Identify the coordinate system that best describes symmetry about the z-axis. 1234567891011121314151617181920 2122232425262728293031323334353637383940.

Slides:



Advertisements
Similar presentations
VEKTORANALYS Kursvecka 6 övningar. PROBLEM 1 SOLUTION A dipole is formed by two point sources with charge +c and -c Calculate the flux of the dipole.
Advertisements

Coordinate Systems Dr. Midori Kitagawa.
Double Integrals Area/Surface Area Triple Integrals.
Lecture 2eee3401 Chapter 2 Coordinate Systems 1)Cartesian (rectangular) 2)Circular cylindrical 3)Spherical 4)Others (elliptic cylindrical, conical,…) A.
ARCH 481 3d Modeling and Rendering lecture four: texture maps.
2006 Fall MATH 100 Lecture 81 MATH 100 Lecture 19 Triple Integral in cylindrical & spherical coordinate Class 19 Triple Integral in cylindrical & spherical.
Lecture 15 Today Transformations between coordinate systems 1.Cartesian to cylindrical transformations 2.Cartesian to spherical transformations.
Lecture 16 Today Gradient of a scalar field

Chapter 15 – Multiple Integrals
Lecture 14 Today Orthogonal coordinate systems 1.The Cartesian (rectangular) coordinate system 2.The cylindrical coordinate system 3.The spherical.
Lecture 18 Today Curl of a vector filed 1.Circulation 2.Definition of Curl operator in Cartesian Coordinate 3.Vector identities involving the curl.
Cylindrical and Spherical Coordinates
Section 16.5 Integrals in Cylindrical and Spherical Coordinates.
Vectors and the Geometry of Space 9. 2 Announcement Wednesday September 24, Test Chapter 9 (mostly )
Cylindrical Coordinate Coordinate Systems. Representing 3D points in Cylindrical Coordinates.  r Start from polar representations in the plane.
Triple Integral in Spherical Coordinates
Spherical Coordinates
15.9 Triple Integrals in Spherical Coordinates
TRIPLE INTEGRALS IN SPHERICAL COORDINATES
(MTH 250) Lecture 26 Calculus. Previous Lecture’s Summary Recalls Introduction to double integrals Iterated integrals Theorem of Fubini Properties of.
Coordinate System VECTOR REPRESENTATION 3 PRIMARY COORDINATE SYSTEMS: RECTANGULAR CYLINDRICAL SPHERICAL Choice is based on symmetry of problem Examples:
Lecture 18: Triple Integrals, Cyclindrical Coordinates, and Spherical Coordinates.
1-1 Engineering Electromagnetics Chapter 1: Vector Analysis.
X y z Point can be viewed as intersection of surfaces called coordinate surfaces. Coordinate surfaces are selected from 3 different sets.
MA Day 46 – March 19, 2013 Section 9.7: Spherical Coordinates Section 12.8: Triple Integrals in Spherical Coordinates.
Darryl Michael/GE CRD Fields and Waves Lesson 2.1 VECTORS and VECTOR CALCULUS.
Vector calculus 1)Differential length, area and volume
EMLAB 1 Chapter 1. Vector analysis. EMLAB 2 Mathematics -Glossary Scalar : a quantity defined by one number (eg. Temperature, mass, density, voltage,...
MA Day 45 – March 18, 2013 Section 9.7: Cylindrical Coordinates Section 12.8: Triple Integrals in Cylindrical Coordinates.
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Double Integrals a. (16.2.1),
Chapter 1 - Vector Analysis. Scalars and Vectors Scalar Fields (temperature) Vector Fields (gravitational, magnetic) Vector Algebra.
Warm-up Problems Sketch the surface 9x 2 + 4y 2 – 36z 2 – 18x – 144z = 171.
Sec 16.7 Triple Integrals in Cylindrical Coordinates In the cylindrical coordinate system, a point P is represented by the ordered triple (r, θ, z), where.
11.7 Cylindrical and Spherical Coordinates. The Cylindrical Coordinate System In a cylindrical coordinate system, a point P in space is represented by.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 13 Multiple Integration.
10.7 Cylindrical and Spherical Coordinates (Curvilinear Coordinates)
Section 17.5 Parameterized Surfaces
Multiple Integrals 12.
Copyright © Cengage Learning. All rights reserved. 15 Multiple Integrals.
Triple Integrals in Cylindrical and Spherical Coordinates
Quadratics cutting axis (2) Algebra Quadratics cutting the x and y axis. In each of the examples which follow, you are asked to a) Find the points where.
Transformations Dr. Hugh Blanton ENTC Dr. Blanton - ENTC Coordinate Transformations 2 / 29 It is important to compare the units that are.
Pharos University ME 253 Fluid Mechanics II
14.7 Day 2 Triple Integrals Using Spherical Coordinates and more applications of cylindrical coordinates This is a Klein bottle, It is a 4 dimensional.
ConcepTest Section 19.2 Question 1 (a) The rectangle is twice as wide in the x-direction, with new corners at the origin, (2, 0, 0), (2, 1, 3), (0, 1,
1 Coordinate Systems and Transformation. Copyright © 2007 Oxford University Press Elements of Electromagnetics Fourth Edition Sadiku2 Figure 2.1 Point.
Wave Equations: EM Waves. Electromagnetic waves for E field for B field.
Triple Integrals in Spherical and Cylindrical In rectangular coordinates: dV = dzdydx In cylindrical coordinates: dV = r dzdrdθ In spherical coordinates:
EMLAB 1 Chapter 1. Vector analysis. EMLAB 2 Mathematics -Glossary Scalar : a quantity defined by one number (eg. Temperature, mass, density, voltage,...
University of Utah Introduction to Electromagnetics Lecture 14: Vectors and Coordinate Systems Dr. Cynthia Furse University of Utah Department of Electrical.
Lecture 19 Flux in Cartesian Coordinates.
Example: use Gauss’ Law to calculate the electric field due to an infinite sheet of charge, with surface charge density . This is easy using Gauss’ Law.
11 Vectors and the Geometry of Space
© 2010 Pearson Education, Inc. All rights reserved
By the end of Week 3: You would learn how to solve many problems involving lines/planes and manipulate with different coordinate systems. These are.
rectangular coordinate system spherical coordinate system
(4, 0) (0, 4) (2, 0) (-4, 0) (0, -4) (0, 2) None of these choices
課程大綱 OUTLINE Double Integrals(二重積分) Triple Integrals(三重積分)
Announcements 3/26/12 Prayer Pearls Before Swine.
Section 17.1 Parameterized Curves
Charged Isolated Conductor
14.7 Triple Integrals with Cylindrical and Spherical Coordinates
11 Vectors and the Geometry of Space
Chapter 15 Multiple Integrals
Lecture 17 Today Divergence of a vector filed
Section 1.3 More on Functions and Their Graphs
Chapter 16: Double and Triple Integrals
Lecture 16 Gradient in Cartesian Coordinates
Presentation transcript:

Identify the coordinate system that best describes symmetry about the z-axis rectangular coordinate system 2.cylindrical coordinate system 3.spherical coordinate system

Change from spherical to cylindrical coordinates. ( 3, 0, 0 ) ( - 3, 0, - 3 ) 2.( 3, 0, 3 ) 3.( 3, 0, 0 ) 4.( 0, 0, 3 ) 5.( 0, 0, - 3 )

none of those mi 3.133,134.4 mi 4.2,221.2 mi 5.2,113.2 mi mi