Excellent collection of guides/resources for Calculus III  - online and e-book (download)*1*THREE DIMENSIONAL SPACE*2*This is the only chapter that exists in two places in my notes. When I originally wrote these notes all of these topics were covered in Calculus II however,*4*we have since moved several of them into Calculus III.  So, rather than split the chapter up I have kept it in the Calculus II notes and also put a copy in the Calculus III notes.*4**4*The 3-D Coordinate System - We will introduce the concepts and notation for the three dimensional coordinate system in this section.*4**4*Equations of Lines - In this section we will develop the various forms for the equation of lines in three dimensional space.*4*Equations of Planes - Here we will develop the equation of a plane.*4*Quadric Surfaces - In this section we will be looking at some examples of quadric surfaces.*4*Functions of Several Variables - A quick review of some important topics about functions of several variables.*4**4*Vector Functions - We introduce the concept of vector functions in this section.  We concentrate primarily on curves in three dimensional space.  We will however, touch briefly on surfaces as well.*4*Calculus with Vector Functions - Here we will take a quick look at limits, derivatives, and integrals with vector functions.*4*Tangent, Normal and Binormal Vectors - We will define the tangent, normal and binormal vectors in this section.*4*Arc Length with Vector Functions - In this section we will find the arc length of a vector function.*4*Curvature - We will determine the curvature of a function in this section.*4**4*Velocity and Acceleration - In this section we will revisit a standard application of derivatives.  We will look at the velocity and acceleration of an object whose position function is given by a vector function.*4*Cylindrical Coordinates - We will define the cylindrical coordinate system in this section.  The cylindrical coordinate system is an alternate coordinate system for the three dimensional coordinate system.*4*Spherical Coordinates - In this section we will define the spherical coordinate system.  The spherical coordinate system is yet another alternate coordinate system for the three dimensional coordinate system.*1*PARTIAL DERIVATIVES*2*Limits - Taking limits of functions of several variables.*4*Partial Derivatives - In this section we will introduce the idea of partial derivatives as well as the standard notations and how to compute them.*4*Interpretations of Partial Derivatives - Here we will take a look at a couple of important interpretations of partial derivatives.*4**4*Higher Order Partial Derivatives - We will take a look at higher order partial derivatives in this section.*4*Differentials - In this section we extend the idea of differentials to functions of several variables.*4*Chain Rule - Here we will look at the chain rule for functions of several variables.*4**4*Directional Derivatives - We will introduce the concept of directional derivatives in this section.  We will also see how to compute them and see a couple of nice facts pertaining to directional derivatives.*1*APPLICATIONS OF PARTIAL DERIVATIVES*2*Tangent Planes and Linear Approximations - We*apos*ll take a look at tangent planes to surfaces in this section as well as an application of tangent planes.*4*Gradient Vector, Tangent Planes and Normal Lines - In this section we*apos*ll see how the gradient vector can be used to find tangent planes and normal lines to a surface.*4*Relative Minimums and Maximums - Here we will see how to identify relative minimums and maximums.*4*Absolute Minimums and Maximums - We will find absolute minimums and maximums of a function over a given region.*4*Lagrange Multipliers  In this section we*apos*ll see how to use Lagrange Multipliers to find the absolute extrema for a function subject to a given constraint.*1*MULTIPLE INTEGRALS*2*Double Integrals - We will define the double integral in this section.*4*Iterated Integrals - In this section we will start looking at how we actually compute double integrals.*4*Double Integrals over General Regions - Here we will look at some general double integrals.*4*Double Integrals in Polar Coordinates - In this section we will take a look at evaluating double integrals using polar coordinates.*4*Triple Integrals - Here we will define the triple integral as well as how we evaluate them.*4*Triple Integrals in Cylindrical Coordinates - We will evaluate triple integrals using cylindrical coordinates in this section.*4*Triple Integrals in Spherical Coordinates - In this section we will evaluate triple integrals using spherical coordinates.*4*Change of Variables - In this section we will look at change of variables for double and triple integrals.*4*Surface Area - Here we look at the one real application of double integrals that we*apos*re going to look at in this material.*4*Area and Volume Revisited - We summarize the area and volume formulas from this chapter.*1*LINE INTEGRALS*2*Vector Fields - In this section we introduce the concept of a vector field.*4*Line Integrals  Part I - Here we will start looking at line integrals.  In particular we will look at line integrals with respect to arc length.*4*Line Integrals  Part II - We will continue looking at line integrals in this section.  Here we will be looking at line integrals with respect to x, y, and/or z.*4*Line Integrals of Vector Fields - Here we will look at a third type of line integrals, line integrals of vector fields.*4*Fundamental Theorem for Line Integrals - In this section we will look at a version of the fundamental theorem of calculus for line integrals of vector fields.*4*Conservative Vector Fields - Here we will take a somewhat detailed look at conservative vector fields and how to find potential functions.*4*Green*apos*s Theorem - We will give Green*apos*s Theorem in this section as well as an interesting application of Green*apos*s Theorem.*4*Curl and Divergence - In this section we will introduce the concepts of the curl and the divergence of a vector field.  We will also give two vector forms of Green*apos*s Theorem.*1*SURFACE INTEGRALS*2*Parametric Surfaces - In this section we will take a look at the basics of representing a surface with parametric equations.  We will also take a look at a couple of applications.*4*Surface Integrals - Here we will introduce the topic of surface integrals.  We will be working with surface integrals of functions in this section.*4*Surface Integrals of Vector Fields - We will look at surface integrals of vector fields in this section.*4*Stokes*apos* Theorem - We will look at Stokes*apos* Theorem in this section.*4*Divergence Theorem - Here we will take a look at the Divergence Theorem.*4**4**4* Extremely useful for teachers of Maths/Mathematics working through Calculus III (Math 2415).