Semester 1, 2018

MAST20009 - Vector Calculus Notes

56 pages

4,600 words




This is a comprehensive compilation of information from MAST20009 lectures, the textbook, tutorials, practicals, workshops, problem booklets and other useful sources I found online to aid my study.

Each section (particularly the harder concepts) is supported by easy to read and understand dot points, diagrams, pictures and thorough example exam-style questions.

Includes all summarised formulae required to know for each topic.

Topics included are:
1. Functions of several variables (limits, Taylor series, matrix version of chain rule, Lagrange multipliers).
2. Vector fields (divergence, curl, identities of vector calculus)
3. Integration techniques (double integrals, triple integrals, polar, cylindrical and spherical coordinate systems).
4. Integrals over paths and surfaces (path integrals, line integrals, surface integrals, flux integrals, oriented surfaces).
5. Integral theorems (Gauss' divergence theorem, Stokes' theorem, Green's theorem, Divergence theorem in the plane).
6. Curvilinear coordinate systems