Books/

access links to Apple Books

Our latest book (“not Div but Grad and Curl”) is a place to start if you are trying

to build a mathematical and geometric foundation for Calculus, Linear Algebra, and Differential Equations from the basic objects of points, vectors, and dual vectors

Note: "not Div but Grad and Curl" is an e-book of 7 chapters and 3 colored sidetracks that is split into 4 separate collections on Apple Books

Collection 1:

Chapters 1, 3, 4, and 5

Collection 2:

Chapters 1,3 plus Blue,Gray

Collection 3:

Chapters 2 and 7

Collection 4:

Chapters 6 plus Green

(see the reel below for a sample of which chapters cover which topics)

more books by

jason m osborne

unconcise/math

In A Curvature Story the concept of Curvature is introduced in pictures and animations with minimal use of or appeal to formulas. Many of the mathematical ideas used in following books are introduced as Graphical Definitions in this first book in the series.

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An Animated

Curvature Story

Follow treasure hunter and future mathematician Brenna from Australia to America to meet new friend and coder Pete as they write a Not-Proof, try their hand at a Thought Experiment, and enlist the help of Tardis (Pete’s computer) to write a Real-Proof and Draw a Real-Map. All with the help of the Professor’s Indecipherable Notes.

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You can find this book as a FREE .epub e-book at Free Book Download/ (get an Access Code at Contact/)

The second book On Tensors: From Linear Algebra to Surface Curvature supplements the imagery of A Curvature Story with the mathematical machinery of tensors needed for a thorough treatment of both the intrinsic and extrinsic computation of surface curvature. The building of this tensor infrastructure is laid down on a solid Linear Algebra foundation that is motivated by an appeal to Color Vectors and Data Storage

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From the book On Tensors, one of the things we learn from Gauss' Theorema Egregium is that curvature is Intrinsic, whereby curvature can be defined completely in terms of The Metric Tensor. In this third book, we focus on illustrating the concept of intrinsic geometry and show how the elevation data of a topo map can be encoded in the metric tensor to obtain intrinsic distance and angle computations on a surface

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or

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With the geometric and computational understanding of curvature gained from the first three books, we delve deeper in this fourth book On Geodesic Triangles into a geometric treatment of Geodesics (on surfaces of revolution with the sphere as a special case) and show how the sum of the angles of these triangles are related to curvature

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