Calculus BLUE Multivariable Volume 4: Fields
Calculus BLUE Multivariable Volume 4: Fields by Robert Ghrist
English | March 31, 2018 | ISBN: 9781944655112, ASIN: B07BVC7SZ1 | True PDF | 464 pages | 241 MB
English | March 31, 2018 | ISBN: 9781944655112, ASIN: B07BVC7SZ1 | True PDF | 464 pages | 241 MB
This volume is the fourth and final in a set of CALCULUS BLUE books on multivariable calculus and is part of a revolutionary series of graphical Mathematics texts optimized for reading on phones/tablets/laptops. Not only is the format novel, the curricular approach is a contemporary take on the classic core, with a particular emphasis on preparation for modern data science.
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 fields
- path integrals
- computing work and flux of a vector field along a path
- conservative fields and the independence of path theorem
- gradients, curl, divergence, and what these mean in physical systems
- Green's theorem, Gauss's theorem, & Stokes' theorem
- a simplified version of differential forms in 3-d
- the wedge product and exterior derivative
- applications 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 dimensions
- the 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).