Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6....

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Jerrold E. Marsden and Anthony J. Tromba Vector Calculus Fifth Edition Chapter 4: Vector-Valued Functions 4.4 Divergence and Curl Copyright © 2003 by W. H. Freeman & Company

Transcript of Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6....

Page 1: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body

Jerrold E. Marsden and Anthony J. Tromba

Vector CalculusFifth Edition

Chapter 4:Vector-Valued Functions

4.4 Divergence and Curl

Copyright © 2003 by W. H. Freeman & Company

Page 2: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 3: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 4: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 5: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 6: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 7: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 8: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 9: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 10: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 11: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 12: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 13: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 14: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 15: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 16: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 17: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 18: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 19: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body
Page 20: Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf · 6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body

arXiv.org e-Print archive · arXiv:1202.3564v3 [math.SG] 5 Feb 2018 RegularReductionofControlledHamiltonianSystemwithSymplectic StructureandSymmetry Jerrold E. Marsden Control andDynamicalSystems

arXiv.org e-Print archive · arXiv:1202.3564v3 [math.SG] 5 Feb 2018 RegularReductionofControlledHamiltonianSystemwithSymplectic StructureandSymmetry Jerrold E. Marsden Control andDynamicalSystems

Course Information Book Department of Mathematicsemerald.tufts.edu/as/math/BookletF.pdf · TEXT: Elementary Classical Analysis, Second Edition by Jerrold E. Marsden and Michael J.

Course Information Book Department of Mathematicsemerald.tufts.edu/as/math/BookletF.pdf · TEXT: Elementary Classical Analysis, Second Edition by Jerrold E. Marsden and Michael J.

Calculo Vectorial (Jerrold Marsden)

Calculo Vectorial (Jerrold Marsden)

Keprid;>I/ed 1..(,.(ht'mtA-fic.s ?1-/;!-It7>I • G. You.:! 1'.5- … · 2019. 7. 24. · 88 Jerrold E. Marsden It is by this general method that one arrives

Keprid;>I/ed 1..(,.(ht'mtA-fic.s ?1-/;!-It7>I • G. You.:! 1'.5- … · 2019. 7. 24. · 88 Jerrold E. Marsden It is by this general method that one arrives

Introduction: Tudor Ratiu and Alan Weinstein · Introduction: Tudor Ratiu and Alan Weinstein Jerrold Eldon Marsden, known to all his friends and colleagues as Jerry, was born in Ocean

Introduction: Tudor Ratiu and Alan Weinstein · Introduction: Tudor Ratiu and Alan Weinstein Jerrold Eldon Marsden, known to all his friends and colleagues as Jerry, was born in Ocean

Variational Methods, Multisymplectic Geometry …lagrange.mechse.illinois.edu/.../MaPeShWe2001.pdfVariational Methods, Multisymplectic Geometry and Continuum Mechanics Jerrold E. Marsden∗

Variational Methods, Multisymplectic Geometry …lagrange.mechse.illinois.edu/.../MaPeShWe2001.pdfVariational Methods, Multisymplectic Geometry and Continuum Mechanics Jerrold E. Marsden∗

Curriculum Vitae: Jerrold E. Marsdencds.caltech.edu/~marsden/wiki/uploads/contact/academics/jem_cv_pubs.pdfCurriculum Vitae: Jerrold E. Marsden November 23, 2009 Contact Information

Curriculum Vitae: Jerrold E. Marsdencds.caltech.edu/~marsden/wiki/uploads/contact/academics/jem_cv_pubs.pdfCurriculum Vitae: Jerrold E. Marsden November 23, 2009 Contact Information

authors.library.caltech.eduauthors.library.caltech.edu/19747/1/MaMiPeRa1998.pdf · Symplectic Reduction for Semidirect Products and Central Extensions. Jerrold E. Marsden Control

authors.library.caltech.eduauthors.library.caltech.edu/19747/1/MaMiPeRa1998.pdf · Symplectic Reduction for Semidirect Products and Central Extensions. Jerrold E. Marsden Control

Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body about

Jerrold E. Marsden and Anthony J. Trombacaiz/math362s11/slides/vc_5e_section_4_4.pdf6. Rotations and the Curl. The vector field describing rigid rota- tional motion of a body about

Jerrold Marsden

Jerrold Marsden

[Jerrold E. Marsden, Michael J. Hoffman] Analisis (BookFi.org)

[Jerrold E. Marsden, Michael J. Hoffman] Analisis (BookFi.org)

Analisis basico-de-variable-compleja-jerrold-marsden

Analisis basico-de-variable-compleja-jerrold-marsden

Dynamical Systems, the Three-Body Problem and Space ...€¦ · Dynamical Systems, the Three-Body Problem and Space Mission Design Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden,

Dynamical Systems, the Three-Body Problem and Space ...€¦ · Dynamical Systems, the Three-Body Problem and Space Mission Design Wang Sang Koon, Martin W. Lo, Jerrold E. Marsden,

Control and Dynamical Systems, Caltech Jerrold Marsden ...sdross/books/cds270/270_5a.pdfexistence of periodic (and quasi-periodic) orbits near L 1. I 3rd order approximation, using

Control and Dynamical Systems, Caltech Jerrold Marsden ...sdross/books/cds270/270_5a.pdfexistence of periodic (and quasi-periodic) orbits near L 1. I 3rd order approximation, using

Darryl D. Holm and Jerrold E. Marsden- Momentum Maps and Measure-valued Solutions (Peakons, Filaments and Sheets) for the EPDiff Equation

Darryl D. Holm and Jerrold E. Marsden- Momentum Maps and Measure-valued Solutions (Peakons, Filaments and Sheets) for the EPDiff Equation

Sergio Grillo Jerrold Marsden SujitNairauthors.library.caltech.edu/24997/1/Grillo2011p15532J...Jerrold Marsden∗ Control and Dynamical Systems California Institute of Technology Pasadena,

Sergio Grillo Jerrold Marsden SujitNairauthors.library.caltech.edu/24997/1/Grillo2011p15532J...Jerrold Marsden∗ Control and Dynamical Systems California Institute of Technology Pasadena,

Computational Mec hanics and Dynamical Systemsmath.usask.ca/~patrick/BIRS/Marsden.pdfComputational Mec hanics and Dynamical Systems Jerrold E. Marsden CDS, Caltec h BIRS, A ugust 13,

Computational Mec hanics and Dynamical Systemsmath.usask.ca/~patrick/BIRS/Marsden.pdfComputational Mec hanics and Dynamical Systems Jerrold E. Marsden CDS, Caltec h BIRS, A ugust 13,

A History Walk Around Marsden Marsden Mechanics ...

A History Walk Around Marsden Marsden Mechanics ...

Internet Supplement for Vector Calculuswilker/Math510Fall09/... · 2009. 9. 9. · for Vector Calculus Fifth Edition Version: October, 2003 Jerrold E. Marsden ... tended to be used

Internet Supplement for Vector Calculuswilker/Math510Fall09/... · 2009. 9. 9. · for Vector Calculus Fifth Edition Version: October, 2003 Jerrold E. Marsden ... tended to be used

Control and Dynamical Systems, Caltech Jerrold …sdross/books/cds270/270_5b.pdf · Dynamical Systems and Space Mission Design Jerrold Marsden, Wang Koon and Martin Lo Wang Sang Koon

Control and Dynamical Systems, Caltech Jerrold …sdross/books/cds270/270_5b.pdf · Dynamical Systems and Space Mission Design Jerrold Marsden, Wang Koon and Martin Lo Wang Sang Koon