The Geometry of Vector Calculus toc:math
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2020-01-26T14:51:00-08:00The Geometry of Vector Calculus
http://sites.science.oregonstate.edu/BridgeBook/
http://sites.science.oregonstate.edu/BridgeBook/lib/images/favicon.icotext/html2013-10-20T13:14:00-08:00toc:math:ch1
http://sites.science.oregonstate.edu/BridgeBook/toc/math/ch1?rev=1382300040
Part I: Mathematics
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)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 Integralstext/html2013-10-20T13:14:00-08:00toc:math:ch2
http://sites.science.oregonstate.edu/BridgeBook/toc/math/ch2?rev=1382300040
Part I: Mathematics
Chapter 1: Coordinates and Vectors
Chapter 2: Multiple Integrals
(ss)Review of Single Variable Integration(ss)Surfaces(ss)Level Sets(ss)Double Integrals(ss)Order of Integration(ss)Triple Integrals(ss)Curvilinear Coordinates(ss)Multiple Integrals in Curvilinear Coordinates(ss)Center of Mass
Chapter 3: Vector Integralstext/html2013-10-20T13:13:00-08:00toc:math:ch3
http://sites.science.oregonstate.edu/BridgeBook/toc/math/ch3?rev=1382299980
Part I: Mathematics
Chapter 1: Coordinates and Vectors
Chapter 2: Multiple Integrals
Chapter 3: Vector Integrals
(ss)Densities(ss)Integration(ss)Line Integrals(ss)Vector Line Integrals(ss)Use What You Know(ss)Surfaces(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)Par…text/html2013-10-20T13:23:00-08:00toc:math:ch4
http://sites.science.oregonstate.edu/BridgeBook/toc/math/ch4?rev=1382300580
Part I: Mathematics
Chapter 1: Coordinates and Vectors
Chapter 2: Multiple Integrals
Chapter 3: Vector Integrals
Chapter 4: Partial Derivatives
(ss)The Multivariable Differential(ss)Chain Rule(ss)Chain Rule via Tree Diagrams(ss)Optimization(ss)Applications of Chain Rule(ss)Rearranging Differentials(ss)Change of Variables
Chapter 5: Gradienttext/html2013-10-20T13:20:00-08:00toc:math:ch5
http://sites.science.oregonstate.edu/BridgeBook/toc/math/ch5?rev=1382300400
Part I: Mathematics
Chapter 1: Coordinates and Vectors
Chapter 2: Multiple Integrals
Chapter 3: Vector Integrals
Chapter 4: Partial Derivatives
Chapter 5: Gradient
(ss)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 Conservative Vector Fields(ss)Lagrange Multipliers(ss)Lagrange Multipliers using Differentials
Chapter 6: Othe…text/html2013-10-20T13:17:00-08:00toc:math:ch6
http://sites.science.oregonstate.edu/BridgeBook/toc/math/ch6?rev=1382300220
Part I: Mathematics
Chapter 1: Coordinates and Vectors
Chapter 2: Multiple Integrals
Chapter 3: Vector Integrals
Chapter 4: Partial Derivatives
Chapter 5: Gradient
Chapter 6: Other Vector Derivatives
(ss)Divergence(ss)The Divergence Theorem(ss)
The Divergence in Curvilinear Coordinates(ss)Curl(ss)Stokes' Theorem(ss)Visualizing Divergence and Curl(ss)Product Rules(ss)Integration by parts(ss)Second derivatives(ss)The Laplacian
Chapter 7: Power Seriestext/html2013-10-20T13:11:00-08:00toc:math:ch7
http://sites.science.oregonstate.edu/BridgeBook/toc/math/ch7?rev=1382299860
Part I: Mathematics
Chapter 1: Coordinates and Vectors
Chapter 2: Multiple Integrals
Chapter 3: Vector Integrals
Chapter 4: Partial Derivatives
Chapter 5: Gradient
Chapter 6: Other Vector Derivatives
Chapter 7: Power Series
(ss)Power Series(ss)Activity:
Finding Power Series Coefficients(ss)Wrap-Up:
Finding Power Series Coefficients(ss)Dimensions in Power Series(ss)Getting Started with Maple(ss)Activity:
Using Technology to Visualize Power Series Approximations (ss)Wrap-Up:
Usi…text/html2013-10-20T13:11:00-08:00toc:math:ch8
http://sites.science.oregonstate.edu/BridgeBook/toc/math/ch8?rev=1382299860
Part I: Mathematics
Chapter 1: Coordinates and Vectors
Chapter 2: Multiple Integrals
Chapter 3: Vector Integrals
Chapter 4: Partial Derivatives
Chapter 5: Gradient
Chapter 6: Other Vector Derivatives
Chapter 7: Power Series
Chapter 8: Delta Functions
(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 Dimen…text/html2016-08-04T09:31:00-08:00toc:math:diff
http://sites.science.oregonstate.edu/BridgeBook/toc/math/diff?rev=1470328260
Differentiation
(ss)Review of Single Variable Differentiation(ss)Thick Derivatives(ss)
Using Differentials to Compute Derivatives(ss)The Multivariable Differential(ss)Chain Rule(ss)Chain Rule via Tree Diagrams(ss)Chain Rule via Differential Tree Diagrams(ss)Optimization(ss)Second Derivative Test(ss)Curvature and the Second Derivative Test(ss)Applications of Chain Rule(ss)Rearranging Differentials(ss)Examples from Thermodynamics(ss)Things not to do with Differentials(ss)Change of Variablestext/html2013-10-20T12:43:00-08:00toc:math:integration
http://sites.science.oregonstate.edu/BridgeBook/toc/math/integration?rev=1382298180
Integration
(ss)
Using Differentials to Compute Derivatives(ss)Densities(ss)Single Integrals(ss)Double Integrals(ss)Order of Integration(ss)Triple Integrals(ss)Polar Coordinates(ss)
Cylindrical and Spherical Coordinates(ss)
Double Integrals in Polar Coordinates(ss)Calculating Infinitesimal Distance
in Cylindrical and Spherical Coordinates(ss)Infinitesimal Distance
in Cylindrical and Spherical Coordinates(ss)
Activity: Scalar Surface and Volume Elements(ss)
Wrapup: Scalar Surface an…text/html2013-10-27T13:36:00-08:00toc:math:math
http://sites.science.oregonstate.edu/BridgeBook/toc/math/math?rev=1382906160
Part I: Mathematics
Chapter 1: Coordinates and Vectors
Chapter 2: Multiple Integrals
Chapter 3: Vector Integrals
Chapter 4: Partial Derivatives
Chapter 5: Gradient
Chapter 6: Other Vector Derivatives
Chapter 7: Power Series
Chapter 8: Delta Functionstext/html2016-04-21T10:49:00-08:00toc:math:new
http://sites.science.oregonstate.edu/BridgeBook/toc/math/new?rev=1461260940
Math Book: Sections Under Development
Arc Length, Curvature, AccelerationLagrange MultipliersChange of VariablesIntegration SummaryReview of Multiple IntegrationOptimizationSecond Derivative TestCurvature and the Second Derivative TestNotationFluxApplications of Chain RuleLagrange Multipliers using DifferentialsChain Rule via Tree DiagramsChain Rule via Differential Tree DiagramsRearranging DifferentialsExamples from ThermodynamicsThings not to do with DifferentialsOrthogonalityVector FieldsLine…