Excellent collection of guides/resources for Calculus II  - online and e-book (download)*1*INTEGRATION TECHNIQUES*2*Integration by Parts - Of all the integration techniques covered in this chapter this is probably the one that students are most likely to run into down the road in other classes.*4*Integrals Involving Trig Functions - In this section we look at integrating certain products and quotients of trig functions.*4**4*Trig Substitutions - Here we will look using substitutions involving trig functions and how they can be used to simplify certain integrals.*4**4*Partial Fractions - We will use partial fractions to allow us to do integrals involving some rational functions.*4**4*Integrals Involving Roots - We will take a look at a substitution that can, on occasion, be used with integrals involving roots.*4*Integrals Involving Quadratics - In this section we are going to look at some integrals that involve quadratics.*4*Using Integral Tables - Here we look at using Integral Tables as well as relating new integrals back to integrals that we already know how to do.*4*Integration Strategy - We give a general set of guidelines for determining how to evaluate an integral.*4*Improper Integrals - We will look at integrals with infinite intervals of integration and integrals with discontinuous integrands in this section.*4*Comparison Test for Improper Integrals - Here we will use the Comparison Test to determine if improper integrals converge or diverge.*4**4*Approximating Definite Integrals - There are many ways to approximate the value of a definite integral.  We will look at three of them in this section.*1*APPLICATIONS OF INTEGRALS*2*Arc Length - We*apos*ll determine the length of a curve in this section.*4*Surface Area - In this section we*apos*ll determine the surface area of a solid of revolution.*4*Center of Mass - Here we will determine the center of mass or centroid of a thin plate.*4**4*Hydrostatic Pressure and Force - We*apos*ll determine the hydrostatic pressure and force on a vertical plate submerged in water.*4**4*Probability - Here we will look at probability density functions and computing the mean of a probability density function.*1*PARAMETRIC EQUATIONS AND POLAR COORDINATES*2*Parametric Equations and Curves - An introduction to parametric equations and parametric curves (i.e. graphs of parametric equations)*4*Tangents with Parametric Equations - Finding tangent lines to parametric curves.*4**4*Area with Parametric Equations - Finding the area under a parametric curve.*4*Arc Length with Parametric Equations - Determining the length of a parametric curve.*4**4*Surface Area with Parametric Equations - Here we will determine the surface area of a solid obtained by rotating a parametric curve about an axis.*4**4*Polar Coordinates - We*apos*ll introduce polar coordinates in this section. We*apos*ll look at converting between polar coordinates and Cartesian coordinates as well as some basic graphs in polar coordinates.*4*Tangents with Polar Coordinates - Finding tangent lines of polar curves.*4*Area with Polar Coordinates - Finding the area enclosed by a polar curve.*4*Arc Length with Polar Coordinates - Determining the length of a polar curve.*4**4*Surface Area with Polar Coordinates - Here we will determine the surface area of a solid obtained by rotating a polar curve about an axis.*4*Arc Length and Surface Area Revisited - In this section we will summarize all the arc length and surface area formulas from the last two chapters.*1*SEQUENCES AND SERIES*2*Sequences - We will start the chapter off with a brief discussion of sequences.  This section will focus on the basic terminology and convergence of sequences*4**4*More on Sequences - Here we will take a quick look about monotonic and bounded sequences.*4*Series The Basics - In this section we will discuss some of the basics of infinite series.*4*Series  Convergence/Divergence - Most of this chapter will be about the convergence/divergence of a series so we will give the basic ideas and definitions in this section.*4*Series  Special Series - We will look at the Geometric Series, Telescoping Series, and Harmonic Series in this section.*4**4*Integral Test - Using the Integral Test to determine if a series converges or diverges.*4*Comparison Test/Limit Comparison Test - Using the Comparison Test and Limit Comparison Tests to determine if a series converges or diverges.*4*Alternating Series Test - Using the Alternating Series Test to determine if a series converges or diverges.*4**4*Absolute Convergence - A brief discussion on absolute convergence and how it differs from convergence.*4*Ratio Test - Using the Ratio Test to determine if a series converges or diverges.*4*Root Test - Using the Root Test to determine if a series converges or diverges.*4**4*Strategy for Series - A set of general guidelines to use when deciding which test to use.*4*Estimating the Value of a Series - Here we will look at estimating the value of an infinite series.*4*Power Series - An introduction to power series and some of the basic concepts.*4*Power Series and Functions - In this section we will start looking at how to find a power series representation of a function.*4**4*Taylor Series - Here we will discuss how to find the Taylor/Maclaurin Series for a function.*4*Applications of Series - In this section we will take a quick look at a couple of applications of series.*4*Binomial Series - A brief look at binomial series.*1*VECTORS*2*Vectors The Basics - In this section we will introduce some of the basic concepts about vectors.*4*Vector Arithmetic - Here we will give the basic arithmetic operations for vectors.*4*Dot Product - We will discuss the dot product in this section as well as an application or two.*4*Cross Product - In this section we*apos*ll discuss the cross product and see a quick application.*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.*4**4**4* Extremely useful for teachers of Maths/Mathematics working through Calculus II (Math 2414).