## Calculus II (Applied) Review Sheets & Study Guides

Here are review sheets for (Applied) Calculus II

Approximation of Higher Degrees

Arc Length

Differential Equations

Improper Integration

Integration by Parts

Linear Approximations

More Integral Properties

Newton’s Method

Numerical Integration

Partial Fractions

Physical Applicatoins

RAMs

Regions Between Curves

Symmetric Integration

Trig Substitutions

Velocity and Net Change

Volumes by Integration

Series:

Alternating Series

Infinite Series

Sequences and Series Overview

Sequences

The Divergence and Integral Tests

The Ratio and Comparison Tests

The following notes are not created by me, but I think you might find them helpful if you’re in need of them. They are made by Paul Dawkins of “Paul’s Online Math Notes,” and they are of stellar quality. You can download the PDF for the entire course here: http://tutorial.math.lamar.edu/downloadfile.aspx?file=B,2,N

For some more basic review material, you can check out my AP Calculus BC Review Sheets at http://sites.tufts.edu/andrewrosen/2012/03/03/ap-calculus-bc-and-ab-review-sheets/

## To Anyone Out There:

Hello world! It’s so nice to see you. Well, I can’t really see you (that’d be creepy), but it’s so nice to have you here. This is a project of mine that I want to share with the world. I’m a student here at Tufts, and the best way that I study is to make review sheets. It allows me to review the material and gives me a way to reference the important parts of topics. I’ve been doing this since high school, so this is certainly not a new method to me. I had (and still have for now) a poorly run Google Sites webpage with all of my high school stuff, but I’d like to transfer all that over to a more professional and successful site, which is this one here! Since I’m in college now and since my study habits won’t be changing, this will become a repository for my college review sheets too, which will hopefully help those taking many sciences, engineering, or math classes. Right now, I only have review material that I have personally created, but one day I hope to have this become a database for review material, so-to-speak.

Anyway, enough of me rambling. I just want to make it clear though that this project is not going to be completed for a little while. Life at Tufts has been insanely busy, but I see this as a Spring break project for sure. It will most likely be essentially completed by the end of break if all goes as planned. I have uploaded two review sheets for Calc III. This is kind of a sample of what’s to come. I’ll upload posts with documents attached to them, and these will be organized in the panel on the right into College and High School Material. The posts will then be organized by individual class so that a user can simply go straight to the class that want to review for without surfing through an endless sea of posts. I have included a Facebook “share” button to share material with friends, and I guess everything else will come as it comes! All I ask is that you don’t try to claim the material as your own if it’s not. I spent a lot of time working on this, and all I ask is that the credit remains in my name.

Thanks for visiting! Let me know of any suggestions you may have as the site begins to take shape.

- Andrew

## Calc III (Multivariable Calculus) Review Sheets & Study Guides

Calculus: Early Transcendentals by Briggs and Cochran

Chapter 11 – Vectors and Vector-Valued Functions

Includes:

11.1 – Vectors in the Plane, 11.2 – Vectors in Three Dimensions, 11.3 – Dot Products, 11.4 – Cross Products, 11.5 – Lines and Curves in Space, 11.6 – Calculus of Vector-Valued Functions, 11.7 – Motion in Space, and 11.8 – Length of Curves

Chapter 12 - Functions of Several Variables

Includes:

12.1 – Planes and Surfaces, 12.2 – Graphs and Level Curves, 12.4 – Partial Derivatives, 12.5 – The Chain Rule, 12.6 – Directional Derivatives and the Gradient, 12.7 – Tangent Planes and Linear Approximations, 12.8 – Maximum/Minimum Problems, 12.9 – Lagrange Multipliers

Chapter 13 - Multiple Integration

Includes:

13.1 – Double Integrals over Rectangular Regions, 13.2 – Double Integrals over General Regions, 13.3 – Double Integrals in Polar Coordinates, 13.4 – Triple Integrals, 13.5 – Triple Integrals in Cylindrical and Spherical Coordinates

Chapter 14, Part I - Vector Fields

Includes:

14.1 – Vector Fields and Integrals, 14.2 – Line Integrals, 14.3 – Conservative Fields

Chapter 14, Part II - Vector Calculus – Part II

Includes:

14.4 – Green’s Theorem, 14.5 – Divergence and Curl, 14.6 – Surface Integrals, 14.7 – Stokes’ Theorem, 14.8 - Divergence Theorem

This is an excellent Calc III review sheet made by my friend Tyler Silber, a student at the University of Connecticut. You can find it here:

Calc III Review by Tyler

Also, this will help you with computing double integrals. It’s a Wolfram|Alpha widget to easily find the answer to a double integral. It can be found at: http://www.wolframalpha.com/widgets/view.jsp?id=f5f3cbf14f4f5d6d2085bf2d0fb76e8a

This review sheet is created by Paul Dawkins of “Paul’s Online Math Notes.” You can download a PDF of his Calc III review sheets at the following domain of his: http://tutorial.math.lamar.edu/downloadfile.aspx?file=B,11,N

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