Questions tagged [calculus]

For questions applying to calculus courses. Topics include derivatives, integrals, limits, continuity, series, application questions, etc.

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4
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1answer
107 views

More advanced (free) alternatives to Geogebra and Math3D?

I teach vector calculus. I love both Math3D and Geogebra. But I have reached a limit in terms of what these programs can do. Some examples of features that I wish Math3D had: Draw vector fields with ...
4
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4answers
209 views

Average Cost to Velocity Analogy

In my Business Calculus class (U.S. college-level), we discuss three aspects of cost: Total Cost $C(q)$, Marginal Cost $MC(q)$, and Average Cost $A(q)$ where $q$ is quantity produced. The defining ...
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1answer
237 views

Is Stewart Calculus a good book for AP calculus exam prep?

I have some background from completing Silvanus Thompson's book, but I didn't fully grasp the later chapters in it. I'm going to use khan academy and maybe other resources as a supplement. How useful ...
7
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6answers
675 views

Distance Between Curves in First-Semester Calculus

In the optimization section of Calculus 1 a common problem is to find the minimum distance between a curve and a point. I'd like to extend this idea and be able to compute the minimum distance between ...
0
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1answer
232 views

Distance from the wall when reading a sign? A Calc I/II problem

Here is a question on a test I asked recently in a Calculus I class I teach on Saturdays. These are students who are planning to major in Math, and they are already taking AP Calculus BC in their high ...
4
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1answer
296 views

Exponential & logarithm in a high school calculus class

So recently I was teaching high school calculus to a high school class and I was wondering about the pedagogically best way to make students actually understand why the derivatives of the exponential &...
8
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3answers
328 views

I'm worried that my struggles with calc 2 mean I won't be able to become a professor later

I have just turned 18 and am in calculus BC (calc 1 & calc 2). I most certainly grasp and understand the concepts of calc 1 however every once in a while a I seem to struggle with the calc 2 work. ...
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2answers
168 views

How to explain the difference between a constant function and a linear function?

Both function types contain a straight line on a plane, so if a student asks for the difference between them what would be a standard or recommended way to explain it?
-4
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2answers
172 views

What is the most fundamental continuous function in calculus after a constant (totally straight) line?

What would be to teach in most countries and education systems? (Taught before "high education frames", i.e. before doing bachelor of arts in mathematics).
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4answers
292 views

implicit differentiation, formula of a tangent line

I need to understand "implicit differentiation" and after that I need to be able to explain it to a student. Here is an example: Find the formula of a tangent line to the following curve at ...
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7answers
2k views

An introductory example for Taylor series (12th grade)

I (a student) am doing a presentation on Taylor series in my class (12th grade, in Germany if this is relevant). I am looking for a good example where you can see when Taylor series might be useful. ...
7
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0answers
149 views

How to recognize possible dyscalculia in a student?

I am looking for input/advice regarding whether a student I just began tutoring may have dyscalculia - and, if so, how to go about broaching the subject / assisting them as best as possible. I'd ...
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17answers
9k views

How shall we teach math online?

Many universities, including mine, are now requiring we teach our courses online because corona. How shall we do this? Let’s brainstorm here. Some challenges: My school provides limited online ...
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5answers
2k views

Source of conceptual, multiple choice calculus questions

I'd like to give my Calculus 1 class periodic multiple choice questions that really test conceptual understanding. Ideally, I'd like these questions to require very little computation. I know that a ...
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2answers
104 views

How can I effectively learn and master Math and Statistics for Data Science?

I completed a BSc in Computer Science recently and am going on to do an MSc in Data Science. However, the only focussed math module I had during CS was in the first year and I didn't do too well. I ...
12
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16answers
6k views

How does one tutor an A-level student past the derivative paradox?

Background: I am new to this site, but have 1500 reputation on the main Maths Stack. I am (age-wise) a secondary student of maths, but for a very long time have been informally learning at home and ...
5
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5answers
2k views

Is Calculus Made Easy by Silvanus P. Thompson a good book for first-time calculus learners?

Specifically the one updated by Martin Gardner. I'm not studying as part of a high school or college course (I, in the near future, will though) just as a personal project.
8
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1answer
348 views

Ideas and/or references for projects for a business calculus course

I have undertaken the teaching a business calculus course for this semester (spring II). The various assesments for the students, include quizzes/hw/midterms/final exams, adjusted with suitable ...
14
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8answers
6k views

Why is differential calculus often presented before integral calculus?

Why is differential calculus often presented before integral calculus? Note: I'm still learning calculus at the moment. It seems that many elementary calculus texts describe differential calculus ...
39
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10answers
2k views

Reasons for (not) distinguishing $f$ from $f(x)$

Formally, if $f$ is a function, $f(x)$ is a value. So for instance, $f$ can be continuous, but not $f(x)$. In teaching at school and university, notation is quite often mixed up, e.g. the function is ...
5
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1answer
206 views

Making the leap from Pre-Calculus to Calculus

This question is targeted at teachers who taught both low and high level mathematics. I have a group of students that I'm currently teaching precalculus and they seem to be doing really well in all ...
2
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2answers
181 views

How to explain continuity and differentiability to highschool students? [closed]

I would say continuity is the idea that points numerically close to the input point of a function agree with the value of the function at that point. Now, suppose I introduce the idea of a derivative, ...
6
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2answers
556 views

Calculus limits taught in the US vs Spain?

So, I realize this can be a broad question, so I'll narrow it down. I have lived in Spain and own several Math textbooks from that country (the equivalent of 8th grade and high school Math). Has ...
4
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4answers
238 views

Showing applications of calculus to intro students

So I'm wrapping up my second year teaching high school calculus, and my first as an AP course. In addition to review, I'd like to end the year by giving the students a taste of the kinds of real-...
2
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4answers
388 views

Is it necessary to teach the definition of a limit for engineering majors? [closed]

I have always wondered whether it is necessary or not. For me, it seems that it is enough to teach them the intuitive idea, that is, limit is just an approximation of a certain process. what do you ...
5
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2answers
217 views

Term for candidates for inflection points

The critical points of a function $f(x)$ are candidates for local extrema, i.e., if a function changes from increasing to decreasing, or vice versa, it must happen at a critical point. Is there an ...
8
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1answer
350 views

Grade on proving |$a_1 +a_2+...+a_n| \le |a_1|+|a_2|+... +|a_n|$

In an Advanced Calculus course, students were asked to prove $$|a_1 +a_2+...+a_n| \le |a_1|+|a_2|+... +|a_n|$$ for $n$ real numbers $a_1,a_2,...a_n$ I am teaching assistant for this course, and one of ...
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4answers
883 views

Multiple students writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ -- why?

I'm currently teaching a couple of courses that have a calculus prerequisite, and within the last week I've had two students make notational mistakes that amount to writing $y\frac{d}{dx}$ rather than ...
12
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3answers
299 views

Are there any applications of $x^x$?

I'm teaching Calculus I. It's time for the derivative of $x^x$. In previous semesters, I've told students we mainly do this just for closure, so that we know that we can find derivatives of every ...
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8answers
9k views

"Real world" examples of implicit functions

When teaching implicit differentiation in freshman calculus I lack good examples which might help students relate the theory to applications in other sciences. So I'm looking for (relatively simple) ...
5
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3answers
470 views

Advice on Full Time Community College Math Instructor Position

I have to do a teaching demo on the following: Please treat the committee as students in your Calculus II class. Please take 12-15 minutes to introduce your lesson on the Taylor Series and its ...
6
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3answers
163 views

Is there a point at which it makes decidedly more sense to learn about a "linear approximation" to a function, rather than a "tangent"?

I'm tutoring a first-semester calculus student, and we were looking over the slides the teacher has used. After teaching (or rather, repeating, for those who completed AP high school math) basic ...
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4answers
274 views

Introducing derivative concept and definition

I need to give a short presentation on introducing a class of engineering students to the concept and definition of the derivative. I'm to assume that the students are currently at the appropriate ...
3
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2answers
191 views

Tabular Fundamental Theorem of Calculus

This semester in first-semester Calculus I've been trying to focus on how to do Calculus calculations when given a table of data since this seems to be of importance to science majors. There are ...
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0answers
59 views

History of business calculus/linear algebra curriculum

I will be teaching a combination of business calculus and business linear algebra, two classes that have been around awhile at my school. I’m assuming people are familiar with these types of classes. ...
10
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2answers
429 views

Why are so many online sources "wrong" about directional derivatives?

I noticed many seemingly reputable online sources have "incorrect" description of directional derivatives for real-valued functions in several variables. Here, by "incorrect" I ...
8
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3answers
540 views

Why teach the algebraic Calculus?

In the context of a standard undergraduate Calculus sequence, I've noticed there is a big emphasis on teaching the algebra part of Calculus. What I mean by this is that a student may feel more ...
12
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6answers
730 views

teach that $\frac10$ not defined properly

there're some students, who belive that $$\frac10 = \infty $$ I need to teach them that this is not true and $\frac10 $ is undefined, mathematically and give a good picture (for their minds) what is ...
2
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1answer
292 views

Are there any university programs that "supersize" calculus courses?

Most differential calculus courses begin with the theory (and analysis) of differentiation, followed by computations, and likewise integral calculus courses. That's a lot for a three credit course, ...
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11answers
5k views

Why do we still teach the determinant formula for cross product? And is it as bad as I think it is?

The cross product is an important vector operation in in any serious multivariable calculus course. In most textbooks that I'm aware of, right after the definition, we always introduce the ...
18
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4answers
565 views

"Function" vs "Function of ...": how much does it contribute to students difficulties?

Most textbooks I've seen (and teachers I've met, myself included) are rather careless about the distinction between variables and functions. For example, when we write $y=f(x)$ we all know that $f$ ...
9
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4answers
973 views

How to teach calculus (book recommendation)

I'm going to teach calculus for the first time to undergraduate students. I would like to know if there is some book about how to teach the concepts of calculus (e.g. limits, derivatives, etc.).
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1answer
311 views

Honors Precalculus: what topics to cut?

We’re precalculus honors teachers. In this year of Covid and reduced instructional time, what topics can we cut (Demana textbook) that would not hurt our kids in either calc AB or BC?
4
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1answer
256 views

Looking for a calculus books with very specific requirements

I plan to record lectures for a MOOC on Calculus sometime next year. The MOOC is targeted at an undergraduate audience that comprises engineers, math majors as well as majors in the sciences, etc. ...
11
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3answers
326 views

Usefulness of $u$-substitution in and beyond early Calculus?

My students, when presented with an integral (source) like $$\int (2x+2)e^{x^2+2x+3} \ dx$$ are apt to recognize derivative patterns like $u' e^{u}$ and reverse-engineer anti-derivatives rather than ...
21
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3answers
851 views

Tutoring a recalcitrant/awkward/exasperating student---special needs?

As part of my duties at a GTA, I spend several hours per week in our department's drop-in tutoring center. The center is open to all students enrolled in 100- and 200-level math courses, with the ...
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0answers
101 views

What notation do they use for mathematical expressions in Polish schools?

I thought of something like Polish notation all by myself and asked the question https://cs.stackexchange.com/questions/111067/could-we-define-the-decimal-notation-of-a-natural-number-as-a-series-of-...
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3answers
2k views

Are differential equations considered calculus and included in a calculus class or is it its own class?

Are differential equations considered calculus and included in a calculus class or is it its own class? Also, if it is its own class then what calculus classes does it come after?
4
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4answers
2k views

How are the basic trigonometric functions introduced to students?

The fundamental trigonometric functions $\sin(x)$ and $\cos(x)$ are used throughout the sciences, but I believe students are often introduced to a very limited initial understanding where it is ...
0
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1answer
241 views

Teaching Hours for AP Calculus AB [closed]

What are the estimated hours for teaching AP Calculus AB for students aiming for a 5? Similar question, how many hours of practice will the student need to put it. Some Clarifications based on ...

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