http://sites.science.oregonstate.edu/coursewikis/GDF/ 2020-01-26T13:06:05-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/ http://sites.science.oregonstate.edu/coursewikis/GDF/lib/images/favicon.ico text/html 2013-03-21T15:56:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/3dext?rev=1363906560 Differentiation of Differential Forms text/html 2013-03-20T14:25:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/3dforms?rev=1363814700 Differential Forms in Three Dimensions text/html 2013-03-21T15:46:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/3dhodge?rev=1363905960 Relationships between Differential Forms text/html 2013-03-21T15:41:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/3dwedge?rev=1363905660 Multiplication of Differential Forms text/html 2013-01-16T13:09:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/acknowledge?rev=1358370540 Acknowledgments text/html 2013-01-28T13:25:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/bases?rev=1359408300 Bases for Differential Forms text/html 2013-05-23T19:34:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/bianchi?rev=1369362840 Bianchi Identities text/html 2011-03-14T09:45:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/books?rev=1300121100 Annotated Bibliography text/html 2013-03-12T14:45:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/calcthms?rev=1363124700 Calculus Theorems text/html 2013-03-20T13:22:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch0?rev=1363810920 Preface Acknowledgments Chapter 0: Motivation * (ss)1. A Review of Vector Calculus * (ss)2. Differential Forms in Three Dimensions * (ss)3. Multiplication of Differential Forms * (ss)4. Relationships between Differential Forms * (ss)5. Differentiation of Differential Forms text/html 2013-03-20T13:25:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch0float?rev=1363811100 text/html 2014-05-01T20:53:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch1?rev=1399002780 Preface Acknowledgments Chapter 0: Motivation Chapter 1: Introduction * (ss)1. Differentials * (ss)2. Integrands * (ss)3. Change of Variables * (ss)4. Multiplying Differentials Chapter 2: The Algebra of Differential Forms Chapter 3: Hodge Duality text/html 2011-03-01T11:51:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch1float?rev=1299009060 (ss)1. Differentials (ss)2. Integrands (ss)3. Change of Variables (ss)4. Multiplying Differentials text/html 2014-05-01T20:53:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch2?rev=1399002780 Preface Acknowledgments Chapter 0: Motivation Chapter 1: Introduction Chapter 2: The Algebra of Differential Forms * (ss)1. Differential Forms * (ss)2. Higher Rank Forms * (ss)3. Polar Coordinates * (ss)4. Linear Maps and Determinants * (ss)5. Cross Product * (ss)6. Dot Product * (ss)7. Products of Differential Forms * (ss)8. Pictures of Differential Forms * (ss)9. Tensors * (ss)10. Inner Products * (ss)11. Polar Coordinates II text/html 2013-01-17T15:50:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch2float?rev=1358466600 (ss)1. Differential Forms (ss)2. Higher Rank Forms (ss)3. Polar Coordinates (ss)4. Linear Maps (ss)5. Cross Product (ss)6. Dot Product (ss)7. Products of Forms (ss)8. Pictures of Forms (ss)9. Tensors (ss)10. Inner Products (ss)11. Polar Coordinates II text/html 2014-05-01T20:53:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch3?rev=1399002780 Preface Acknowledgments Chapter 0: Motivation Chapter 1: Introduction Chapter 2: The Algebra of Differential Forms Chapter 3: Hodge Duality * (ss)1. Bases for Differential Forms * (ss)2. The Metric Tensor * (ss)3. Signature * (ss)4. Inner Products of Higher Rank Forms * (ss)5. The Schwarz Inequality * (ss)6. Orientation * (ss)7. The Hodge Dual * (ss)8. Example: Minkowski 2-space * (ss)9. Example: Euclidean 2-space * (ss)10. Example: Polar Coordinates * (ss)11. Dot and… text/html 2013-02-06T20:20:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch3float?rev=1360210800 (ss)1. Basis Forms (ss)2. The Metric Tensor (ss)3. Signature (ss)4. Higher Rank Forms (ss)5. The Schwarz Inequality (ss)6. Orientation (ss)7. The Hodge Dual (ss)8. Ex: Minkowski 2-space (ss)9. Ex: Euclidean 2-space (ss)10. Ex: Polar Coordinates (ss)11. Dot+Cross Product II (ss)12. Pseudovectors (ss)13. The general case (ss)14. Technical Note (ss)15. Decomposable Forms text/html 2014-05-01T20:54:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch4?rev=1399002840 Preface Acknowledgments Chapter 0: Motivation Chapter 1: Introduction Chapter 2: The Algebra of Differential Forms Chapter 3: Hodge Duality Chapter 4: Differentiation of Differential Forms * (ss)1. Gradient * (ss)2. Exterior Differentiation * (ss)3. Divergence and Curl * (ss)4. Example: Laplacian in Polar Coordinates * (ss)5. Properties of Exterior Differentiation * (ss)6. Product Rules * (ss)7. Example: Maxwell's Equations I * (ss)8. Example: Maxwell's Equations II * (s… text/html 2013-01-22T11:46:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch4float?rev=1358883960 (ss)1. Gradient (ss)2. Exterior Differentiation (ss)3. Divergence and Curl (ss)4. Ex: Polar Laplacian (ss)5. Properties (ss)6. Product Rules (ss)7. Ex: Maxwell's Eqns I (ss)8. Ex: Maxwell's Eqns II (ss)9. Ex: Maxwell's Eqns III (ss)10. Orthogonal Coords (ss)11. Aside: Div, Grad, Curl (ss)12. Uniqueness text/html 2014-05-01T20:54:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch5?rev=1399002840 Preface Acknowledgments Chapter 0: Motivation Chapter 1: Introduction Chapter 2: The Algebra of Differential Forms Chapter 3: Hodge Duality Chapter 4: Differentiation of Differential Forms Chapter 5: Integration of Differential Forms * (ss)1. Vectors and Differential Forms * (ss)2. Line and Surface Integrals * (ss)3. Integrands Revisited * (ss)4. Stokes' Theorem * (ss)5. Calculus Theorems * (ss)6. Integration by Parts * (ss)7. Further Corollaries text/html 2013-03-11T17:04:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch5float?rev=1363046640 (ss)1. Vectors and Forms (ss)2. Line & Surface Integrals (ss)3. Integrands Revisited (ss)4. Stokes' Theorem (ss)5. Calculus Theorems (ss)6. Integration by Parts (ss)7. Further Corollaries text/html 2014-05-01T20:54:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch6?rev=1399002840 Preface Acknowledgments Chapter 0: Motivation Chapter 1: Introduction Chapter 2: The Algebra of Differential Forms Chapter 3: Hodge Duality Chapter 4: Differentiation of Differential Forms Chapter 5: Integration of Differential Forms Chapter 6: Connections * (ss)1. Polar Coordinates II * (ss)2. Differential Forms which are also Vector Fields * (ss)3. Exterior Derivatives of Vector Fields * (ss)4. Properties of Differentiation * (ss)5. Connections * (ss)6. The Levi-Civita C… text/html 2013-01-22T11:48:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch6float?rev=1358884080 (ss)1. Polar Coordinates II (ss)2. Vector-Valued Forms (ss)3. Vector Field Derivatives (ss)4. Differentiation Properties (ss)5. Connections (ss)6. Levi-Civita Connection (ss)7. Polar Coordinates III (ss)8. Uniquesness (ss)9. Tensor Algebra (ss)10. Commutators text/html 2014-05-01T20:54:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch7?rev=1399002840 Preface Acknowledgments Chapter 0: Motivation Chapter 1: Introduction Chapter 2: The Algebra of Differential Forms Chapter 3: Hodge Duality Chapter 4: Differentiation of Differential Forms Chapter 5: Integration of Differential Forms Chapter 6: Connections text/html 2013-03-11T16:51:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch7float?rev=1363045860 (ss)1. Curves (ss)2. Surfaces (ss)3. Examples in 3D (ss)4. Curvature (ss)5. Curvature in 3D (ss)6. Components (ss)7. Bianchi Identities (ss)8. Geodesic Curvature (ss)9. Geodesic Triangles (ss)10. Gauss-Bonnet Thm (ss)11. The Torus text/html 2014-05-01T20:54:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch8?rev=1399002840 Preface Acknowledgments Chapter 0: Motivation Chapter 1: Introduction Chapter 2: The Algebra of Differential Forms Chapter 3: Hodge Duality Chapter 4: Differentiation of Differential Forms Chapter 5: Integration of Differential Forms Chapter 6: Connections text/html 2013-04-10T14:55:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/ch8float?rev=1365630900 (ss)1. Geodesics (ss)2. Geodesics in 3D (ss)3. Examples of Geodesics (ss)4. Solving for Geodesics (ss)5. Polar Geodesics (ss)6. 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text/html 2013-05-11T20:48:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/dpolar?rev=1368330480 Polar Coordinates II text/html 2011-02-19T23:19:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/dprop?rev=1298186340 Properties of Differentiation text/html 2011-02-19T23:12:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/dvector?rev=1298185920 Exterior Derivative of Vector Fields text/html 2013-12-21T14:29:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/equiv?rev=1387664940 The Equivalence Problem text/html 2013-05-11T20:48:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/euclid?rev=1368330480 Hodge Dual in Euclidean 2-space text/html 2011-01-31T22:15:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/exterior?rev=1296540900 Exterior Differentiation text/html 2013-05-11T20:22:00-08:00 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Geodesic Curvature text/html 2013-05-11T20:27:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/geodesics?rev=1368329220 Geodesics text/html 2011-03-02T19:48:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/geodesics3d?rev=1299124080 Geodesics in Three Dimensions text/html 2013-05-11T20:28:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/geoex?rev=1368329280 Examples of Geodesics text/html 2013-05-11T20:54:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/geopolar?rev=1368330840 Geodesics in Polar Coordinates text/html 2013-05-11T20:48:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/geosol?rev=1368330480 Solving the Geodesic Equation text/html 2013-05-11T20:53:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GDF/book/gdf/geosphere?rev=1368330780 Geodesics on The Sphere text/html 2013-03-12T20:27:00-08:00 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