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!
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Search the site: (WARNING- search not yet comprehensive)
- 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.
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 - 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)
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)
- 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)
MATH 0090 (FIRST-YEAR CALCULUS) (top)
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 page last updated 31 October, 2008 5:03 PM