# Brown University Calculus Review

This page is currently a work in progress. It contains content modeled to supplement the material covered in Brown University's Calculus courses. If you have any comments at all and a little time to spare, please drop us a line at our Feedback Form. It will e-mail your comments to the creators of the page. Thank you for your help in constructing this review site!

IMPORTANT NOTES:

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-We have a new, more logical url for our site: math.brown.edu/help/. Please update any links and/or bookmarks soon!

Search the site: (WARNING- search not yet comprehensive)

### PRE-CALCULUS (top)

Algebra Basics

Expanding & Factoring - How to multiply and expand polynomials, and tricks for factoring large polynomials. (DEC)

Domain and Range - An important page on the significance of the domain and range of a function, and how to find them. Never forget to check the domain and range of a function! (DEC)

Discontinuities - A page on the different types of discontinuities found in functions. (DEC)

Manipulating Graphs - A page with great demos on how functions and graphs are related. Checking out this page will give you a better sense of how algebra and graphing are related - guaranteed or your money back. (JVE)

Functions (Composition of & Inverses) - This page covers the composition of functions, like computing , as well as how to find the inverse of any function. Even yours! (DEC)

Limits - Methods for calculating limits, pre-calc style (No derivatives needed!).

Function Families
Polynomials - A page dedicated to polynomials - what they are, how to graph them, and how to manipulate them. (JVE)

Rationals - This page deals with the graphing and manipulation of rational functions, which are functions that can be expressed as a function. (JVE)

Exponential Functions - Graphing and examples of exponential functions; i.e. functions of the form f(x) = ax (JVE)

Logarithms - Rules and graphs of Logarithmic functions, like f(x) = loga x (JVE)

Trigonometry
Trigonometry - An extensive coverage of pre-calc trigonometry topics, including trig identities, graphs, and lots of pretty diagrams. Our AAA page. (JVE)
Review & "Cheat-Sheet" Study Guides

Algebra Pitfalls - A page that identifies common problems students have with the material and how to avoid them. Check this out if you find yourself making a lot of mistakes. (DEC)

Trig Quick Review - A cheat-sheet-styled page that has a quick summary of identities and values of trigonometric functions. Very helpful to print out and glance at. (JVE)

### MATH 0090 (FIRST-YEAR CALCULUS) (top)

Differentiation

Basic Derivative Rules - The page has all you need to do basic derivatives, including a summary of your major rules and some examples. (JVE)

Equation of a Line; Equation of Tangent Line - If you ever need to know how to find the equation of a line, or find the equation of a tangent line to a function, check this page out. (DEC)

Derivatives of Trig Functions - Quick and dirty statements of the derivatives of basic, reciprocal, and inverse trig functions, as well as proofs of these derivatives for the more skeptically-minded. (JVE)

Derivatives of Exponential & Logarithmic Functions - Exactly what it sounds like. Also includes description and examples of the technique of logarithmic differentiation. (JVE)

Implicit Differentiation and Related Rates - More methods to find rates of change and derivatives, for when we can't use our simple, explicit differentiation means. (DEC)

Max/Min Word Problems - A general method to solve word problems that require maximization or minimization. (JVE)

Newton's Method & Linear Approximation - All about how to use tangent lines to approximate curves, both for estimating zeroes and for estimating the value of a function at a point. (JVE)

Integration
U-Substitution - This page discusses when and how to use the integration techinique of u-substitution, also known as "chunking." (JVE)
Review and "Cheat-Sheet" Study Guides

Outline/Study Guide for First-Year Calculus - This page features a complete outline of the first-year of Calculus. It covers everything, from differentiation to integration. Also a great thing to print out and keep around. (JVE)

Tips for Taking Derivatives - Check out this page if you have any trouble finding derivatives. An insider's guide on everything differentiation. This page leads naturally to... (DEC)

Worked Examples of Difficult Derivatives - PAGE UNDER CONSTRUCTION (DEC)

Garden behind Kassar House, Brown's Math Department

### MATH 0100 (SECOND-YEAR CALCULUS) (top)

Material for Math 10 will be added over the course of the Fall Semester of 2008. In the meantime, enjoy this limerick:

A student as smart as could be
Had to integrate x to the 3
He said "x to the 4
over 4, I am sure"
But was off by a constant of C.

This website is being designed by Dylan Cashman '10 and Jonathan Eldridge '11 under the supervision of Professors Thomas Banchoff and Steven Miller during the Summer and Fall of 2008.

This page last updated 31 October, 2008 5:03 PM