The Geometry of Vector Calculus toc:pguide
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2020-01-26T14:51:34-08:00The Geometry of Vector Calculus
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Symmetries and Idealizations
Unit 1: Point Charges
Unit 2: Power Series Approximations
Unit 3: Continuous Charge Distributions
Unit 4: Potentials
Unit 5: Electric Fields
Unit 6: Electrostatic Energy
Unit 7: Review
(ss)Reviewtext/html2011-10-15T08:02:54-08:00toc:pguide:422review
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Static Vector Fields
Unit 1: Gauss's Law
Unit 2: Current and Magnetic Fields
Unit 3: Ampère's Law
Unit 4: Conductors and Boundary Conditions
Unit 5: Conservative Fields and Energy
Unit 6: Review
(ss)The Relationship between Electrostatic Potentials, Fields, and Sources(ss)The Relationship between Magnetostatic Potentials, Fields, and Sources(ss)Reviewtext/html2011-10-15T08:02:54-08:00toc:pguide:ampere
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Static Vector Fields
Unit 1: Gauss's Law
Unit 2: Current and Magnetic Fields
Unit 3: Ampère's Law
(ss)Curl(ss)Stokes' Theorem(ss)The Magnetic Field of a Uniform Planar Current(ss)Ampère's Law and Symmetry(ss)More Ampère's Law and Symmetry(ss)Differential Form of Ampère's Law
Unit 4: Conductors and Boundary Conditionstext/html2011-10-15T08:02:54-08:00toc:pguide:boundary
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Static Vector Fields
Unit 1: Gauss's Law
Unit 2: Current and Magnetic Fields
Unit 3: Ampère's Law
Unit 4: Conductors and Boundary Conditions
(ss)Step Functions(ss)The Dirac Delta Function(ss)Exercise: Delta Functions 1(ss)Properties of the Dirac Delta Function(ss)Exercise: Delta Functions 2(ss)Representations of the Dirac Delta Function(ss)The Dirac Delta Function in Three Dimensions(ss)The Dirac Delta Function and Densities(ss)Dot Products and Components(ss)Boundary Conditions on Electric…text/html2012-10-31T17:31:00-08:00toc:pguide:continuous
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Symmetries and Idealizations
Unit 1: Point Charges
Unit 2: Power Series Approximations
Unit 3: Continuous Charge Distributions
(ss)Curvilinear Coordinates(ss)Basis Vectors:
Instructor's Guide(ss)Basis Vectors(ss)More Basis Vectors(ss)The Position Vector
as a Vector Field(ss)The Vector Differential(ss)Other Coordinate Systems(ss)Activity:
Determining $d\rr$ in Cylindrical and Spherical Coordinates:
Instructor's Guide(ss)Activity
Determining $d\rr$ in Cylindrical and Spherical Coord…text/html2011-10-15T08:02:54-08:00toc:pguide:eenergy
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Symmetries and Idealizations
Unit 1: Point Charges
Unit 2: Power Series Approximations
Unit 3: Continuous Charge Distributions
Unit 4: Potentials
Unit 5: Electric Fields
Unit 6: Electrostatic Energy
(ss)Concept Map: VEUF(ss)More Concept Map: VEUF(ss)Electrostatic Energy(ss)More Electrostatic Energy
Unit 7: Reviewtext/html2011-10-15T08:02:54-08:00toc:pguide:efields
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Symmetries and Idealizations
Unit 1: Point Charges
Unit 2: Power Series Approximations
Unit 3: Continuous Charge Distributions
Unit 4: Potentials
Unit 5: Electric Fields
(ss)Partial Derivatives(ss)Chain Rule(ss)Gradient(ss)Directional Derivatives(ss)The Gradient in Curvilinear Coordinates(ss)The Hill: Instructor's Guide(ss)The Hill(ss)More Hill(ss)The Gradient Activity: Instructor's Guide(ss)The Gradient Activity(ss)More Gradient Activity(ss)Electric Field(ss)Drawing Electric Fields: Instr…text/html2011-10-15T08:02:54-08:00toc:pguide:energy
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Static Vector Fields
Unit 1: Gauss's Law
Unit 2: Current and Magnetic Fields
Unit 3: Ampère's Law
Unit 4: Conductors and Boundary Conditions
Unit 5: Conservative Fields and Energy
(ss)Product Rules(ss)Integration by Parts(ss)Electrostatic Energy(ss)Independence of Path(ss)Conservative Vector Fields(ss)Finding Potential Functions(ss)Finding the Potential from the Electric Field(ss)Curl-Free Vector Fields(ss)Divergence-Free Vector Fields(ss)Second Derivatives(ss)The Laplacian(ss)Second Deri…text/html2011-10-15T08:02:54-08:00toc:pguide:fields
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Static Vector Fields
Unit 1: Gauss's Law
Unit 2: Current and Magnetic Fields
Unit 3: Ampère's Law
Unit 4: Conductors and Boundary Conditions
Unit 5: Conservative Fields and Energy
Unit 6: Reviewtext/html2011-10-15T08:02:54-08:00toc:pguide:gauss
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Static Vector Fields
Unit 1: Gauss's Law
(ss)Surfaces(ss)The Cross Product(ss)Surface Elements(ss)More Surface Elements on Surfaces and Spheres(ss)More Surface Elements on Planes, Cylinders, and Spheres(ss)Flux(ss)Flux of the Electric Field(ss)Gauss's Law(ss)Example: Flux through a Cube(ss)More Flux through a Cube(ss)Gauss's Law and Symmetry(ss)Gauss's Law: Cylinders and Spheres(ss)More Gauss's Law: Cylinders and Spheres(ss)Divergence(ss)The Divergence in Curvilinear Coordinates(ss)Visualizing …text/html2011-10-15T08:02:54-08:00toc:pguide:magfield
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Static Vector Fields
Unit 1: Gauss's Law
Unit 2: Current and Magnetic Fields
(ss)Current(ss)Line Integrals(ss)Vector Line Integrals(ss)Use What You Know(ss)Magnetic Vector Potential(ss)Ring of Current(ss)More Ring of Current(ss)Curl(ss)The Biot Savart Law(ss)The Magnetic Field of a Straight Wire(ss)The Magnetic Field of a Spinning Ring(ss)More Magnetic Field of a Spinning Ring(ss)Compare A and B for a Spinning Ring
Unit 3: Ampère's Lawtext/html2011-10-15T08:02:54-08:00toc:pguide:pguide
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Part II: Physics
UNDER CONSTRUCTION
Our long-term plan is to include links within the physics sections to the
relevant sections from the math part of the book, at which point we will post
a standalone table of contents for the physics part of the book here.text/html2011-10-15T08:02:54-08:00toc:pguide:potentials
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Symmetries and Idealizations
Unit 1: Point Charges
Unit 2: Power Series Approximations
Unit 3: Continuous Charge Distributions
Unit 4: Potentials
(ss)
Potentials from Continuous Charge Distributions(ss)A Uniformly Charged Ring(ss)More on a Uniformly Charged Ring(ss)The Ring: Limits Near and Far(ss)
Potential Due to a Finite Line of Charge(ss)
Potential Due to an Infinite Line of Charge
Unit 5: Electric Fieldstext/html2011-10-15T08:02:54-08:00toc:pguide:pseries
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Symmetries and Idealizations
Unit 1: Point Charges
Unit 2: Power Series Approximations
(ss)Power Series(ss)Finding Power Series: Instructor's Guide(ss)Finding Power Series Coefficients(ss)More Finding Coefficients for Power Series(ss)Dimensions in Power Series(ss)Approximations Using Power Series(ss)Using Technology to Visualize Power Series Approximations: Instructor's Guide(ss)Using Technology to Visualize Power Series Approximations (ss)More Using Technology to Visualize Power Series Appro…text/html2012-10-31T17:36:00-08:00toc:pguide:ptcharges
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Symmetries and Idealizations
Unit 1: Point Charges
(ss)Introduction(ss)Dimensions(ss)Electric and
Gravitational Potentials(ss)Voltmeters(ss)Voltmeters(ss)
Activity: Visualization of Potentials: Instructor's Guide(ss)
Activity: Visualization of Potentials(ss)
Wrap-Up: Visualization of Potentials(ss)Getting Started with Maple:
Instructor's Guide(ss)Getting Started with Maple(ss) Activity:
Using Technology to Visualize Potentials: Instructor's Guide(ss)
Activity: Using Technology to …text/html2011-10-15T08:02:54-08:00toc:pguide:symmetries
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Symmetries and Idealizations
Unit 1: Point Charges
Unit 2: Power Series Approximations
Unit 3: Continuous Charge Distributions
Unit 4: Potentials
Unit 5: Electric Fields
Unit 6: Electrostatic Energy
Unit 7: Review