INSANE H1 Vector Calculus Course Notes!
Subject notes for UniMelb MAST20009
Comprehensive course notes that I created that summarise the core content and include many applications and proofs, worked examples, as well as useful warnings.
Take a look through the beautifully typeset and detailed pages in the preview! The entire course is covered and in great detail. I achieved a high H1 (93 First Class Honours) in the subject and found that building notes was an effective part of the learning process.
Outline of topics
1. Functions of Several Variables (Multivariable limits, continuity and differentiability, Taylor polynomials, matrix chain rule, Lagrange multipliers).
2. Space Curves and Vector Fields (arclength, TNB frames, flow lines, differentiation operators and identities )
3. Double and Triple Integrals (double integrals, triple integrals, polar, cylindrical and spherical coordinate systems, change of variables).
4. Line and Surface integrals (path integrals, line integrals, scalar and vector surface integrals, flux integrals, oriented surfaces).
5. Integral Theorems (Green's theorem, Divergence theorem in the plane, Stokes' theorem. Gauss' theorem).
6. Curvilinear coordinate systems (cylindrical and spherical orthogonal coordinate systems, vector operators, volume and surface area elements)
Semester 1, 2020