Topics typically covered in Math 2310, Calculus III (Multivariable Calculus)


VECTORS AND THE GEOMETRY OF SPACE

3D coordinate systems. Vectors. Dot & Cross products. Lines and Planes. Quadric Surfaces.

VECTOR FUNCTIONS

Space curves. Derivatives & Integrals. Arc Length. Curvature.  Motion in Space: Velocity and Acceleration

PARTIAL DERIVATIVES

Multivariable Functions, Limits and Continuity, Partial Derivatives. Tangent Planes  and  Linear Approximation. Chain Rule. Directional Derivatives, Gradient
Maximum and Minimum Values. Lagrange Multipliers

MULTIPLE INTEGRALS

Double & Triple Integrals.  Applications. Change of Variables.

VECTOR CALCULUS

Vector Fields.  Line Integral. Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence.  Surface Integrals. Stokes' Theorem. The Divergence Theorem.