Vectors. Chapter 12. Objectives. Intro Vectors Representing Vectors Algebra and Geometry of Vectors Cartesian Representation of Vectors in 2-D and 3-D Properties of Vectors in 2-D and 3-D Scalar Product of 2 Vectors Vector Equation of a Line. Scalars and Vectors.

ByIterative Solution Methods. Starts with an initial approximation for the solution vector (x 0 ) At each iteration updates the x vector by using the sytem Ax=b During the iterations A, matrix is not changed so sparcity is preserved Each iteration involves a matrix-vector product

ByWhich came first: Vector Product or Torque?. by Antonia Katsinos. CROSS PRODUCT 1844 – Hermann Grassman 1843 – William Rowan Hamilton 1880-1884 Josiah Willard Gibbs 1880 - Oliver Heaviside. TORQUE Rotational/angular force

ByCE 102 Statics. Chapter 3 Rigid Bodies: Equivalent Systems of Forces. Contents. I ntroduction External and Internal Forces Principle of Transmissibility: Equivalent Forces Vector Products of Two Vectors Moment of a Force About a Point Varigon’s Theorem

ByExperimental Mathematics. 25 August 2011. Linear Equations in 2D Space. var('x,y') p=implicit_plot(2*x+3*y==5, (x,-10,10),(y,-10,10)) show(p). Problem 1. Open a new Sage worksheet and do today’s problems within this worksheet.

ByVECTOR CALCULUS. multiplication VECTOR. a b. b. a. Vector Product. CROSS PRODUCT. . Magnitude : Area of the parallelogram generated by a and b. . b. a. Vector Product (contd.). b. a. Vector Product (contd.). . Magnitude :. Direction : Perpendicular to

ByVectors. Addition is commutative. ( vi ) If vector u is multiplied by a scalar k , then the product k u is a vector in the same direction as u but k times the magnitude. Vector Directions. Hold your right hand out in front of you as if to shake hands.

ByChapter 3 Rigid Bodies : Equivalent Systems of Forces. Introduction. In previous lessons, the bodies were assumed to be particles. . Actually the bodies are a combination of a large number of particles. . body . particle . Introduction.

ByMatrix Multiplication. The Myth, The Mystery, The Majesty. Matrix Multiplication. Simple, yet important problem Many fast serial implementations exist Atlas Vendor BLAS Natural to want to parallelize. The Problem. Take two matrices, A and B, and multiply them to get a 3 rd matrix C

ByLow Rank Approximation and Regression in Input Sparsity Time. David Woodruff IBM Almaden Joint work with Ken Clarkson (IBM Almaden). Talk Outline. Least-Squares Regression Known Results Our Results Low-Rank Approximation Known Results Our Results Experiments. Least-Squares Regression.

ByProfiling & Tuning Applications. Overview. Performance limiters Bandwidth, computations, latency Using the Visual Profiler “Checklist” Case Study: molecular dynamics code Command-line profiling (MPI) Auto-tuning. Introduction. Why is my application running slow? Follow on Emerald

ByWireless & Emerging Networking System Laboratory. Chapter 15. The Fast Fourier Transform. 09 December 2013 Oka Danil Saputra (20136135) IT Convergence Kumoh National Institute of Technology. Fourier Analysis . Represent continuous function by sinusoidal (sine and cosine) functions.

ByLossy Trapdoor Functions. Definition and applications. Lossy Trapdoor Functions. Definition [PW08]. Invertible. Lossy. Lossy Trapdoor Functions. Implications. [BKPW12] What about the IB setting ?. Lossy Trapdoor Functions. Constructing a primitive. Setup. Encrypt. Decrypt. Gen.

ByChapter 12 – Vectors and the Geometry of Space. 12.4 The Cross Product. Definition – Cross Product. Note: The result is a vector. Sometimes the cross product is called a vector product . This only works for three dimensional vectors. Cross Product as Determinants.

ByConjugate gradients, sparse matrix-vector multiplication, graphs, and meshes. Thanks to Aydin Buluc , Umit Catalyurek , Alan Edelman, and Kathy Yelick for some of these slides. T he middleware of scientific computing. Continuous physical modeling. Ax = b. Linear algebra. Computers.

ByCDP Tutorial 4 Basics of Parallel Algorithm Design. uses some of the slides for chapters 3 and 5 accompanying “Introduction to Parallel Computing”, Addison Wesley, 2003. http://www-users.cs.umn.edu/~karypis/parbook. Preliminaries: Decomposition, Tasks, and Dependency Graphs.

ByFictitious Force. The Lagrangian is defined in an inertial system. Follows Newton’s laws Equivalent in other inertial systems Hamilton’s equations are similarly unaffected by a change to another inertial system. Inertial Lagrangian. Accelerating Coordinates.

ByContinuum Mechanics. Mathematical Background. Syllabus Overview. Week 1 – Math Review (Chapter 2). Week 2 – Kinematics (Chapter 3). Week 3 – Stress & Conservation of mass, momenta and energy (Chapter 4 & 5). Week 4 – Constituative Equations & Linearized Elasticity (Chapter 6 & 7).

ByWK 2 Homework – due Friday , 9/16 Reading assignment: 1.7 – 1.9 Posted notes on website Reading question: 1.13; 1.16 Questions: 1.32, 31, 38, 41, 55, 59, 68 – the solutions are on the school website. Homework – due Tuesday, 9/20 – 11:00 pm Mastering physics wk 2. Vectors.

ByNumerical Methods for Sparse Systems. Ananth Grama Computer Sciences, Purdue University ayg@cs.purdue.edu http://www.cs.purdue.edu/people/ayg. Review of Linear Algebra. A square matrix can be viewed as a graph. Rows (or columns) form vertices. Entries in the matrix correspond to edges.

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