Vector Calculus Notes and Summary

Description

Clear and concise MAST20009 Vector Calculus notes and summary that I created and typeset. This summary prepares you for the topics that's yet to come as well as is perfect for revising for the final exam. Overview of topics 1. Functions of Several Variables (Sandwich Theorem, continuity and differentiability, Chain Rule for Functions of Several Variable, Taylor polynomials, Extrema, Lagrange multipliers). 2. Space Curves and Vector Fields (Parametric Paths, Vector Fields, Differential Operators, Identities, Scalar and Vector Potentials) 3. Double and Triple Integrals (Area, Fubini's Theorem, Density, Volume, Polar, Cylindrical and Spherical coordinate systems, Centre of Mass, Moments of Inertia). 4. Line and Surface integrals (path integrals, line integrals, scalar and vector surface integrals, flux integrals, oriented surfaces). 5. Path and Surface Integrals (Path and Line Integrals, Parametrised Surfaces, Tangents and Normals to Surfaces, Tangent Planes, Surface Areas, Integral of Scalar Functions and Vector Fields over Surfaces) 6. Integral Theorems (Green's theorem, Divergence Theorem, Stokes' Theorem, Conservative Fields, Gauss' Divergence Theorem, Maxwell's Equations). 7. Curvilinear Coordinate Systems (Scale Factors, Unit Vectors, Tangent to Curves)