<p>I am taking vector calculus (cal 3, w/e) and my teacher is garbage. I am making good grades on my exams, but not necessarily knowing whats happening. I could go figure it out, but I am unsure on the importance of these concept. Likely, I should be going to a petroleum program next year.</p>
<p>What exactly are the important concepts to grasp out of vector calculus?</p>
<p>Thanks</p>
<p>vectors in different coordinate systems, divergence, gradients, curls and surface, volume and line integrals.</p>
<p>I had an atrocious Calc 3D professor in undergrad, and I never really got what most of the more complicated functions are. I did find a solid understanding of what partial derivatives to be very useful, though.</p>
<p>In simpler terms (very elementary level) our world isn’t as flat as our 2-D graphing paper.
You see it’s a lot easier to define things in terms of vectors.
Many applications in physical sciences require the use of vector. For example, defining a vector field. The concept may be as simple as just every point has a vector attach to it.
If you have to deal with E&M, fluid dynamics, you will end up using vector caculusu: curl F, div, etc.</p>
<p>As basic as introductory physics, think about the relationship between normal, tangent with the normal and tangential vectors in vector calculus. We may see our worlds in 2-D terms. But when you are in space, you have a surface, a plane.</p>
<p>In real life, we don’t integrate things over a straight line. 99% of the time it’s going to be a curve, a joint-curves, in space. </p>
<p>As far as for engineers, these things will appear later in other courses that require vector calculus. If you are neither a physics major, nor a math major, I don’t think you need to dive into too deep.</p>
<p>Since I teach E&M - I can tell you that the main weakness students have coming into my class is a lack of understanding of vector calculus. Even those who seem to have a slight understanding, don’t seem to have a clue that there are physical applications of these concepts.</p>
<p>Now I remember why I left EE after taking E&M. I NEVER liked vectors and E&M soured me even more…and once I became a Math major, I went the computational route, so I was done with vectors.</p>
<p>It can be a problem that many of the professors teach “pure” mathematics, and they lack of interest to teach vector calculus in respect with engineering.</p>
<p>At CCNY, this is how calculus and vector calculus works.
For calc 3, which is mutli-variable calculus, basic vector calculus (everything until vector fields and beyond are not consider as basic vectors) are taught. So you learn cross product, dot product, finding tangent line, parametric equation, double and triple integrals.</p>
<p>But beyond basics, the actual vector calculus, that is starting from parameterizing a curve, line integral, vector field, green’s theorem, Stork’s theorem, surface integral, and beyond are taught in vector calculus. </p>
<p>In fact, for engineers and scientist (mainly for engineers and physics major), we combine linear algebra and vector calculus together into one course, instead of two like other schools do. </p>
<p>My professor has background in physics and mathematics, so in class he talks a lot about the applications used in engineering and physical science. I only have two problems: hand writing sucks, and he speaks too quickly - not too informative, which I would love to do. The mathematics - he just teaches us how to do the problem, unlike my previous calc3 professor who writes copious notes on the board, and does pure math explanations.</p>
<p>But it’s very difficult to find a perfect candidates that match everyone’s taste. </p>
<p>I think that could be a potential reason why some mathematicians claim Math =/= Physics.</p>
<p>I read this a few weeks ago when I started vector field in class. At this point I am still not able to interpret the concept of field (which is totally outside of our scope - that’s a pure math thing).
<a href=“http://www.physics.orst.edu/bridge/papers/calculus.pdf[/url]”>http://www.physics.orst.edu/bridge/papers/calculus.pdf</a></p>
<p>OP, your problem is that you are relying heavily on your teacher. Your best option is to find several vector calculus books + khan academy + paul’s online notes + etc. and gain understanding on your own.</p>
<p>The best students teach themselves.</p>