dimension Geometry: Modeling with Geometry Number and/ by the Test Coordinator Manual and Examiner Manual 39 /

1 An Overview of Trilinos Mark Hoemmen Sandia National Laboratories 30 June 2014 Sandia is a multiprogram laboratory managed and operated by Sandia.

and leaders Framework, Tools, & Interfaces (Jim Willenbring) Software Engineering Technologies & Integration (Ross Bartlett) Discretizations (Pavel Bochev) Geometry/coordinate-based) methods: Recursive Coordinate Bisection Recursive Inertial Bisection Space Filling Curves Refinement-tree Partitioning Hypergraph and/), H(div) Extensively exercised in practice Broad user base with hard problems However/ Energy minimization Smoothers and direct solvers Ifpack(2) (Jacobi, Gauss-Seidel, ILU, polynomial, …) Amesos(2/

The Finite Element Method A Practical Course

– plane stress and plane strain LINEAR TRIANGULAR ELEMENTS Less accurate than quadrilateral elements Used by most mesh generators for complex geometry Linear triangular element/For evaluation of integrals in ke and me (in practice) In 1 direction: m gauss points gives exact solution of polynomial integrand of n = 2m - /functions for coordinate interpolation and displacement interpolation do not have to be the same. Using the different shape functions for coordinate interpolation and displacement interpolation/

Perceptrons “From the heights of error, To the valleys of Truth” Piyush Kumar Computational Geometry.

Compare And correct Where is the geometry? Class 1 : (+1) Class 2 : (-1) Is this unique? Assumption Lets assume for this talk that the red and green/“Homogenize” the coordinates by adding a new coordinate to the input. Think of it as moving the whole red and blue points in/polynomial time guarantee (Using smoothed analysis)! Why learn Perceptrons Multiple perceptrons clubbed together are used to learn almost anything in practice. (Idea behind multi layer neural networks) Perceptrons have a finite capacity and/

Parameterization. Introduction The goal of parameterization is to attach a coordinate system to the object –In particular, assign (2D) texture coordinates.

(no flips). 20 Quadratic Optimization Quadratic form: a polynomial function that the degree is not larger than two. /, Pierre Alliez and Bruno Levy, AK Peters, 2010 “Mesh Parameterization: Theory and Practice”, Kai Hormann, Bruno Lévy and Alla Sheffer,/and Jérome Maillot, ACM SIGGRAPH conference proceedings, 2002 38 AiAi AbAb AiAi AbAb 39 BACK [From Siggraph Course 2007] Study inverse of parameterization (X,Y)  (u,v) ( i,  j,  k ) barycentric coordinates, computed as: 40 M T solely depends on the geometry/

1 Percolation, Cluster and Pair Correlation Analysis (L22) Texture, Microstructure & Anisotropy, Fall 2009 A.D. Rollett, P. Kalu Last revised: 22 nd Nov.

is connected to z neighbours, where z is called the coordination number. It can be seen as a tree-like structure/. This is easiest to understand with the help of practical, physical examples. As an example of a time-based/. 64. R. J. Baxter, S. B. Kelland and F. Y. Wu, Equivalence of the Potts model or Whitney polynomial with an ice-type model, J. Phys. A 9 /#91. 99. D. A. Klarner, Polyminoes, Handbook of Discrete and Computational Geometry, ed. J. E. Goodman and J. ORourke, CRC Press, 1997, pp. 225-240. 77 /

Ship Computer Aided Design MR 422. Geometry of Surfaces 1.Introduction 2.Mathematical Surface Definitions: Parametric vs. Explicit vs. Implicit. 3.Analytic.

Geometry/. Parametric surface definition: In either 2-D or 3-D, each coordinate is expressed as an explicit function of two common dimensionless parameters: x /polynomial) surface in u and v. Within each span, the surface is analytic (continuous derivatives of all orders) At the knotlines, the spans join with levels of continuity depending on the spline degree. Cubic spline surfaces have C 2 continuity across their knotlines, which is generally considered adequate continuity for all practical visual and/

Dynamic Data Driven Application Systems (DDDAS) A new paradigm for

Management Manufacturing Product DBs Inventory Shipping Application Integration Interoperability Process Coordination Management & Monitoring Business to Enterprise Messaging Data Integration Interoperability Mobile Workers/data and computational resources. Modeling Uncertainty Stochastically-excited structures Irreducible versus epistemic uncertainty Stochastically-excited structures Boundary conditions, geometry, properties Sensitivity/failure analysis Gaussian and non-Gaussian processes Polynomial /

Layered Graph Drawing (Sugiyama Method). Drawing Conventions and Aesthetics n a digraph n A possible layered drawing.

Graham nNetwork Simplex Grafo1012 (Di Battista et al., Computational Geometry: Theory and Applications, (7), 1997) Longest Path Layering Coffman-/ 3. Minimizing # of dummy vertices none can compute a layering in polynomial time that minimizes the number of dummy vertices [GKNV93] f = /and to the right of p otherwise –Apply recursively to the left & right of p –O(|L2| 2 ) time in worst case; O((|L2|log (|L2|) in practice Adjacent-Exchange Split 2. The Barycenter Method nThe most common method nx-coordinate/

Begin with the End in Mind: Common Core State Standards and Next Generation Assessments Susan A Gendron Senior Fellow International Center for Leadership.

Structure in Expressions Arithmetic with Polynomials and Rational Expressions Creating Equations Reasoning with Equations and Inequalities Functions Interpreting Functions Building Functions Linear, Quadratic and Exponential Models Trigonometric Functions Modeling Identify the problem Formulate a model Analyze and perform operations Interpret results Validate the conclusion Report on the conclusion Geometry Congruence Similarity, Right Triangles, and Trigonometry Circles Expressing Geometric Properties/

Welcome to Curriculum Night! Lindsay Hawkins 8A Linear Algebra, Algebra, and Geometry.

that are aligned to Arizona State Standards –Geometric Properties –Basic Concepts and Proofs –Transformation of Shapes –Coordinate Geometry http://www.kyrene.org/curriculum/Math%20Resources/Middle%20school/Geometry_2006_math_curriculum_map.doc Topics include… Patterns and Sequences Geometric Probabilities Similarities Circles and Circle Theorems Transformation Matrices 3D Geometry Surface Area and Volume Trigonometry of the Right Triangle Honors Geometry 1-2 –May change in the upcoming month… How Do I/

Reaching for the Stars Using Data Analysis and Effective Teaching Strategies to improve the achievement of ALL students Prepared for the Loudoun County.

.64 Coordinate Rel.//Geometry – 6Q/50Q – 12% of test(33% of questions < 70% correct) Given the equation for a conic section, describe its graph.50 Given the x-intercepts of a polynomial/and linguistically relevant; and strives to be culturally and linguistically relevant; and relies on shared responsibility and collaboration. relies on shared responsibility and collaboration. Office of Educational Research and Improvement (OERI), US DOE, 2000 7.6 The student will use proportions to solve practical/


Creating, reading, and manipulating expressions –Understanding the structure of expressions –Includes operating with polynomials and simplifying rational expressions Solving equations and inequalities – Symbolically and graphically Algebra Required for higher math and/or STEM / Functions, Modeling, Geometry, Statistics & Probability Standards of Mathematical Practice 1.Choose a partner at your table and “Pair Share” the Standards of Practice between you and your partner. 2. When you and your partner feel you/

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