So you have decided to tackle of the beast of Calculus III? Like many other college courses there are simple tips and tricks that the "pros" can hand down to give you a helping hand. The following three tips will give you that extra information you will need to walk in the first day feeling prepared. So by all means use these tips as best you can!
Tip #1: Carry Multiple Colored Pens!
In Calculus III you will be encountering graphs in both two dimensions and three dimensions that are far more complex than Calculus II. The first time you graph two 3D functions intersecting each other you will realize you have lines drawn everywhere! Using different colored pens allows you to easily distinguish one graph from another and allow you recognize exactly what functions you are looking at.
Tip #2: Have Your Calculus II Notes Ready to Review!
That's right! Right when you thought Calculus II was over with you now have refer back to your notes for Calculus III. In this class you will encounter multiple cases of U-substituion, trig substitution, polar coordinates, arc length, and others. All of these things will be integrated into the new material that you will be learning and chances are your professor will expect you to remember everything you learned in Calculus II. The good news is that after a few weeks in Calculus III chances are you remember these topics with no trouble.
Tip #3: Memorize All Common Functions In Three Dimensions!
In Calculus Three you will be integrating sections between functions in three dimensions. Nothing makes this process harder than not knowing what the three dimensional functions look like. Be sure to study and memorize functions like an Ellipsoid, Elliptic Paraboloid, Hyperboloid of One Sheet, Hyperboloid of Two Sheets, Elliptic Cone, and the Hyperbolic Paraboloid. If the time is taken to get familiar with these functions your efforts in Calculus III will be far more rewarding!
Happy Calculating!
-Dylan Miller
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