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Fisika Matematika I (5 - 7) Reviewof vectoranalysis

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Pertemuan 5 – 6 ANALISA VEKTOR Drs. Tasman Abbas Jurusan Fisika Fakultas Matematika dan Ilmu Pengetahuan Alam
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Review of Vector Analysis 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],Thus which completely specifies in terms of A and its direction 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object]
The Radius Vector ,[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
Vector Algebra ,[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],Direction of and using (a) right-hand rule, (b) right-handed screw rule 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],Cross product using cyclic permutation: (a) moving clockwise leads to positive results; (b) moving counterclockwise leads to negative results 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],Consider the contribution of the path segment located at the angle 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],The flux of a vector field A through surface S 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
V is not perpendicular to S, except at one point on the Z axis Surface S 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Review of Vector Analysis 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],Clearly the divergence operator is a scalar operator . 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Review of Vector Analysis 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],[object Object],[object Object],The intersection of three orthogonal infinite places (x=const, y= const, and z = const) defines point P. Constant x, y and z surfaces 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
Differential elements in the right handed Cartesian coordinate system
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
[object Object],Relationship between (x,y,z) and 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
Point P and unit vectors in the cylindrical coordinate system 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
semi-infinite plane with its edge along the z - axis Constant surfaces 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
Differential elements in cylindrical coordinates Metric coefficient 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
Planar surface ( = const) Cylindrical surface ( =const) Planar surface ( z =const)
[object Object],[object Object],[object Object],[object Object],[object Object],02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
A vector A in spherical coordinates may be written as Point P and unit vectors in spherical coordinates 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
Relationships between space variables 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
Constant surfaces
Differential elements in the spherical coordinate system 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
1. 2. 3. POINTS TO REMEMBER 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
4 . 5. 6. 7. Review of Vector Analysis 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

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Fisika Matematika I (5 - 7) Reviewof vectoranalysis

  • 1. Pertemuan 5 – 6 ANALISA VEKTOR Drs. Tasman Abbas Jurusan Fisika Fakultas Matematika dan Ilmu Pengetahuan Alam
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  • 17. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
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  • 19. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
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  • 24. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
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  • 28. V is not perpendicular to S, except at one point on the Z axis Surface S 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 29. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
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  • 37. Differential elements in the right handed Cartesian coordinate system
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  • 41. Point P and unit vectors in the cylindrical coordinate system 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 42. semi-infinite plane with its edge along the z - axis Constant surfaces 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 43. Differential elements in cylindrical coordinates Metric coefficient 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 44. Planar surface ( = const) Cylindrical surface ( =const) Planar surface ( z =const)
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  • 46. A vector A in spherical coordinates may be written as Point P and unit vectors in spherical coordinates 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 47. Relationships between space variables 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 48. Constant surfaces
  • 49. Differential elements in the spherical coordinate system 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
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  • 51. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 52. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 53. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 54. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 55. 1. 2. 3. POINTS TO REMEMBER 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 56. 4 . 5. 6. 7. Review of Vector Analysis 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |