Multivariable-Calculus-Study

This project shares QSD's Multivariable Calculus Study files.
The project follows University of Oxford's Prelims Multivariable Calculus courses, with lecture notes and problem sheets available here: https://courses.maths.ox.ac.uk/node/43944.
The project majorly includes re-organising lecture notes to separate markdown files plus merging some additional materials from other sources.
The project works fine with obsidian.

Course Synopsis

Multiple integrals: Two dimensions. Informal definition and evaluation by repeated integration; example over a rectangle; properties. General domains. Change of variables. Examples.
Volume integrals: Jacobians for cylindrical and spherical polars, examples.
Recap on surface and line integrals. Flux integrals including solid angle. Work integrals and conservative fields.
Scalar and vector fields. Vector differential operators: divergence and curl; physical interpretation. Calculation. Identities.
Divergence theorem. Example. Consequences: Green's 1st and second theorems.
Uniqueness of solutions of Poisson's equation. Derivation of heat equation. Divergence theorem in plane. Informal proof for plane.
Stokes's theorem. Examples. Consequences. The existence of potential for a conservative force.
Gauss' Flux Theorem. Examples. Equivalence with Poisson's equation.

Some contents are summarised from various Internet sources, such as Wikipedia and Khan Academy.