The Geometry of Vector Calculus toc:math2 http://sites.science.oregonstate.edu/BridgeBook/ 2020-01-26T14:50:53-08:00 The Geometry of Vector Calculus http://sites.science.oregonstate.edu/BridgeBook/ http://sites.science.oregonstate.edu/BridgeBook/lib/images/favicon.ico text/html 2015-08-21T11:07:00-08:00 toc:math2:ch01 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch01?rev=1440180420 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors (ss)Vectors(ss)The Dot Product(ss)The Law of Cosines(ss)Curvilinear Coordinates(ss)Activity: Curvilinear Basis Vectors(ss)Wrap-Up: Curvilinear Basis Vectors(ss)Vector Fields(ss)Orthogonality(ss)Lines and Planes(ss)The Vector Differential(ss)Other Coordinate Systems(ss)Activity: Determining $d\rr$ in Cylindrical and Spherical Coordinates(ss)Wrap-Up: Coordinate Expressions for $d\rr$ Chapter 2: Multiple Integrals text/html 2015-08-26T17:50:00-08:00 toc:math2:ch02 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch02?rev=1440636600 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals (ss)Review of Single Variable Integration(ss)Surfaces(ss)Level Sets(ss)Double Integrals(ss)Triple Integrals(ss)Order of Integration(ss)Non-Constant Limits of Integration(ss)Polar Coordinates(ss)Curvilinear Coordinates(ss)Double Integrals in Polar Coordinates(ss)Calculating Infinitesimal Distance in Cylindrical and Spherical Coordinates(ss)Infinitesimal Distance in Cylindrical and Spherical… text/html 2015-08-21T11:35:00-08:00 toc:math2:ch03 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch03?rev=1440182100 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals (ss)Densities(ss)Integration(ss)Curves(ss)Line Integrals(ss)Scalar Line Integrals(ss)Vector Line Integrals(ss)Circulation(ss)Use What You Know(ss)Parametric Curves(ss)Line Integrals on Parametric Curves Chapter 4: Surface Integrals text/html 2015-08-21T11:38:00-08:00 toc:math2:ch04 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch04?rev=1440182280 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals (ss)Surfaces(ss)Simple Surface Elements(ss)The Cross Product(ss)Surface Elements(ss)Activity: Surface Elements on Planes, Cylinders and Spheres(ss)Wrapup: Surface Elements on Planes, Cylinders, and Spheres(ss)Flux(ss)Highly Symmetric Surfaces(ss)Less Symmetric Surfaces(ss)Spheres in Cylindrical Coordinates(ss)Parametric Surfaces(ss)Sca… text/html 2015-08-21T11:40:00-08:00 toc:math2:ch05 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch05?rev=1440182400 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals (ss)The Triple Product(ss)Volume Integrals(ss)Integrating Vectors(ss)Integrating Vectors II Chapter 6: Partial Derivatives text/html 2015-08-29T12:54:00-08:00 toc:math2:ch06 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch06?rev=1440878040 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals Chapter 6: Partial Derivatives (ss) Review of Single Variable Differentiation(ss)Thick Derivatives(ss)Differentials(ss)The Multivariable Differential(ss)Chain Rule(ss)Chain Rule via Tree Diagrams(ss)Applications of Chain Rule(ss)Rearranging Differentials(ss)Things not to do with Differentials Chapter … text/html 2015-08-21T11:44:00-08:00 toc:math2:ch07 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch07?rev=1440182640 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals Chapter 6: Partial Derivatives Chapter 7: Gradient (ss)Gradient(ss)The Geometry of the Gradient(ss)Properties of the Gradient(ss)Directional Derivatives(ss) The Gradient in Curvilinear Coordinates(ss)Independence of Path(ss)Conservative Vector Fields(ss)Finding Potential Functions(ss) Visualizing Co… text/html 2015-08-27T15:38:00-08:00 toc:math2:ch08 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch08?rev=1440715080 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals Chapter 6: Partial Derivatives Chapter 7: Gradient Chapter 8: Applications (ss)Optimization(ss)Second Derivative Test(ss)Lagrange Multipliers(ss)Lagrange Multipliers Revisited(ss)Lagrange Multipliers using Differentials(ss)Motion in Space(ss)Arc Length(ss)Curvature(ss)Curvature and the Second Derivat… text/html 2015-08-21T11:46:00-08:00 toc:math2:ch09 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch09?rev=1440182760 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals Chapter 6: Partial Derivatives Chapter 7: Gradient Chapter 8: Applications text/html 2015-08-21T11:48:00-08:00 toc:math2:ch10 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch10?rev=1440182880 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals Chapter 6: Partial Derivatives Chapter 7: Gradient Chapter 8: Applications text/html 2017-04-04T09:41:00-08:00 toc:math2:ch11 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/ch11?rev=1491324060 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals Chapter 6: Partial Derivatives Chapter 7: Gradient Chapter 8: Applications text/html 2015-08-22T15:13:00-08:00 toc:math2:intro http://sites.science.oregonstate.edu/BridgeBook/toc/math2/intro?rev=1440281580 Part I: Mathematics PrefaceAcknowledgmentsIntroductionNotation Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals Chapter 6: Partial Derivatives text/html 2015-08-21T10:37:00-08:00 toc:math2:math2 http://sites.science.oregonstate.edu/BridgeBook/toc/math2/math2?rev=1440178620 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals Chapter 6: Partial Derivatives Chapter 7: Gradient Chapter 8: Applications text/html 2015-08-21T10:37:00-08:00 toc:math2:start http://sites.science.oregonstate.edu/BridgeBook/toc/math2/start?rev=1440178620 Part I: Mathematics Introduction Chapter 1: Coordinates and Vectors Chapter 2: Multiple Integrals Chapter 3: Line Integrals Chapter 4: Surface Integrals Chapter 5: Other Vector Integrals Chapter 6: Partial Derivatives Chapter 7: Gradient Chapter 8: Applications