The Geometry of Vector Calculus toc:pguide http://sites.science.oregonstate.edu/BridgeBook/ 2020-01-26T14:51:34-08:00 The Geometry of Vector Calculus http://sites.science.oregonstate.edu/BridgeBook/ http://sites.science.oregonstate.edu/BridgeBook/lib/images/favicon.ico text/html 2011-10-15T08:02:54-08:00 toc:pguide:320review http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/320review?rev=1318690974 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)Review text/html 2011-10-15T08:02:54-08:00 toc:pguide:422review http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/422review?rev=1318690974 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)Review text/html 2011-10-15T08:02:54-08:00 toc:pguide:ampere http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/ampere?rev=1318690974 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 Conditions text/html 2011-10-15T08:02:54-08:00 toc:pguide:boundary http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/boundary?rev=1318690974 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/html 2012-10-31T17:31:00-08:00 toc:pguide:continuous http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/continuous?rev=1351729860 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/html 2011-10-15T08:02:54-08:00 toc:pguide:eenergy http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/eenergy?rev=1318690974 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: Review text/html 2011-10-15T08:02:54-08:00 toc:pguide:efields http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/efields?rev=1318690974 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/html 2011-10-15T08:02:54-08:00 toc:pguide:energy http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/energy?rev=1318690974 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/html 2011-10-15T08:02:54-08:00 toc:pguide:fields http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/fields?rev=1318690974 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 text/html 2011-10-15T08:02:54-08:00 toc:pguide:gauss http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/gauss?rev=1318690974 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/html 2011-10-15T08:02:54-08:00 toc:pguide:magfield http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/magfield?rev=1318690974 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 Law text/html 2011-10-15T08:02:54-08:00 toc:pguide:pguide http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/pguide?rev=1318690974 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/html 2011-10-15T08:02:54-08:00 toc:pguide:potentials http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/potentials?rev=1318690974 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 Fields text/html 2011-10-15T08:02:54-08:00 toc:pguide:pseries http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/pseries?rev=1318690974 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/html 2012-10-31T17:36:00-08:00 toc:pguide:ptcharges http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/ptcharges?rev=1351730160 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/html 2011-10-15T08:02:54-08:00 toc:pguide:symmetries http://sites.science.oregonstate.edu/BridgeBook/toc/pguide/symmetries?rev=1318690974 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