ENTC 3331 RF Fundamentals. Dr. Hugh Blanton ENTC 3331. Gradient, Divergence and Curl: the Basics . We first consider the position vector, l : where x , y , and z are rectangular unit vectors. . Since the unit vectors for rectangular coordinates are constants, we have for d l :.

ByHydrodynamics in Porous Media. We will cover: How fluids respond to local potential gradients (Darcy’s Law) Add the conservation of mass to obtain Richard’s equation. Darcy’s Law for saturated media. In 1856 Darcy hired to figure out the water supply to the town’s central fountain.

ByQuasi-Random Techniques. Don P. Mitchell. MC Integration for Rendering. Ray tracing yields point samples f(x i ) Discontinuous f thwarts efficient methods High dimensionality of distributed RT. Truly Random x i. Useful mostly in cryptography Tricky to get uniform distribution

ByObservers and Kalman Filters. CS 393R: Autonomous Robots. Slides Courtesy of Benjamin Kuipers. Good Afternoon Colleagues. Are there any questions?. Stochastic Models of an Uncertain World. Actions are uncertain. Observations are uncertain. i ~ N (0, i ) are random variables.

ByIntroducing…. Resource governor in SQL SERVER 2008. Hosted by Steve Wright, Director of Product Support, SQL Sentry Presentation created by Aaron Bertrand, SQL Server MVP. A technology that enables you to manage SQL Server workload and resources by specifying limits on resource consumption

ByWireless Continuum Networks. Stavros Toumpis Department of Informatics Athens University of Economics and Business SNOW 2012. Scope. Nodes communicating exclusively over a shared wireless medium Nodes are so many as to form a continuum : There is a node at practically every location

ByMAE 5130: VISCOUS FLOWS. Lecture 2: Introductory Concepts August 19, 2010 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk. IMPORTANT RELATIONSHIPS. If the curl of the velocity field is zero Flow is irrotational

ByApplications of Gauss’s Law. LINE CHARGE. In terms of Charge Density,. Application to Coaxial Cable. Physical Interpretation of Divergence of a Vector Field. Water Flow out of a bath tub Air flow out of a Punctured Tire

ByVector-Valued Functions. Section 10.3b. Differentiation Rules for Vector Functions. Let u and v be differentiable functions of t , and C a constant v ector. 1. Constant Function Rule:. 2. Scalar Multiple Rules:. c any scalar. f any differentiable scalar function. 3. Sum Rule:.

BySec 17.1 Vector Fields. DEFINITIONS: 1. 2. Examples : Sketch the following vector fields. 1. F ( x , y ) = − y i + x j 2. F ( x , y ) = 3 x i + y j. Example :. If f is a scalar function of three variables, then its gradient,

ByECE 6341 . Spring 2014. Prof. David R. Jackson ECE Dept. Notes 25. Scalar Wave Transformation. z . Incident wave:. (scalar function , e.g. pressure of sound wave). y . x. Notes: N o variation m = 0 Must be finite at the origin (only j n )

ByDifferential Calculus: f ( x ) : a function of a variable ( x ). Change in f ( x ) w.r.t x Slope of a graph f vs x d f /d x: Ordinary derivative. f ( x ) . x. Differential Calculus: f ( x,y,z ) : function of more than one variables. Del is a vector operator. The Del Operator.

ByPHYS 241 Recitation. Kevin Ralphs Week 4. Overview. HW Questions Potential Quiz Questions. HW Questions. Ask away…. Potential. What does it tell me? The change in potential energy per unit charge an object has when moved between two points Why do I care?

ByChapter 3: Mathematical Tools. We will be reviewing Exponents and Logarithms. Scalar Calculus Partial Derivatives of a Scalar Function of a Vector. The Ln Function. ln ab = ln a + ln b ln (a/b) = ln a – ln b ln a b = b ln a ln e a = a ln e = 1 ln 1 = 0. ln a = c if

ByChap. 8. Vector Differential Calculus. Grad. Div. Curl. 8.1. Vector Algebra in 2-Space and 3-Space Scalar: a quantity only with its magnitude; temperature, speed, mass, volume, … Vector: a quantity with its magnitude and its direction; velocity, acceleration, force, …

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ByBasic vector operations. Repeated vector operations a) divergence of the curl of a vector. The curl gives the magnitude and sense of the vector rotation confined within a prescribed region.

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