Math 314: Calculus of Several Variables.

Fall Semester 2015

Class Notes

Three Dimensional Coordinate Systems

Vectors Representation. Unit Vectors. Problem #37

The Dot Product

The Cross Product Product

Equations of Lines and Planes

Equations of Lines and Planes. Slides

Vector Functions

More on Vector Functions

Vector Functions. Some Problems

Motion in Space. Velocity and Acceleration

Chapter 14: Functions of two variables

Level Curves and Graph of a Function of Two Variables

Limits in 2D and 3D

Continuity

Partial Derivatives

Tangent Planes

Tangent Planes, Linear Approximations, Differentiability, and Differentials

Chain Rule. Implicit Differentiation

Directional Derivatives and the Gradient Vector

Maximum and Minimum Values

Maximum and Minimum Values for Closed Regions

Iterated Integrals

Integrals over General Regions

Double Integrals in Polar Coordinates

Applications of Double Integrals

Area computation: 1D Integral and double Integral. Volume Computation: Double and triple integrals

Triple Integrals

Triple Integrals in Cylindrical Coordinates

Integration in spherical coordinates

Change of Variables for Multiple Integrals

Vector Fields. Examples

Vector Fields

Line Integrals

The Fundamental Theorem of Line Integrals

Green Theorem

Curl and Divergence

Vector Calculus

Parametric Surfaces and Their Areas

Surface Integrals

Summary Surface Area and Surface Integrals

Stokes Theorem