SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Fields and Waves

darby avatar
darby
16 diapositives · 363 Views · Sep 13, 2014

Fields and Waves. Lesson 2.1. VECTORS and VECTOR CALCULUS. VECTORS. Today’s Class will focus on:. vectors - description in 3 coordinate systems. vector operations - DOT & CROSS PRODUCT. vector calculus - AREA and VOLUME INTEGRALS. z. y. x. VECTOR NOTATION. VECTOR NOTATION:.

Fields and Waves - slide 1
01 / 16Fields and Waves
1 / 17

Télécharger la présentation

Fields and Waves
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Fields and Waves Lesson 2.1 VECTORS and VECTOR CALCULUS Darryl Michael/GE CRD

  2. VECTORS Today’s Class will focus on: • vectors - description in 3 coordinate systems • vector operations - DOT & CROSS PRODUCT • vector calculus - AREA and VOLUME INTEGRALS

  3. z y x VECTOR NOTATION VECTOR NOTATION: Rectangular or Cartesian Coordinate System Dot Product (SCALAR) Cross Product (VECTOR) Magnitude of vector

  4. Choice is based on symmetry of problem VECTOR REPRESENTATION 3 PRIMARY COORDINATE SYSTEMS: • RECTANGULAR • CYLINDRICAL • SPHERICAL Examples: Sheets - RECTANGULAR Wires/Cables - CYLINDRICAL Spheres - SPHERICAL

  5. z r P z x f y VECTOR REPRESENTATION: CYLINDRICAL COORDINATES UNIT VECTORS: Cylindrical representation uses: r ,f , z Dot Product (SCALAR)

  6. z P q r x f y VECTOR REPRESENTATION: SPHERICAL COORDINATES UNIT VECTORS: Spherical representation uses: r ,q , f Dot Product (SCALAR)

  7. z y x VECTOR REPRESENTATION: UNIT VECTORS Rectangular Coordinate System Unit Vector Representation for Rectangular Coordinate System The Unit Vectors imply : Points in the direction of increasing x Points in the direction of increasing y Points in the direction of increasing z

  8. z r P z f x y VECTOR REPRESENTATION: UNIT VECTORS Cylindrical Coordinate System The Unit Vectors imply : Points in the direction of increasing r Points in the direction of increasing j Points in the direction of increasing z

  9. z P q r f y x VECTOR REPRESENTATION: UNIT VECTORS Spherical Coordinate System The Unit Vectors imply : Points in the direction of increasing r Points in the direction of increasing q Points in the direction of increasing j

  10. Do Problem 1 VECTOR REPRESENTATION: UNIT VECTORS Summary RECTANGULAR Coordinate Systems CYLINDRICAL Coordinate Systems SPHERICAL Coordinate Systems NOTE THE ORDER! r,f, z r,q ,f Note: We do not emphasize transformations between coordinate systems

  11. Unit is in “meters” y df r x METRIC COEFFICIENTS 1. Rectangular Coordinates: When you move a small amount in x-direction, the distance is dx In a similar fashion, you generate dy and dz ( dx, dy, dz ) Generate: 2. Cylindrical Coordinates: Differential Distances: Distance = r df ( dr, rdf, dz )

  12. z P q r r sinq f y x y df x METRIC COEFFICIENTS 3. Spherical Coordinates: Differential Distances: Distance = r sinq df ( dr, rdq, r sinq df )

  13. METRIC COEFFICIENTS Representation of differential length dl in coordinate systems: rectangular cylindrical spherical

  14. dy dx y 6 2 3 7 x AREA INTEGRALS • integration over 2 “delta” distances Example: AREA = = 16 Note that: z = constant In this course, area & surface integrals will be on similar types of surfaces e.g. r =constant or f = constant or q = constant et c….

  15. PROBLEM 2 PROBLEM 2A What is constant? How is the integration performed? What are the differentials? Representation of differential surface element: Vector is NORMAL to surface

  16. DIFFERENTIALS FOR INTEGRALS Example of Line differentials or or Example of Surface differentials or Example of Volume differentials