Mr. MacAulay’s Homework Blog

Math 611B Resources

If you miss a class or just need a little more of an explanation with a certain topic, have a look at these …  kindly let me know if you find any broken links.

Preparing for University Calculus at Atlantic Universities — excellent tips with practice problems/solutions of concepts you’ll need to have mastered going in

Coping with Math Anxiety” — worth a read if you have a moment

Graphing Resources: a couple of (free!) ones include Graphmatica and Desmos

  • No calculator at home?  Try this online scientific calculator or this one with a few extra bells and whistles.
  • HippoCampus — EXCELLENT resource!!  Check under Calculus I and II … links to many math and calculus topics; each one includes a mini-lesson with examples and audio.
  • There are a few decent YouTube video collections that each contain dozens of examples of different math topics, including things we cover in every one of our high school math courses!!  DEFINITELY worth taking a look through on your own … just use the search box to look for a particular topic in each one.  Some good ones:  PatrickJMT, Paul’s Online Math Notes, Math Videos from Heather, The Infinite Looper, and Professor Leonard
  • Need some extra help with certain topics?  Why not Ask Dr. Math!
  • An excellent variety of tutorials and videos is online at the Kahn Academy.  Click on the “Subjects” link at the top of the page, then on “Math.”
  • Another good general-purpose site: Math is Fun! (No, really!)
  • Examples of many topics we’ll cover can be found at Visual Calculus

A few selections on the concept of limits and derivatives … (also, check out HippoCampus above)

  • “Introduction to Limits” (YouTube) … again, pretty good basic explanations here if you don’t mind all the colours, and a few of his other videos are also helpful here
  • “What is a Limit?” (YouTube) … this video and a few others that follow it are worth a look, as they go through different examples involving calculations
  • “Limits at Infinity” (YouTube) … shows a couple of worked examples
  • “Calculating Limits with the Limit Laws” — four good worked and explained examples, involving radicals and rational expressions (Parts 2-4 are on the right)
  • Limits involving Conjugates: Video 1, Video 2
  • Continuity:  Video 1, Video 2
  • Secants to Tangents (and Normals):  Video 1, Video 2, Video 3
  • Tutorials for the Calculus Phobe — a nice treatment of the basics:  limits and derivatives.
  • Some websites and videos dealing with differentiation:
    • “First principles” examples (use h in place of their Δx)
    • More worked examples with solutions
    • Product Rule, Quotient Rule and Chain Rule examples
    • Another great playlist: Chain Rule, trig derivatives, inverse trig derivatives, … don’t worry about the hyperbolic trig derivatives at the end of the list
  • Critical Points and Increasing/Decreasing Intervals: Video 1, Video 2, Video 3
  • Concavity and Inflection Points:  Explanation, Example 1, Example 2 [many more in YouTube links shown to the right on these videos, too)
  • Curve Sketching: PatrickJMT has a several videos of worked examples — start with this one (Part 1 and Part 2) and look for more videos in the right sidebar; also use this chapter from another calculus textbook for more worked examples (3.5), and this site has several more examples (all but #5 and #11).  Avoid any slant asymptotes!
  • Implicit/Logarithmic Differentiation and Related Rates: a playlist of examples
  • Optimization Problems:
    • Several good examples (i.e. minimizing cost) can be found here (links on the right will take you to more examples by the same instructor)
    • Patrick JMT has several good examples here (again, follow links on the right to see the other examples)
    • A few more worked examples can be found on this site

Finally, some videos and sites for integral calculus:

  • Riemann Sum applets:  a couple can be found at Wolfram and at
  • Fundamental Theorem of Calculus:  an explanation
  • Patrick JMT’s playlist of integration basics: everything from Riemann sums to u-substitutions (don’t look at the trig substitutions or integration by parts videos)
  • Professor Leonard has several excellent videos as well (Lectures 4.1-5.1, down at the bottom of the list of videos)
  • Paul’s Math Notes – definite integrals and u-substitutions (this page and the next one)