Calculus 3 Notes

Three Dimensional Space:

• Three Dimensional Space

• The 3-D Coordinate System

• Equations of Lines

• Equations of Planes

• Quadric Surfaces

• Functions of Several Variables

• Vector Functions

• Calculus with Vector Functions

• Tangent, Normal and Binormal Vectors

• Arc Length with Vector Functions

• Curvature

• Velocity and Acceleration

• Cylindrical Coordinates

• Spherical Coordinates

Partial Derivatives:

• Partial Derivatives

• Limits

• Partial Derivatives

• Interpretations of Partial Derivatives

• Higher Order Partial Derivatives

• Differentials

• Chain Rule

• Directional Derivatives

Applications of Partial Derivatives:

• Applications of Partial Derivatives

• Tangent Planes and Linear Approximations

• Gradient Vector, Tangent Planes and Normal Lines

• Relative Minimums and Maximums

• Absolute Minimums and Maximums

• Lagrange Multipliers

Multiple Integrals:

• Multiple Integrals

• Double Integrals

• Iterated 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

• Surface Area

• Area and Volume Revisited

Line Integrals:

• Line Integrals

• Vector Fields

• Line Integrals  Part I

• Line Integrals  Part II

• Line Integrals of Vector Fields

• Fundamental Theorem for Line Integrals

• Conservative Vector Fields

• Green’s Theorem

• Curl and Divergence

Surface Integrals:

• Surface Integrals

• Parametric Surfaces

• Surface Integrals

• Surface Integrals of Vector Fields

• Stokes’ Theorem

• Divergence Theorem