Math 135: Calculus I (Fall 2005)

Course Information:

• See the Math 135 course website for more information about this class.
• * Syllabus
• Homework Problems
• Class Log -- a list of topics covered in each recitation section, and of homework problems to turn in

Useful Links:

• So you want to review trigonometry...
  • Trig Functions and the Unit Circle (you should know the first diagram here by heart)
  • University of Idaho Trig Review -- Series of online lectures reviewing basic trig definitions, includes some practice problems and solutions to test what you learn.
  • Trigonometry Realms -- Another online review of basic trigonometry, has good illustrations.
  • Mathwords.com: Trig Identities -- A list of common trig identities. You should learn the first few sections by heart.
  
  
• important theorems and ideas...
  • chapter 2
    • The Intermediate Value Theorem -- with a very good picture explanation (requires flash plug-in)
    • CoolMath.com: What's a Limit? -- a quick explanation with lots of pictures
    • Oregon State's Calculus Practice Pages -- especially check out the "compute limits" and the "more challenging examples" to practice and get instant feedback!
    • Harvey Mudd College's Review of Limits -- don't worry about the epsilon/delta definition, but the examples and questions on the first half of the page are good practice
  • chapter 3
    • practice finding the derivative of various functions using the limit definition
    • step by step examples with implicit differentiation
    • practice problems and solutions for implicit differentiation
    • implicit differentiation script -- see the steps to differentiate any function you want implicitly. (use this to check answers and to practice, not to do your homework for you! :P )
    • related rates tutorial -- complete with multiple choice questions to test that you're catching on as you go
    • *some notes on section 3.8 -- since there aren't many links about linear approximation or error analysis online, here's a few quick examples i've made up for you all. if you have questions or find typos, let me know :) (requires adobe reader)
  • chapter 4
    • the first derivative -- a good explanation of what the first derivative tells you about max/min/increasing/decreasing
    • first derivative test -- some practice problems (with solutions/explanations) on using the first derivative to find max/min and intervals of increase/decrease
    • second deriatives -- some illustrated examples of concavity and the second derivative test
    • curve sketching -- some practice problems (with explanations) for graphing functions by hand from the 1st and 2nd derivatives
    • limits at infinity -- practice problems (and solutions) for limits as x approaches infinity
    • L'Hopital's rule -- a few practice problems (and answer key) for taking limits with L'Hopital's rule
  • chapter 5
    • antiderivatives -- good explanation, and excellent drills (at the bottom of the page) with solutions.
  
  
• So you want some practice problems for the next exam....
  • the Rutgers Math 135 Main Course Page -- click on any previous semester to check out old exam review problems. if practice makes perfect, here's plenty of chance to practice. :)