- 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.
- 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.
React
Typescript
Django
Laravel
Facebook
Microsoft
Google
Alibaba
D3
Tencent