<p>@mikeh5 Math 254 and Math 153 are generally different. However, they both briefly touch upon polar and parametric coordinates and equations that were also kinda in calc 2. In 254, you will need to know how to convert coordinates between spherical, cylindrical, and rectangular coordinates in 3D; which isn’t too bad.</p>
<p>However, both classes implement concepts you’ve learned in calc 1 and 2. If you’re going to take 254 and 153, I would recommend you nail down things like “u-substitution,” integration by parts, and partial fraction decomposition from calc 2 as those will be prevalent in at least both of these classes. Trig-substitution gets no love and was only used in my differential equations class, once.</p>
<p>Overall, 153 and 254 are vastly different; you probably won’t be missing out if you took 254 first. This is because both classes have different themes. The important aspects of 153 are the definitions and ways to determine the convergence and divergence of series and sequences (e.g. ratio test, integral test, etc.) and the ability to evaluate transcendental functions with Taylor and Maclaurin series as well as determine the ‘error’. In 254, it generally focuses on introducing 3D functions, how to do calculus with them, and multivariable calculus. All these concepts will be fleshed out more if you decide to take Math 255, vector calculus AKA ‘calc 5’.</p>
<p>If you want the skim over the course materials for these classes, here is the open-source Hoffman textbook:
<a href=“Calculus, Contemporary Calculus, Hoffman”>http://scidiv.bellevuecollege.edu/dh/Calculus_all/Calculus_all.html</a>
As a caveat, it seems like the author gave up near the end because section 13.8 and chapter 14 is riddled with errors which frustrated the hell out of me when I was taking that class.</p>
<p>Edit: Another reason to take those classes here is because the instructors at BC tend to be more lenient on beneficial curves than at UW.</p>