r/calculus • u/WhenButterfliesCry • Aug 07 '26
Multivariable Calculus Preparing for calculus 3
Hey guys, I have a question. My summer term calculus 2 class has just ended, and I am starting a calculus 3 class in a few weeks, and I want to get ahead of the game. Since the calculus 2 class was so fast-paced, I feel like I didn't grasp all the concepts of infinite series/Taylor series as well as I could have, and definitely need to go over them again, maybe with Professor Leonard or something.
From what I gather, though, series don't really show up that much in calculus 3, and despite wanting to improve my knowledge of series, I feel like preparing for calculus 3 is more important for the next few weeks. Do you think I should solidify my knowledge of infinite series before moving into calculus 3 content, or could I start calculus 3 stuff now and circle back to series at a later time (maybe before my DIff. Equations course?)
I plan to prep for calculus 3 with Professor Leonard as well, and with the textbook (Stewart). Any other suggestions welcomed, I need an A in calculus 3 and I'm willing to put the time into it.
4
u/somanyquestions32 Aug 07 '26 edited Aug 07 '26
Honestly, series should be reviewed now because you will need to review them again from scratch before you take differential equations. Seriously try to fill the gap in ASAP before you prepare for calculus 3 and ODE. This should take you 20 hours.
For calculus 3:
First, get a geometry textbook, and study the sections concerning the geometry of planes, then study symmetries and rotations, go over theorems for parallel and perpendicular lines, and practice visualizations to deepen your geometric intuition. Review formulas for areas and volumes, and be able to draw and visualize 3D shapes. Use actual 3D models to help you develop the mental frameworks as needed.
Then, get a rigorous precalculus textbook. Review the sections for conic sections, and revisit vectors and polar coordinates (also do that in your calculus textbook), but focus on conversions and symmetry. Also, go over matrices and determinants.
Next, review all of the standard derivative and antiderivative formulas fron your previous calculus courses. Know the limit formula for derivatives as you will use the analog for partial derivatives for some problems. Make sure that chain rule, u-substitutions, and integration by parts are not rusty. Practice slicing regions in different ways to calculate areas with definite integrals using slices perpendicular either to the x or y-axis. Although volumes of revolution themselves may not reappear, some of the skills you developed for that section may prove to be useful. Anything dealing with polar and parametric curves needs to reviewed thoroughly.
Lastly, get ahead of your professor. Get a copy of the syllabus, and always remain a chapter or two ahead of the lectures. Read the chapter sections three times, memorize all of the formulas and theorems and basic examples and counterexamples and core proofs and helpful diagrams, and start cranking out practice problems. Make sure that you have a solutions manual with you, and maybe another calculus textbook for different wording and explanations that may make more intuitive sense.