Questions tagged [calculus]

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

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Deriving Jerk Equations without using Calculus

I am thinking about the links between SUVAT equations (constant acceleration), and equations for motion when higher-order measurements are constant (for example, when jerk is constant, or snap is ...
214 views

Simple initial value problems - pros and cons of different methods

Consider the problem: Find $f(x)$ if $f’(x)=4x$ and $f(3)=12$ I have always done this, and taught it, as a two-step problem: First, find the general anti-derivative, $f(x)=2x^2+C$, and then plug ...
946 views

Ideas for a 2 weeks project focused in polynomial functions

Right now I’m teaching precalculus in high school and I want to propose a project to my students about polynomial functions. They already know enough about quadratic functions and we study variation ...
158 views

Alternative ways of thinking about the one-variable Riemann integral for elementary calculus,

I think I've done a decent job with teaching my students limits and derivatives so far in elementary calculus -- they were particularly intrigued with how easy and how accurate a first-order, linear ...
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When analytic form of derivatives is preferred over numerical form?

Is there a specific example when the analytic form of a derivative $\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$ is preferred to the numerical form $\frac{f(x+h)-f(x)}{h}$, $h \ll 1$? Are there cases when the ...
941 views

Is Calculus Necessary?

That title is a quote from Fred Roberts: Fred Roberts. "Is Calculus Necessary?" Proceedings of the Fourth International Congress on Mathematical Education. 1980. p.52ff. "Calculus is not ...
2k views

Activities for biology undergraduates taking integral calculus

After searching for applications of calculus for biology students, I've found that many of the results are all either contrived exercises, or are way over the heads of students that are seeing ...
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Notebook software for exploring integral approximation with finite sums?

Calc 2 (integration) courses often begin by introducing the idea of approximating the area under curves by rectangles, drawing pictures like this one of $y=\sqrt{x}$ Here we can approximate the area ...
303 views

calculus without analytic geometry

How much of introductory calculus can be learned without using analytic geometry or for that matter any algebraic notations but simple euclidean geometry? Are there any resources(new ones not the old ...
988 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 ...
240 views

How to catch students from different subjects' interest to math?

I have just started to teach Calculus to freshmans and sophomores who study non-mathematical subjects, e.g., international relations, psychology. They have to take few mathematics classes -including ...
340 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. ...
7k views

Why are calculators not allowed in post-secondary exams?

Before you downvote this question, I actually want an answer to this. Is the calculator going to give me my derivative? No. Is it going to give me my integral? No. It can sure give me the answer to my ...
955 views

We tell undergraduate students that they should study two to three hours for every hour they spend in class. We know that many students don't follow through with this nearly to the degree that they ...
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Why is the convergence of infinite series covered in Calculus II?

I'm teaching AP Calculus BC for the first time this year. The AP curriculum is an attempt to cover most of the material in a two-semester university freshman calculus series, and so I am reminded of ...
111 views

books of mathematics [closed]

a)I am trying to get a book that would give describe all the coordinate systems and their transformations(e.g. cartesian,polar,spherical,homogeneous,curvilinear,generalized,etc). b) And I need to ...
351 views

Functions can be divided into odd and even components - name of theorem?

I'm explaining to a student that all functions can be divided into odd and even (symmetric and anti-symmetric) components. It is easy to prove (basic algebra or Taylor series) but is not referenced in ...
399 views

Alternative limit for e

I have recently worked with some students motivating the development of $e^t$ and $e^{t i}$ as summing change over time, basically informally solving differential equations. My motivation for this is ...
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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 ...
3k 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 ...
My students are often getting confused while using chain rule for complicated functions. For example $$f(x)=\tan^3\left(\sqrt{x^2+x+1}\right)$$ Most of the students wrote $f'(x)$ wrongly as f'(x)=...