Calculus BLUE Multivariable Volume 2: Derivatives by Robert Ghrist
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Overview: This volume is the second 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 2: Derivatives uses vector and matrix algebra to understand derivatives and their applications to multivariable calculus. Topics covered in this text include:
* multivariate functions with arbitrary numbers of inputs & outputs
* partial derivatives
* the derivative as a linear transformation on vectors of rates of change
* differentiation rules, including the chain rule as matrix multiplication
* the inverse and implicit function theorems, with applications
* gradients and directional derivatives
* linearization and Taylor expansion of multivariate functions
* optimization of multivariate functions
* applications to linear regression, game theory, & Nash equilibria
* constrained optimization and the Lagrange multiplier
* a hint of deeper applications in optimization theory, dynamical system, & more
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 3), each containing exercises for practice, for 475 pages of mathematics and color and joy and hard work.
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