(Not so) Mathematics Basics

This material is part of the basics-books project. It is also available as a .pdf document.

Contents.

• Linear Algebra. …, matrix factorization,…; basics of lots of numerical methods; Vector and Tensor Algebra provides the mathematical framework for manipulating vectors and tensors, the mathematical objects meant to represent absolute quantities - invariant under coordinate transformations - fundamental in geometry and physics.

• Multivariable Calculus provides the tools for working with continuous functions of many variables; Differential Geometry studies smooth curves, surfaces, volumes (and manifolds in general), within the framework of a Riemann structure, providing a metric to define distances, angles, curvatures and other geometric properties; Vector and Tensor Calculus studies vector and tensor fields defined on a manifold, along with their differentiation and integration, and thus being essential for a mature approach to geometry and physics;

• Functional analysis and Complex Calculus (complex analysis, transforms,…)

• ODEs

• PDEs

• Calculus of Variations: theoretical background; Lagrange multiplier method for constraints; sensitivty; gradient-based methods,…

• Optimization