Calculus BLUE Multivariable Volume 3: Integrals by Robert Ghrist
Requirements: .PDF reader, 215.7 MB
Overview: This volume is the third in a 4-volume 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.
Genre: Non-Fiction > Educational
Calculus BLUE Multivariable Volume 3: Integrals continues the journey through multivariable calculus, building on previous material from linear algebra and multivariate derivatives in volumes 1 and 2. Topics covered in this text include:
* multivariate 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 Change of Variables Theorem and its applications
* surface integrals, with applications to surface area and more
* multivariate Gaussians, the Kalman filter, and high-dimensional geometry
Throughout, the text is filled with contemporary applications to robotics, data, 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 19 chapters (plus a prologue, epilogue, and foreshadowing of volume 4), each containing exercises for practice, for over 450 pages of mathematics and color and joy and hard work. The 3rd edition includes a new chapter, updated graphics throughout, and more efficient compression for faster navigation.
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