SlideShare uma empresa Scribd logo

Fisika Matematika I (5 - 7) Reviewof vectoranalysis

•
•
J
jayamartha

unj fmipa-fisika

Educação
1 de 56
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 |

Recomendados

ME6603 - FINITE ELEMENT ANALYSIS FORMULA BOOK
ME6603 - FINITE ELEMENT ANALYSIS FORMULA BOOKME6603 - FINITE ELEMENT ANALYSIS FORMULA BOOK
ME6603 - FINITE ELEMENT ANALYSIS FORMULA BOOKASHOK KUMAR RAJENDRAN
 
Lecture 1 test
Lecture 1 testLecture 1 test
Lecture 1 testfalcarragh
 
fea qb
fea qb fea qb
fea qbamsubra manian
 
Scilab Finite element solver for stationary and incompressible navier-stokes ...
Scilab Finite element solver for stationary and incompressible navier-stokes ...Scilab Finite element solver for stationary and incompressible navier-stokes ...
Scilab Finite element solver for stationary and incompressible navier-stokes ...Scilab
 
Finite Element Analysis - UNIT-1
Finite Element Analysis - UNIT-1Finite Element Analysis - UNIT-1
Finite Element Analysis - UNIT-1propaul
 
Finite Element Analysis Lecture Notes Anna University 2013 Regulation
Finite Element Analysis Lecture Notes Anna University 2013 Regulation Finite Element Analysis Lecture Notes Anna University 2013 Regulation
Finite Element Analysis Lecture Notes Anna University 2013 Regulation NAVEEN UTHANDI
 
Fem notes
Fem notesFem notes
Fem notesVIGNESH C
 
Computational electromagnetics
Computational electromagneticsComputational electromagnetics
Computational electromagneticsAwaab Fakih
 

Recomendados

ME6603 - FINITE ELEMENT ANALYSIS FORMULA BOOK
ME6603 - FINITE ELEMENT ANALYSIS FORMULA BOOKME6603 - FINITE ELEMENT ANALYSIS FORMULA BOOK
ME6603 - FINITE ELEMENT ANALYSIS FORMULA BOOKASHOK KUMAR RAJENDRAN
 
Lecture 1 test
Lecture 1 testLecture 1 test
Lecture 1 testfalcarragh
 
fea qb
fea qb fea qb
fea qbamsubra manian
 
Scilab Finite element solver for stationary and incompressible navier-stokes ...
Scilab Finite element solver for stationary and incompressible navier-stokes ...Scilab Finite element solver for stationary and incompressible navier-stokes ...
Scilab Finite element solver for stationary and incompressible navier-stokes ...Scilab
 
Finite Element Analysis - UNIT-1
Finite Element Analysis - UNIT-1Finite Element Analysis - UNIT-1
Finite Element Analysis - UNIT-1propaul
 
Finite Element Analysis Lecture Notes Anna University 2013 Regulation
Finite Element Analysis Lecture Notes Anna University 2013 Regulation Finite Element Analysis Lecture Notes Anna University 2013 Regulation
Finite Element Analysis Lecture Notes Anna University 2013 Regulation NAVEEN UTHANDI
 
Fem notes
Fem notesFem notes
Fem notesVIGNESH C
 
Computational electromagnetics
Computational electromagneticsComputational electromagnetics
Computational electromagneticsAwaab Fakih
 
IRJET- Kinematic Analysis of Planar and Spatial Mechanisms using Matpack
IRJET- Kinematic Analysis of Planar and Spatial Mechanisms using MatpackIRJET- Kinematic Analysis of Planar and Spatial Mechanisms using Matpack
IRJET- Kinematic Analysis of Planar and Spatial Mechanisms using MatpackIRJET Journal
 
FEA unit 1 to 5 qb
FEA unit 1 to 5 qbFEA unit 1 to 5 qb
FEA unit 1 to 5 qbgokulfea
 
Finite Element Methode (FEM) Notes
Finite Element Methode (FEM) NotesFinite Element Methode (FEM) Notes
Finite Element Methode (FEM) NotesZulkifli Yunus
 
Me6603 sd by easy engineering.net
Me6603 sd by easy engineering.netMe6603 sd by easy engineering.net
Me6603 sd by easy engineering.netZackVizeman1
 
Varaiational formulation fem
Varaiational formulation fem Varaiational formulation fem
Varaiational formulation fem Tushar Aneyrao
 
recko_paper
recko_paperrecko_paper
recko_paperTereza Mlynářová
 
Finite element week 1
Finite element week 1Finite element week 1
Finite element week 1Charlton Inao
 
Finite Element Analysis -Dr.P.Parandaman
Finite Element Analysis -Dr.P.ParandamanFinite Element Analysis -Dr.P.Parandaman
Finite Element Analysis -Dr.P.ParandamanDr.P.Parandaman
 
Fem
FemFem
FemBoopathi Yoganathan
 
Static and Dynamic Reanalysis of Tapered Beam
Static and Dynamic Reanalysis of Tapered BeamStatic and Dynamic Reanalysis of Tapered Beam
Static and Dynamic Reanalysis of Tapered BeamIJERA Editor
 
Modeling of Granular Mixing using Markov Chains and the Discrete Element Method
Modeling of Granular Mixing using Markov Chains and the Discrete Element MethodModeling of Granular Mixing using Markov Chains and the Discrete Element Method
Modeling of Granular Mixing using Markov Chains and the Discrete Element Methodjodoua
 
Fem presentation
Fem presentationFem presentation
Fem presentationIndian dental academy
 
Finite element method
Finite element methodFinite element method
Finite element methodSantosh Chavan
 
SIAM-AG21-Topological Persistence Machine of Phase Transition
SIAM-AG21-Topological Persistence Machine of Phase TransitionSIAM-AG21-Topological Persistence Machine of Phase Transition
SIAM-AG21-Topological Persistence Machine of Phase TransitionHa Phuong
 
30120140503002
3012014050300230120140503002
30120140503002IAEME Publication
 
Paper id 71201964
Paper id 71201964Paper id 71201964
Paper id 71201964IJRAT
 
20 ms-me-amd-06 (simple linear regression)
20 ms-me-amd-06 (simple linear regression)20 ms-me-amd-06 (simple linear regression)
20 ms-me-amd-06 (simple linear regression)HassanShah124
 
Komputasi Fisika 02 (Solusi Persamaan Non Linear)
Komputasi Fisika 02 (Solusi Persamaan Non Linear)Komputasi Fisika 02 (Solusi Persamaan Non Linear)
Komputasi Fisika 02 (Solusi Persamaan Non Linear)jayamartha
 
Contoh contoh soal dan pembahasan integral
Contoh contoh soal dan pembahasan integralContoh contoh soal dan pembahasan integral
Contoh contoh soal dan pembahasan integraloilandgas24
 
Persamaan differensial
Persamaan differensialPersamaan differensial
Persamaan differensialAlbara I Arizona
 
Remidi matematika Bab Integral
Remidi matematika Bab IntegralRemidi matematika Bab Integral
Remidi matematika Bab IntegralXII IPA - 1
 
Integral soal-jawab
Integral soal-jawabIntegral soal-jawab
Integral soal-jawabMella Nofri
 

Mais conteúdo relacionado

Mais procurados

IRJET- Kinematic Analysis of Planar and Spatial Mechanisms using Matpack
IRJET- Kinematic Analysis of Planar and Spatial Mechanisms using MatpackIRJET- Kinematic Analysis of Planar and Spatial Mechanisms using Matpack
IRJET- Kinematic Analysis of Planar and Spatial Mechanisms using MatpackIRJET Journal
 
FEA unit 1 to 5 qb
FEA unit 1 to 5 qbFEA unit 1 to 5 qb
FEA unit 1 to 5 qbgokulfea
 
Finite Element Methode (FEM) Notes
Finite Element Methode (FEM) NotesFinite Element Methode (FEM) Notes
Finite Element Methode (FEM) NotesZulkifli Yunus
 
Me6603 sd by easy engineering.net
Me6603 sd by easy engineering.netMe6603 sd by easy engineering.net
Me6603 sd by easy engineering.netZackVizeman1
 
Varaiational formulation fem
Varaiational formulation fem Varaiational formulation fem
Varaiational formulation fem Tushar Aneyrao
 
Finite element week 1
Finite element week 1Finite element week 1
Finite element week 1Charlton Inao
 
Finite Element Analysis -Dr.P.Parandaman
Finite Element Analysis -Dr.P.ParandamanFinite Element Analysis -Dr.P.Parandaman
Finite Element Analysis -Dr.P.ParandamanDr.P.Parandaman
 
Static and Dynamic Reanalysis of Tapered Beam
Static and Dynamic Reanalysis of Tapered BeamStatic and Dynamic Reanalysis of Tapered Beam
Static and Dynamic Reanalysis of Tapered BeamIJERA Editor
 
Modeling of Granular Mixing using Markov Chains and the Discrete Element Method
Modeling of Granular Mixing using Markov Chains and the Discrete Element MethodModeling of Granular Mixing using Markov Chains and the Discrete Element Method
Modeling of Granular Mixing using Markov Chains and the Discrete Element Methodjodoua
 
SIAM-AG21-Topological Persistence Machine of Phase Transition
SIAM-AG21-Topological Persistence Machine of Phase TransitionSIAM-AG21-Topological Persistence Machine of Phase Transition
SIAM-AG21-Topological Persistence Machine of Phase TransitionHa Phuong
 
Paper id 71201964
Paper id 71201964Paper id 71201964
Paper id 71201964IJRAT
 
20 ms-me-amd-06 (simple linear regression)
20 ms-me-amd-06 (simple linear regression)20 ms-me-amd-06 (simple linear regression)
20 ms-me-amd-06 (simple linear regression)HassanShah124
 

Mais procurados (17)

IRJET- Kinematic Analysis of Planar and Spatial Mechanisms using Matpack
IRJET- Kinematic Analysis of Planar and Spatial Mechanisms using MatpackIRJET- Kinematic Analysis of Planar and Spatial Mechanisms using Matpack
IRJET- Kinematic Analysis of Planar and Spatial Mechanisms using Matpack
 
FEA unit 1 to 5 qb
FEA unit 1 to 5 qbFEA unit 1 to 5 qb
FEA unit 1 to 5 qb
 
Finite Element Methode (FEM) Notes
Finite Element Methode (FEM) NotesFinite Element Methode (FEM) Notes
Finite Element Methode (FEM) Notes
 
Me6603 sd by easy engineering.net
Me6603 sd by easy engineering.netMe6603 sd by easy engineering.net
Me6603 sd by easy engineering.net
 
Varaiational formulation fem
Varaiational formulation fem Varaiational formulation fem
Varaiational formulation fem
 
recko_paper
recko_paperrecko_paper
recko_paper
 
Finite element week 1
Finite element week 1Finite element week 1
Finite element week 1
 
Finite Element Analysis -Dr.P.Parandaman
Finite Element Analysis -Dr.P.ParandamanFinite Element Analysis -Dr.P.Parandaman
Finite Element Analysis -Dr.P.Parandaman
 
Fem
FemFem
Fem
 
Static and Dynamic Reanalysis of Tapered Beam
Static and Dynamic Reanalysis of Tapered BeamStatic and Dynamic Reanalysis of Tapered Beam
Static and Dynamic Reanalysis of Tapered Beam
 
Modeling of Granular Mixing using Markov Chains and the Discrete Element Method
Modeling of Granular Mixing using Markov Chains and the Discrete Element MethodModeling of Granular Mixing using Markov Chains and the Discrete Element Method
Modeling of Granular Mixing using Markov Chains and the Discrete Element Method
 
Fem presentation
Fem presentationFem presentation
Fem presentation
 
Finite element method
Finite element methodFinite element method
Finite element method
 
SIAM-AG21-Topological Persistence Machine of Phase Transition
SIAM-AG21-Topological Persistence Machine of Phase TransitionSIAM-AG21-Topological Persistence Machine of Phase Transition
SIAM-AG21-Topological Persistence Machine of Phase Transition
 
30120140503002
3012014050300230120140503002
30120140503002
 
Paper id 71201964
Paper id 71201964Paper id 71201964
Paper id 71201964
 
20 ms-me-amd-06 (simple linear regression)
20 ms-me-amd-06 (simple linear regression)20 ms-me-amd-06 (simple linear regression)
20 ms-me-amd-06 (simple linear regression)
 

Destaque

Komputasi Fisika 02 (Solusi Persamaan Non Linear)
Komputasi Fisika 02 (Solusi Persamaan Non Linear)Komputasi Fisika 02 (Solusi Persamaan Non Linear)
Komputasi Fisika 02 (Solusi Persamaan Non Linear)jayamartha
 
Contoh contoh soal dan pembahasan integral
Contoh contoh soal dan pembahasan integralContoh contoh soal dan pembahasan integral
Contoh contoh soal dan pembahasan integraloilandgas24
 
Remidi matematika Bab Integral
Remidi matematika Bab IntegralRemidi matematika Bab Integral
Remidi matematika Bab IntegralXII IPA - 1
 
Integral soal-jawab
Integral soal-jawabIntegral soal-jawab
Integral soal-jawabMella Nofri
 
Contoh contoh soal-dan_pembahasan_integral_untuk_sma
Contoh contoh soal-dan_pembahasan_integral_untuk_smaContoh contoh soal-dan_pembahasan_integral_untuk_sma
Contoh contoh soal-dan_pembahasan_integral_untuk_smaImam Lestari
 
Pembahasan soal kalkulus pada buku karangan edwin j. purcell dan dale varberg...
Pembahasan soal kalkulus pada buku karangan edwin j. purcell dan dale varberg...Pembahasan soal kalkulus pada buku karangan edwin j. purcell dan dale varberg...
Pembahasan soal kalkulus pada buku karangan edwin j. purcell dan dale varberg...Faris Audah
 

Destaque (9)

Komputasi Fisika 02 (Solusi Persamaan Non Linear)
Komputasi Fisika 02 (Solusi Persamaan Non Linear)Komputasi Fisika 02 (Solusi Persamaan Non Linear)
Komputasi Fisika 02 (Solusi Persamaan Non Linear)
 
Contoh contoh soal dan pembahasan integral
Contoh contoh soal dan pembahasan integralContoh contoh soal dan pembahasan integral
Contoh contoh soal dan pembahasan integral
 
Persamaan differensial
Persamaan differensialPersamaan differensial
Persamaan differensial
 
Remidi matematika Bab Integral
Remidi matematika Bab IntegralRemidi matematika Bab Integral
Remidi matematika Bab Integral
 
Integral soal-jawab
Integral soal-jawabIntegral soal-jawab
Integral soal-jawab
 
Soal integral dan pembahasan
Soal integral dan pembahasanSoal integral dan pembahasan
Soal integral dan pembahasan
 
Contoh contoh soal-dan_pembahasan_integral_untuk_sma
Contoh contoh soal-dan_pembahasan_integral_untuk_smaContoh contoh soal-dan_pembahasan_integral_untuk_sma
Contoh contoh soal-dan_pembahasan_integral_untuk_sma
 
Kalkulus 2 integral
Kalkulus 2 integralKalkulus 2 integral
Kalkulus 2 integral
 
Pembahasan soal kalkulus pada buku karangan edwin j. purcell dan dale varberg...
Pembahasan soal kalkulus pada buku karangan edwin j. purcell dan dale varberg...Pembahasan soal kalkulus pada buku karangan edwin j. purcell dan dale varberg...
Pembahasan soal kalkulus pada buku karangan edwin j. purcell dan dale varberg...
 

Semelhante a Fisika Matematika I (5 - 7) Reviewof vectoranalysis

Listrik Magnet (1)
Listrik Magnet (1)Listrik Magnet (1)
Listrik Magnet (1)jayamartha
 
Kalkulus II (19 - 20)
Kalkulus II (19 - 20)Kalkulus II (19 - 20)
Kalkulus II (19 - 20)jayamartha
 
Notes notes vector calculus made at home (wecompress.com)
Notes notes vector calculus made at home (wecompress.com)Notes notes vector calculus made at home (wecompress.com)
Notes notes vector calculus made at home (wecompress.com)Ashish Raje
 
Introduction To Vector Integrals.pptx
Introduction To Vector Integrals.pptxIntroduction To Vector Integrals.pptx
Introduction To Vector Integrals.pptxveenatanmaipatlolla
 
Mekanika Klasik (4 - 6)
Mekanika Klasik (4 - 6)Mekanika Klasik (4 - 6)
Mekanika Klasik (4 - 6)jayamartha
 
Application of vector integration
Application of vector integration Application of vector integration
Application of vector integration Varuna Kapuge
 
Lecture: Two-Way Kinematics
Lecture: Two-Way Kinematics Lecture: Two-Way Kinematics
Lecture: Two-Way Kinematics JasonMooney9
 
Ap Calculus BC Final Project (1).pptx
Ap Calculus BC Final Project (1).pptxAp Calculus BC Final Project (1).pptx
Ap Calculus BC Final Project (1).pptxNimanshaVerma
 
Pend Fisika Zat Padat (4) indexing
Pend Fisika Zat Padat (4) indexingPend Fisika Zat Padat (4) indexing
Pend Fisika Zat Padat (4) indexingjayamartha
 
General Curvilinear Motion &Motion of a Projectile
General Curvilinear Motion &Motion of a ProjectileGeneral Curvilinear Motion &Motion of a Projectile
General Curvilinear Motion &Motion of a ProjectileAbduljalil AlAbidi
 
Final m3 march 2019
Final m3 march 2019Final m3 march 2019
Final m3 march 2019drdivakaras
 
AAPPLICATION OF VECTOR CALCULUS (1).pptx
AAPPLICATION OF VECTOR CALCULUS (1).pptxAAPPLICATION OF VECTOR CALCULUS (1).pptx
AAPPLICATION OF VECTOR CALCULUS (1).pptxkhushiashok3105
 
Mekanika Klasik (21 - 22)
Mekanika Klasik (21 - 22)Mekanika Klasik (21 - 22)
Mekanika Klasik (21 - 22)jayamartha
 
complete-notes-on-vector-analysis.pdf
complete-notes-on-vector-analysis.pdfcomplete-notes-on-vector-analysis.pdf
complete-notes-on-vector-analysis.pdfdiriba chali
 
2. Vector Algebra.pptx
2. Vector Algebra.pptx2. Vector Algebra.pptx
2. Vector Algebra.pptxMehrija
 
Class 11 important questions for physics Scalars and Vectors
Class 11 important questions for physics Scalars and VectorsClass 11 important questions for physics Scalars and Vectors
Class 11 important questions for physics Scalars and VectorsInfomatica Academy
 
Scalars and Vectors
Scalars and VectorsScalars and Vectors
Scalars and Vectorsirfan sultan
 
Activity 1 (Directional Derivative and Gradient with minimum 3 applications)....
Activity 1 (Directional Derivative and Gradient with minimum 3 applications)....Activity 1 (Directional Derivative and Gradient with minimum 3 applications)....
Activity 1 (Directional Derivative and Gradient with minimum 3 applications)....loniyakrishn
 
Aplicaciones de espacios y subespacios vectoriales en la carrera de Electróni...
Aplicaciones de espacios y subespacios vectoriales en la carrera de Electróni...Aplicaciones de espacios y subespacios vectoriales en la carrera de Electróni...
Aplicaciones de espacios y subespacios vectoriales en la carrera de Electróni...MATEOESTEBANCALDERON
 

Semelhante a Fisika Matematika I (5 - 7) Reviewof vectoranalysis (20)

Listrik Magnet (1)
Listrik Magnet (1)Listrik Magnet (1)
Listrik Magnet (1)
 
Kalkulus II (19 - 20)
Kalkulus II (19 - 20)Kalkulus II (19 - 20)
Kalkulus II (19 - 20)
 
lec1.ppt
lec1.pptlec1.ppt
lec1.ppt
 
Notes notes vector calculus made at home (wecompress.com)
Notes notes vector calculus made at home (wecompress.com)Notes notes vector calculus made at home (wecompress.com)
Notes notes vector calculus made at home (wecompress.com)
 
Introduction To Vector Integrals.pptx
Introduction To Vector Integrals.pptxIntroduction To Vector Integrals.pptx
Introduction To Vector Integrals.pptx
 
Mekanika Klasik (4 - 6)
Mekanika Klasik (4 - 6)Mekanika Klasik (4 - 6)
Mekanika Klasik (4 - 6)
 
Application of vector integration
Application of vector integration Application of vector integration
Application of vector integration
 
Lecture: Two-Way Kinematics
Lecture: Two-Way Kinematics Lecture: Two-Way Kinematics
Lecture: Two-Way Kinematics
 
Ap Calculus BC Final Project (1).pptx
Ap Calculus BC Final Project (1).pptxAp Calculus BC Final Project (1).pptx
Ap Calculus BC Final Project (1).pptx
 
Pend Fisika Zat Padat (4) indexing
Pend Fisika Zat Padat (4) indexingPend Fisika Zat Padat (4) indexing
Pend Fisika Zat Padat (4) indexing
 
General Curvilinear Motion &Motion of a Projectile
General Curvilinear Motion &Motion of a ProjectileGeneral Curvilinear Motion &Motion of a Projectile
General Curvilinear Motion &Motion of a Projectile
 
Final m3 march 2019
Final m3 march 2019Final m3 march 2019
Final m3 march 2019
 
AAPPLICATION OF VECTOR CALCULUS (1).pptx
AAPPLICATION OF VECTOR CALCULUS (1).pptxAAPPLICATION OF VECTOR CALCULUS (1).pptx
AAPPLICATION OF VECTOR CALCULUS (1).pptx
 
Mekanika Klasik (21 - 22)
Mekanika Klasik (21 - 22)Mekanika Klasik (21 - 22)
Mekanika Klasik (21 - 22)
 
complete-notes-on-vector-analysis.pdf
complete-notes-on-vector-analysis.pdfcomplete-notes-on-vector-analysis.pdf
complete-notes-on-vector-analysis.pdf
 
2. Vector Algebra.pptx
2. Vector Algebra.pptx2. Vector Algebra.pptx
2. Vector Algebra.pptx
 
Class 11 important questions for physics Scalars and Vectors
Class 11 important questions for physics Scalars and VectorsClass 11 important questions for physics Scalars and Vectors
Class 11 important questions for physics Scalars and Vectors
 
Scalars and Vectors
Scalars and VectorsScalars and Vectors
Scalars and Vectors
 
Activity 1 (Directional Derivative and Gradient with minimum 3 applications)....
Activity 1 (Directional Derivative and Gradient with minimum 3 applications)....Activity 1 (Directional Derivative and Gradient with minimum 3 applications)....
Activity 1 (Directional Derivative and Gradient with minimum 3 applications)....
 
Aplicaciones de espacios y subespacios vectoriales en la carrera de Electróni...
Aplicaciones de espacios y subespacios vectoriales en la carrera de Electróni...Aplicaciones de espacios y subespacios vectoriales en la carrera de Electróni...
Aplicaciones de espacios y subespacios vectoriales en la carrera de Electróni...
 

Mais de jayamartha

Kalkulus 1 - Kuis 4
Kalkulus 1 - Kuis 4Kalkulus 1 - Kuis 4
Kalkulus 1 - Kuis 4jayamartha
 
Kalkulus 1 - Kuis 3
Kalkulus 1 - Kuis 3Kalkulus 1 - Kuis 3
Kalkulus 1 - Kuis 3jayamartha
 
Kalkulus 1 - Kuis 2
Kalkulus 1 - Kuis 2Kalkulus 1 - Kuis 2
Kalkulus 1 - Kuis 2jayamartha
 
Kalkulus 1 - Kuis 1
Kalkulus 1 - Kuis 1Kalkulus 1 - Kuis 1
Kalkulus 1 - Kuis 1jayamartha
 
Week 15 kognitif
Week 15 kognitifWeek 15 kognitif
Week 15 kognitifjayamartha
 
15-superconductivity
15-superconductivity15-superconductivity
15-superconductivityjayamartha
 
12-14 d-effect_of_electron_-_electron_interaction
12-14 d-effect_of_electron_-_electron_interaction12-14 d-effect_of_electron_-_electron_interaction
12-14 d-effect_of_electron_-_electron_interactionjayamartha
 
7-metal_vs_semiconductor
7-metal_vs_semiconductor7-metal_vs_semiconductor
7-metal_vs_semiconductorjayamartha
 
12 -14 c-spin_paramagnetism
12 -14 c-spin_paramagnetism12 -14 c-spin_paramagnetism
12 -14 c-spin_paramagnetismjayamartha
 
12 -14 b-diamagnetism
12 -14 b-diamagnetism12 -14 b-diamagnetism
12 -14 b-diamagnetismjayamartha
 
12-14 a-magnetic_effects_in_quantum _mechanics
12-14 a-magnetic_effects_in_quantum _mechanics12-14 a-magnetic_effects_in_quantum _mechanics
12-14 a-magnetic_effects_in_quantum _mechanicsjayamartha
 
Week4-5 tb-kognitif
Week4-5 tb-kognitifWeek4-5 tb-kognitif
Week4-5 tb-kognitifjayamartha
 
10-11 a-energy_bands
10-11 a-energy_bands10-11 a-energy_bands
10-11 a-energy_bandsjayamartha
 
7 -metal_vs_semiconductor
7 -metal_vs_semiconductor7 -metal_vs_semiconductor
7 -metal_vs_semiconductorjayamartha
 
Week-13 model pembelajaran
Week-13 model pembelajaranWeek-13 model pembelajaran
Week-13 model pembelajaranjayamartha
 
5-6-definition_of_semiconductor
5-6-definition_of_semiconductor5-6-definition_of_semiconductor
5-6-definition_of_semiconductorjayamartha
 
Week-15 kognitif
Week-15 kognitifWeek-15 kognitif
Week-15 kognitifjayamartha
 
Week 15 kognitif
Week 15 kognitifWeek 15 kognitif
Week 15 kognitifjayamartha
 

Mais de jayamartha (20)

Kalkulus 1 - Kuis 4
Kalkulus 1 - Kuis 4Kalkulus 1 - Kuis 4
Kalkulus 1 - Kuis 4
 
Kalkulus 1 - Kuis 3
Kalkulus 1 - Kuis 3Kalkulus 1 - Kuis 3
Kalkulus 1 - Kuis 3
 
Kalkulus 1 - Kuis 2
Kalkulus 1 - Kuis 2Kalkulus 1 - Kuis 2
Kalkulus 1 - Kuis 2
 
Kalkulus 1 - Kuis 1
Kalkulus 1 - Kuis 1Kalkulus 1 - Kuis 1
Kalkulus 1 - Kuis 1
 
P6
P6P6
P6
 
Week 15 kognitif
Week 15 kognitifWeek 15 kognitif
Week 15 kognitif
 
15-superconductivity
15-superconductivity15-superconductivity
15-superconductivity
 
12-14 d-effect_of_electron_-_electron_interaction
12-14 d-effect_of_electron_-_electron_interaction12-14 d-effect_of_electron_-_electron_interaction
12-14 d-effect_of_electron_-_electron_interaction
 
7-metal_vs_semiconductor
7-metal_vs_semiconductor7-metal_vs_semiconductor
7-metal_vs_semiconductor
 
12 -14 c-spin_paramagnetism
12 -14 c-spin_paramagnetism12 -14 c-spin_paramagnetism
12 -14 c-spin_paramagnetism
 
12 -14 b-diamagnetism
12 -14 b-diamagnetism12 -14 b-diamagnetism
12 -14 b-diamagnetism
 
12-14 a-magnetic_effects_in_quantum _mechanics
12-14 a-magnetic_effects_in_quantum _mechanics12-14 a-magnetic_effects_in_quantum _mechanics
12-14 a-magnetic_effects_in_quantum _mechanics
 
Week4-5 tb-kognitif
Week4-5 tb-kognitifWeek4-5 tb-kognitif
Week4-5 tb-kognitif
 
10-11 a-energy_bands
10-11 a-energy_bands10-11 a-energy_bands
10-11 a-energy_bands
 
7 -metal_vs_semiconductor
7 -metal_vs_semiconductor7 -metal_vs_semiconductor
7 -metal_vs_semiconductor
 
Week-13 model pembelajaran
Week-13 model pembelajaranWeek-13 model pembelajaran
Week-13 model pembelajaran
 
5-6-definition_of_semiconductor
5-6-definition_of_semiconductor5-6-definition_of_semiconductor
5-6-definition_of_semiconductor
 
Week-15 kognitif
Week-15 kognitifWeek-15 kognitif
Week-15 kognitif
 
Week 15 kognitif
Week 15 kognitifWeek 15 kognitif
Week 15 kognitif
 
Pert 1-4
Pert 1-4Pert 1-4
Pert 1-4
 

Último

Class 11th Physics NEET formula sheet pdf
Class 11th Physics NEET formula sheet pdfClass 11th Physics NEET formula sheet pdf
Class 11th Physics NEET formula sheet pdfAyushMahapatra5
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)eniolaolutunde
 
APM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across SectorsAPM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across SectorsAssociation for Project Management
 
Holdier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdfHoldier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdfagholdier
 
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdfQucHHunhnh
 
Measures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SDMeasures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SDThiyagu K
 
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactdawncurless
 
Sanyam Choudhary Chemistry practical.pdf
Sanyam Choudhary Chemistry practical.pdfSanyam Choudhary Chemistry practical.pdf
Sanyam Choudhary Chemistry practical.pdfsanyamsingh5019
 
Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17Celine George
 
Grant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingGrant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingTechSoup
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactPECB
 
Key note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdfKey note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdfAdmir Softic
 
IGNOU MSCCFT and PGDCFT Exam Question Pattern: MCFT003 Counselling and Family...
IGNOU MSCCFT and PGDCFT Exam Question Pattern: MCFT003 Counselling and Family...IGNOU MSCCFT and PGDCFT Exam Question Pattern: MCFT003 Counselling and Family...
IGNOU MSCCFT and PGDCFT Exam Question Pattern: MCFT003 Counselling and Family...PsychoTech Services
 
Unit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptxUnit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptxVishalSingh1417
 
Disha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdfDisha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdfchloefrazer622
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introductionMaksud Ahmed
 
Measures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and ModeMeasures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and ModeThiyagu K
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformChameera Dedduwage
 

Último (20)

Class 11th Physics NEET formula sheet pdf
Class 11th Physics NEET formula sheet pdfClass 11th Physics NEET formula sheet pdf
Class 11th Physics NEET formula sheet pdf
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)
 
APM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across SectorsAPM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across Sectors
 
Holdier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdfHoldier Curriculum Vitae (April 2024).pdf
Holdier Curriculum Vitae (April 2024).pdf
 
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf
 
INDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptx
INDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptxINDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptx
INDIA QUIZ 2024 RLAC DELHI UNIVERSITY.pptx
 
Measures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SDMeasures of Dispersion and Variability: Range, QD, AD and SD
Measures of Dispersion and Variability: Range, QD, AD and SD
 
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impact
 
Sanyam Choudhary Chemistry practical.pdf
Sanyam Choudhary Chemistry practical.pdfSanyam Choudhary Chemistry practical.pdf
Sanyam Choudhary Chemistry practical.pdf
 
Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17
 
Grant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingGrant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy Consulting
 
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
 
Beyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global ImpactBeyond the EU: DORA and NIS 2 Directive's Global Impact
Beyond the EU: DORA and NIS 2 Directive's Global Impact
 
Key note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdfKey note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdf
 
IGNOU MSCCFT and PGDCFT Exam Question Pattern: MCFT003 Counselling and Family...
IGNOU MSCCFT and PGDCFT Exam Question Pattern: MCFT003 Counselling and Family...IGNOU MSCCFT and PGDCFT Exam Question Pattern: MCFT003 Counselling and Family...
IGNOU MSCCFT and PGDCFT Exam Question Pattern: MCFT003 Counselling and Family...
 
Unit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptxUnit-IV- Pharma. Marketing Channels.pptx
Unit-IV- Pharma. Marketing Channels.pptx
 
Disha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdfDisha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdf
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
 
Measures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and ModeMeasures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and Mode
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
 

Fisika Matematika I (5 - 7) Reviewof vectoranalysis

  • 1. Pertemuan 5 – 6 ANALISA VEKTOR Drs. Tasman Abbas Jurusan Fisika Fakultas Matematika dan Ilmu Pengetahuan Alam
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 18.
  • 19. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 20.
  • 21.
  • 22.
  • 23.
  • 24. 02/02/11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 25.
  • 26.
  • 27.
  • 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 |
  • 30.
  • 31.
  • 32.
  • 33.
  • 34.
  • 35.
  • 36.
  • 37. Differential elements in the right handed Cartesian coordinate system
  • 38.
  • 39.
  • 40.
  • 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)
  • 45.
  • 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 |
  • 50.
  • 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 |