Unit · year 2

MU-203 · Multivariable & Vector Calculus

Threads space · change26 lectures5 theorems

Calculus in many dimensions, culminating in the great integral theorems.

PREREQUISITES

L01	Euclidean Space, Curves, and Surfaces —
L02	Limits and Continuity in Several Variables —
L03	Partial Derivatives and Differentiability —
L04	The Total Derivative and the Jacobian Matrix Change of variables and the Jacobian
L05	The Chain Rule in Several Variables —
L06	Directional Derivatives and the Gradient —
L07	The Inverse Function Theorem —
L08	The Implicit Function Theorem —
L09	Taylor's Theorem in Several Variables —
L10	Critical Points and the Hessian —
L11	Constrained Optimisation: Lagrange Multipliers The method of Lagrange multipliers
L12	Applications of Lagrange Multipliers The method of Lagrange multipliers
L13	Multiple Integrals and Fubini's Theorem —
L14	Change of Variables and the Jacobian Change of variables and the Jacobian
L15	Polar, Cylindrical, and Spherical Coordinates Change of variables and the Jacobian
L16	Line Integrals and Work —
L17	Conservative Fields and Path Independence —
L18	Vector Fields: Divergence and Curl —
L19	Green's Theorem Green's theorem
L20	Surface Integrals and Flux —
L21	Stokes' Theorem Stokes' theorem
L22	The Divergence Theorem The divergence theorem
L23	Applications: Flux, Circulation, and Field Equations The divergence theorem, Stokes' theorem
L24	Differential Forms: A First Look —
L25	The Generalised Stokes Theorem Stokes' theorem, Green's theorem, The divergence theorem
L26	Synthesis: One Theorem in Many Dresses Stokes' theorem