Calculus Blue Multivariable Volume 3: Integrals
by Robert Ghrist /
2017 / English / PDF
196 MB Download
This volume is the third in a 4-volume set of CALCULUS BLUE books on multivariable calculus, part of a revolutionary series of graphical Mathematics texts optimized for reading on phone/tablet/kindle devices.
Calculus BLUE Multivariable Volume 3: Integrals continues the journey through multivariable calculus, incorporating all we have learned about linear algebra and multivariate derivatives. Topics covered in this text include:
* Riemann sums, Riemann integrals, and the Fubini Theorem
* double, triple, and higher-dimensional integrals, with motivations & applications
* using integrals to compute averages
* using integrals to compute mass, centroids, and centers of mass
* moments of inertia, the inertia matrix, and basic solid body mechanics
* probability in single and multiple variables independence and expectation
* the variance-covariance matrix and its applications
* cylindrical & spherical coordinates
* the Changes of Coordinates Theorem and its applications
* Gaussians, the Kalman filter, and higher-dimensional geometry
Throughout, the text is filled with contemporary applications to data, robotics, mechanics, economics, probability, networks, and biology. Theory and application are brought to life in full eye-scorching color (though a lot of it is blue).
This volume consists of 18 chapters (plus a prologue, epilogue, and foreshadowing of volume 4), each containing exercises for practice & deeper understanding, for a total of over 415 pages of mathematics and color and joy and sweat.
