-4
votes
1answer
69 views

Are variables the same in pure mathematics???

my question is In pure mathematics, $x$ always $=x$ $x = x$, the variables are abstract. In modelling, $t$ could mean the time that has elapsed since you started a machine for example. Or ...
5
votes
2answers
48 views

Intuitive characterization of the graph of a twice differentiable function

In high school textbooks, the following characterizations are often found: A function is continuous if its graph can be drawn without lifting the pencil. and A function is differentiable if ...
5
votes
1answer
205 views

A question about a mathematical analysis book

I am a newcomer to Analysis. All knowledge I know about "Analysis" are differentials,limit and integration (basically, what we have been taught in high school) I am studying Principles of ...
0
votes
1answer
25 views

Finding eq of tan to the curve

I am trying to figure out how to find the eq to the tan to the curve x = cost + cos2t, y = sint + sin2t, (-1,1) I'm lost at the point where you plug in t in order to find the slope. I have the ...
6
votes
3answers
62 views

Interesting, unusual max/min problems?

So I've got to that stage of my elementary mathematics subject for engineers when we talk about differentiation and solution of max/min problems. And I'd like to entertain and engage the students ...
0
votes
2answers
77 views

What are the differences between mathematics courses taken by engineering majors and by math majors? [closed]

I am curious to know what are the differences between mathematics taken by engineering students and by math majors. Let's say in terms of the approach, depth and in the topics covered. And even within ...
1
vote
3answers
152 views

Is tutor essential for success in mathematics? [closed]

Everyone in my Pre-Calc - Calc I class is failing, except the kids who go tutor. They get top percentile ranks in the class. Should I drop maths all together so I don't have to invest in a tutor? I ...
1
vote
1answer
185 views

Gilbert Strang's books on calculus and linear algebra?Are they for math majors?

I would to know what are the best resources to use to teach and learn elementary subjects (calculus,linear algebra),I remember when learning calculus, I used Spivak's book which had wonderful ...
0
votes
1answer
22 views

Can i calculate velocity at a point P without using calculus in this case

I actually wanted to understand calculus. And read many a times, that concept of differentiation is about splitting the path into infinitesimally small divisions. In most cases the such division is ...
0
votes
0answers
50 views

Prerequisites of Vector Calculus for Freshman

I'm doing BSc as Physics major, i had studied Calculus and Vectors in 12th grade. For now i want to study Mathematical physics myself, i had decided to follow Arfken but it starts from the topics ...
3
votes
0answers
52 views

Where to post a Calculus review guide?

I created a PDF document (using LaTeX) in which I wrote relevant review materials and Calculus problems for Calculus 1, 2, and 3. Is there an appropriate forum where I could try to post this to ...
2
votes
1answer
82 views

How to get the domain of $x^x$?

The function $$f(x)=x^x.$$ is defined on $(0,\infty)$ because it is equal to $\exp\left(x\log\left(x\right)\right)$. But what happen when $x\leqslant0$? I tried for example $x=-1$, so ...
2
votes
1answer
108 views

Structured Self-Learning Program for Calculus I & II

I'm interested in a organised program which comprehensively covers the topics of Calculus I and Calculus II. I've recently finished taking my secondary school's university-level Calculus I course, ...
7
votes
3answers
295 views

Is formal logic necessary for pure/“higher” mathematics?

I'm asking this as an autodidact who wants to learn math rigorously for its own sake. And I was just wondering if understanding proofs could be achieved without a formal grounding in symbolic logic. I ...
1
vote
2answers
50 views

school exersise/ Differentiation

If $f$ is differentiable in ${\bf R}$ and for every $x \in {\bf R}$, $$ f(x+\cos x)-f(1-x) \leq x\cos x , $$ then prove that $f'(1)=1/2$. How is a school kid supposed to solve this exercise ? ...
10
votes
4answers
687 views

Why would you expand a square wave in a Fourier series?

The periodic square wave $$ f(x) = \cases{ 1 \text{ if } 0 \le x \le \pi \\ 0 \text { if } -\pi \le x < 0} $$ seems easy enough to work with. Why transform it into a series of sines and cosines? ...
16
votes
11answers
912 views

Why limits work

I'm currently a first year student in electrical engineering and computer science. I know how to compute limits, derivatives, integrals with respect to one variable that is things from one variable ...
7
votes
6answers
353 views

Evaluating the reception of (epsilon, delta) definitions

There is much discussion both in the education community and the mathematics community concerning the challenge of (epsilon, delta) type definitions in real analysis and the student reception of it. ...
8
votes
1answer
219 views

Darboux's Integral vs. the “High School” Integral

The definition of the integral below is what I usually call the "High School definition," because that's usually where I've seen it in use. Take a partition $\Delta = \{ x_0, x_1, x_2, \ldots, ...
19
votes
5answers
589 views

$\epsilon, \delta$…So what?

Over the course of my studies I often encounter phrases in reference material of the type "and this avoids the need for using $\epsilon$, $\delta$ definitions" or "by this we can omit those ...
5
votes
2answers
612 views

Examples of open ended calculus “class project” ideas

I have instructed calculus I an II, each once, at the college level and would like to emphasize that math is not just about memorizing formulas and concepts for a test and that applied math is not a ...
2
votes
3answers
104 views

On the nature of a first derivative

This is a very, very basic question. Never been very involved in math but I've been learning calculus in my free time, so here goes. I have observed some various things that happen with derivatives, ...
0
votes
2answers
986 views

How to learn calculus for beginners? [duplicate]

As a precalculus student interested in teaching myself calculus, where should I start and how should I go about learning? This question is different than past questions as I am not solely interested ...
2
votes
0answers
66 views

(Actual) applications of basic differential and integral methods

If this isn't the place, I apologize: At the end of my calculus class, we asked the students (among other things) what some applications of calculus methods are. Disappointingly, many focused on the ...
1
vote
3answers
125 views

How to show $\Bbb R$ is Archimedean?

Suppose $X$ is a real number such that $X > 0$. We want to show there exists and $n \in \mathbb{N}$ such that $X \geq \frac{1}{n} $. MY attempt: If $X < \frac{1}{n} \; \; \; \forall n $ then $X ...
0
votes
1answer
48 views

On the largest and smallest values of $ {D_{\mathbf{u}} f}(x,y) $, assuming that $ ∇f(x,y) ≠ 0 $.

I appreciate your time. If anyone can explain this problem, I would be most grateful. I need to understand this for a test, but I was not given any explanation. Assume that $ ∇f(x,y) ≠ 0 $. Show ...
3
votes
2answers
127 views

Trying to teach supremum and infimum.

I'm helping out my former calculus teacher as a volunteer calculus advisor, and I have under my supervision 5 students. They've already had an exam and... well, they failed. I read their exams and I ...
3
votes
2answers
345 views

What is the distance between the line and plane if it is parallel?

So far, I've gotten that the line is parallel to the plane $x = 2 + t$, $y = -3 + 2t$, $z = 1 + 4t$ With the vector of that being $U$ is $(1,2,4)$ and the plane $2y-z = 1$ with the vector $V$ being ...
0
votes
1answer
156 views

teaching inverse functions using ideas of codomain and onto functions

I am looking for some resources (books, Web sites, etc.) for teaching calculus students about inverse functions, using the ideas of codomain and onto functions (as well as one-to-one functions, of ...
15
votes
8answers
960 views

Should a high school introductory calculus class teach $\varepsilon$-$\delta$ proofs?

It seems to me that most high school students are comfortable with the intuitive notion of a limit ("as $x$ gets arbitrarily close to $c$, $f(x)$ gets arbitrarily close to $L$") and gain little ...
2
votes
1answer
239 views

What textbook should I get to self-learn Calculus? [duplicate]

I did not have the option to take calculus during high school. I would like to pick up this subject during my free time. I am a software engineer. I would like to improve my understanding of maths. ...
2
votes
3answers
154 views

Darboux integral too sophisticated for Calculus 1 students?

I strongly prefer Darboux's method to the one commonly found in introductory level calculus texts such as Stewart, but I'm worried that it might be a bit overwhelming for my freshman level calculus ...
2
votes
0answers
112 views

What is $0^0$? Should we define $0^0$ on its correctness or convenience? [duplicate]

What is $0^0$ ? I have read many debates about this question. The debate has been going on at least since the early 19th century. At that time, most mathematicians agreed that $0^0$ = 1, until in ...
5
votes
3answers
137 views

Is there a simple geometrical description of $e$? [duplicate]

Of course I am not looking for a definition through $\int_1^e{1\over x} \, \mathrm{d}x=1$ or that slope of $a^x$ at $x=0$ is $1$ when $a=e$. I am looking for something understandable by a kid who has ...
3
votes
1answer
417 views

Math refresher that covers several courses?

This is my first post in Mathematics but I'm not new to these forums. I use stakoverflow as I'm in software as a professional. This is going to be long post - not to mention a lot of what may seem a ...
1
vote
1answer
189 views

Question about the greatest lower bound of sets.

Let $A$ and $B$ be sets of real numbers. Define a set $A+B$ by $A+B =\{a+b|a \in A, b \in B\}$. Show that if $A$ and $B$ are bounded sets, then $g.l.b.(A+B) = (g.l.b. A)+(g.l.b.B)$. (The g.l.b. ...
1
vote
2answers
90 views

Can anyone explain the method used for finding the answer to this question?

I was practising questions on principles on mathematics. I stumbled onto this question and I don't know where to start. Can anyone please help?? If $P_1\,P_2\,\ldots\,P_n$ is a regular polygon in ...
8
votes
2answers
497 views

Strengthening My Foundation in Mathematics

"For every equation you introduce, you cut your audience in half." This expression, which I believe came from Stephen Hawking, summarizes why I believe that I have a weak foundation in ...
2
votes
1answer
84 views

What does brace below the equation mean?

An example of what I am trying to understand is found on this page, at Eq. 3. There are two braces under the equation... What is the definition of the brace(s) and how does it relate to Sp(t) and ...
1
vote
1answer
116 views

Randomly place $n$ balls in $n$ buckets - how many empty buckets?

A question posed on John D. Cook's blog asks: Suppose you have a large number of buckets and an equal number of balls. You randomly pick a bucket to put each ball in one at a time. When you’re ...
45
votes
13answers
6k views

Why do we need to learn integration techniques?

After a lifetime of approaching math the wrong way, I took two college math courses this quarter with a newfound zest for math. These classes are integral calc and multivariable calc. Integral calc ...
3
votes
0answers
67 views

Calculus in undergraduate programme [closed]

How would calculus (multivariable calculus, vector calculus, integral calculus, differential calculus) be taught in undergraduate programme (U.S.)? For example, in freshman, what would be taught, in ...
1
vote
1answer
170 views

Should students be taught that $\int dx/x = \log(|x|)$? [closed]

I think in precalculus students should be taught the following: Euler's identity for $e^{i \theta}$. The principal value of $log(x)$ for $x<0$. Then in Calculus they should be taught that $\int ...
12
votes
5answers
6k views

Which calculus text should I use for self-study?

I am 36 years old, and have forgotten a lot of math from high school, of which I only took up to Algebra 2. However I am teaching myself mathematics and am now, as an adult, completely fascinated ...
8
votes
2answers
339 views

Outline and Goals of a One-Year Calculus Sequence

Our department is considering restructuring our traditional three semester calculus sequence so that the calculus requirement for our majors is satisfied in two semesters. Does your department ...
43
votes
3answers
7k views

What is the importance of Calculus in today's Mathematics?

For engineering (e. g. electrical engineering) and physics, Calculus is important. But for a future mathematician, is the classical approach to Calculus still important? What is normally taught, as a ...
-1
votes
1answer
320 views

preparation for calculus [closed]

What are the differences in the level and kind of preparedness for calculus typically found in students beginning a calculus course at a university in the USA today, and those beginning such a course ...
1
vote
1answer
1k views

Differences among James Stewart calculus texts?

Can anyone describe the differences between James Stewarts's Calculus and Calculus: Concepts and Context? They appear to be nearly identical, though slightly arranged versions of exactly the same ...
16
votes
4answers
3k views

Bridging any “gaps” between AP Calculus and College/Univ level Calculus II

I've been asked to tutor a soon-to-be college freshman who has taken AP Calculus and successfully earned college credit for first semester calculus. He has been admitted to an Engineering program, ...
1
vote
1answer
2k views

Would it be fine to use Serge Lang's two Calculus books as textbooks for freshman as Maths major?

I'm a freshman in Maths major, but the recommanded textbook(Calculus:A Complete Course by Robert A. Adams) by Prof. of Calculus course is too much expensive, well, I found there're Serge Lang's two ...