# Questions tagged [vector-calculus]

For questions about differential and integral calculus with more than one independent variable.

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### Advanced Calculus vs. Analysis for a first proof-based course

Question: Why was advanced calculus removed as the first proof-based course in favor of real analysis in most curriculums? I regularly see in advanced calculus books either that: its purpose is, ...
6answers
2k views

2answers
249 views

### Is there a study that compares 8-week vs 16-week math classes?

I see a push toward having undergraduate curriculums built around 8-week classes. This is mostly in the online education in the USA. Recently I have seen a number of these in sophomore or junior-level ...
3answers
148 views

### How to motivate the surface element

$\newcommand{\RR}{\mathbb{R}} \newcommand{\dd}{\mathrm{d}}$ In teaching multivariable integration on sub-manifolds in $\RR^n$, i.e. integrals over $k$-dimensional surfaces $M\subset \RR^n$ you define ...
4answers
426 views

### A question about Vector Analysis problems

Why is it difficult to find really challenging vector analysis problems (problems about Green's, Stokes' and Gauss' theorems in a Calculus 3 course) in Calculus books? Most of the problems are ...
2answers
196 views

### Undergraduate Vector Calculus Notation Mess

Question 1: What are your arguments in favor of the big array of different notations used in the context of undergraduate vector calculus: line integrals, surface integrals (of scalars and fields), ...
2answers
164 views

### What is a good way to teach Taylor expansion of multi-variable calculus?

I found teaching Taylor expansion for multivariable functions rather challenging. It is a bit complicated to prove and to to compute. So what happened to me last year was that my students simply ...
1answer
169 views

### Low-tech ways of visualizing multivariable and vector calculus

One way, which is the most obvious, is do sketches of 3d shapes that tend to be the ones that we can all draw (like rectangle, cone, cylinder, sphere, etc.) Another way is by analogy so even if we can'...
2answers
178 views

### In a typical 3rd-semester multivariate calculus course in the US, what kind of area integrals do students actually learn to do?

I teach mostly physics and a little math at a California community college. I've never taught the multivariate calculus course, but I have taught the electricity and magnetism course for which the ...
1answer
121 views

### Refreshing math knowledge

How do I refresh advanced math I learned at a graduate level? I once was able to do the full solution of a particle in a parabolic well and other advanced math, however 20 years later I'm struggling ...
0answers
325 views

### A proof based Multivariable Calculus and Linear Algebra

May I know how can I teach a proof-based Multivariable Calculus and linear algebra as a single course? While there are quite a few known books in the field such as: 1) Vector Calculus, Linear Algebra ...
1answer
454 views

### Downloadable MCQs on Mathematics

I am looking for multiple choice question (MCQ) based tests on some Mathematics' topics (details below), which could be downloaded in most preferably tex (LaTex) format or doc/docx format. Kindly ...
1answer
121 views

### Advanced textbook for vector fields [closed]

I am currently reading Spivak Calculus on Manifolds and Munkres Analysis on Manifolds. I am looking for a more advanced text, especially on vector fields as they relate to the great conserved fields ...
4answers
210 views

### Analogy for nested loops/integrals

In teaching students how to do iterated integrals, I would like to find some analogy using a finite task nested inside another finite task. It would be especially nice if it satisfied the following ...
1answer
165 views

### Vector Algebra Text [closed]

Recent developments in Geometric Algebra have extended vector algebra to include the outer product (wedge product) and bivectors. Is there a Vector Algebra text (preferably at the advanced high ...
1answer
76 views

### Multivariable limit problem [closed]

Im triying to explain this delta-epsilon problem, but I didnt find a way to attack effectively this rigorous demonstration I actually i tried a lot of inequalities (Cauchy-Schwarz etc), but nothing ...