MATH 2310: Calculus III

Vectors and the Geometry of Space

• 3-Dimensional Space
• Cylinders & Quadric Surfaces
• Vector Algebra
• Dot Product
• Cross Product
• Lines & Planes

Vector Functions

• Parametric Curves
• Basic Calculus of Vector Functions
• Arc Length, Curvature, & the TNB Frame
• Tangential & Normal Components of Acceleration

Partial Derivatives

• Functions of Several Variables
• Limits & Continuity
• Partial Derivatives
• Tangent Planes & Linear Approximation
• Chain Rule
• Gradient Vector & Directional Derivatives
• Lagrange Multipliers
• Extreme Values

Multiple Integrals

• Introduction to Double Integrals
• Double Integrals over General Regions
• Double Integrals in Polar Coordinates
• Triple Integrals
• Triple Integrals in Cylindrical Coordinates
• Triple Integrals in Spherical Coordinates
• Change of Variables in Multiple Integrals

Vector Calculus

• Vector Fields, Curl, & Divergence
• Line Integrals
• Fundamental Theorem for Line Integrals
• Green's Theorem
• Parametric Surfaces & Their Areas
• Surface Integrals
• Stokes' Theorem
• Divergence Theorem