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Vector calculus is often included in multi variable calculus, aka calc 3. ODE and PDE, assuming you mean differential equations, has their own classes from my experience called Differential Equtions I and II. In America, it goes from all the basic knowledge like algebra and trig, to Calc 1, 2, 3, Differential Equations, and Linear Algebra.
If anyone's currently taking calc 3, I can't recommend khan academy's multivariable calc playlist enough. It's taught by the 3Blue1Brown guy and unlike on his own channel he actually dumbs things down enough for us average IQ people while still providing both an intuitive and rigorous understanding.
Schools on quarter systems tend to cover limits, derivatives, and applications of derivatives (optimization, related rates) in Calc 1, antiderivatives, integration and its applications in Calc 2, and infinite series in Calc 3. Where I taught, multivariable calculus was Calc 4, and vector calculus was covered in a fifth term.
I have just finished my Calc 3 course with an A minus. I found it harder than Calc 1 and Calc 2. I dont know how is it taught in US, but where I live we had a great emphasis on sketching the graphs and specially applying coordinate changes, specially being able to identify patterns regarding when to transform to polar and spheric coordinates.
Hey smartass, i was finishing up calc 3 when i made that comment. Calc 3 was by far the hardest. calc 2 was just as easy as calc 1, its the same shit except with series. as long as its 2-dimensional, you shouldnt struggle at all if you put the time into it. calc 3 is a whole different type of math, the beginning of true math is how i would describe calc 3
After calc 3 (multivariable and vector calculus), you are encouraged to continue math classes woth linear algebra and/or differential equations. Regarding college class numbers: it varies between schools, but one rule of thumb I've seen is that the first digit typically hints at when the student "should" take the class.
Calculus three is the calculus you learned in calc one and two, applied to a three dimensional vector space (x,y, and z) instead of just (x,y). Really important ideas for understanding physics on a more conceptual level.
The majority of lin alg wont be used in calc 3. That said, getting an exposure to a proof based course is a good idea, so try learning linear algebra the proof way (how everyone should learn it). It wont help you build intuition for calculus though. Linear algebra is one of the most fundamental courses as a math or physics major.
Calc 3 really doesn't teach you anything new. It's moreso a culmination of all the ideas of Calc 1 and 2, so more than learning something new, you'll be applying what you already know to more advanced problems. One very important thing in Calc 3 is the ability to visualize stuff, but you can't really prepare for that, it'll come with practice.
So far, I am finding Differential Equations to be simple compared to Calc 3. In Calc 3, you will need to get used to memorizing the equations and theorems in the latter part of the course. Setting up the integrals is probably the hardest part of Calc 3. </p> <p>Diff Eq involves way more memorization than Calc 3.