Calculus BLUE Multivariable Volume 4: Fields introduces and extends the classical vector calculus to a calculus of fields. Topics covered in this text include:
vector fieldspath integralscomputing work and flux of a vector field along a pathconservative fields and the independence of path theoremgradients, curl, divergence, and what these mean in physical systemsGreen's theorem, Gauss's theorem, & Stokes' theorema simplified version of differential forms in 3-dthe wedge product and exterior derivativeapplications to fluid dynamics [Kelvin's theorem & Helmholtz' theorem]applications to electromagnetics [Maxwell's equations]applications to data analysis [volume estimation, time series data, & more]an introduction to differential forms in higher dimensionsthe generalized Stokes' theorem and its connection to the FTIC
Throughout, the text is filled with contemporary applications to data, mechanics, economics, probability, networks, and more. Theory and application are brought to life in full eye-scorching color (though a lot of it is blue).