Questions tagged [calculus]
For questions applying to calculus courses. Topics include derivatives, integrals, limits, continuity, series, application questions, etc.
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Does this explanation of integration and the Fundamental Theorems of Calculus make any sense?
First, Sue Pemberton (Pure Mathematics 1 Coursebook, 2018, Cambridge University Press) introduces
integration as the reverse process of differentiation ...
$\int x^3 \mathrm d x$ is called the ...
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Earliest real-world uses of Calculus and Linear Algebra
I want to illustrate in class that real-world applications of mathematics might take time to come to fruit. In this context, I want to find what the earliest real-world applications of Calculus and ...
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A visualization for the quotient rule
Context: first year didactics of mathematics course for middle school teacher students (in Norway).
I have a reasonable visualization for the product rule of derivatives: Consider a rectangle with ...
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Advice and Remedial Algebra Resources for Students Committed to Calculus
I've got a student in my introductory calculus course. They're failing because they lack algebra skills. They understand the concepts just fine, and can articulate their understanding fine, but get ...
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What theorems from single-variable calculus break down in the multi-variable context?"
In teaching multi-variable calculus, it's insightful to discuss with students not only how certain concepts from single-variable calculus extend to multiple variables but also where these extensions ...
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Motivating a definition of "gap" in a line just barely more advanced than the one used in the typical first-year calculus course
Imagine a course barely getting into some topics more theoretical than what is done in the typical very staid first-year calculus course, and the kind of students for whom such a course is appropriate....
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What is the terminology for "self-referral" integrals in calculus?
In the topic of integration and anti-derivatives in Calculus we come across cases where the attempt at integration by parts brings us back to the original integral, the most basic example being $\int ...
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Define logarithmic function by functional relation [closed]
My son was working the other day with exercises such as: Find all the mappings $f:\mathbb{N}\rightarrow\mathbb{Z}$ verifying
$$\forall m,n \in \mathbb{N}, f(m+n)=f(n)+f(m).$$
As another example: Find ...
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Any examples of calculus sequence that deemphasizes calculation tricks?
I'm considering creating a series of classes that explore deeper ideas in calculus without overemphasizing the various computational tricks used in integration and differentiation.
My vision is ...
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How can we explain intuitively the convergence and divergence of these two series?
It is known that $\displaystyle\sum_1^{\infty} \frac{1}{n^{1.000001}}$ converges while $\displaystyle\sum_{n\text{ is a prime number}}\frac{1}{n}$ diverges. Though we can logically prove these results,...
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Is this a viable Calculus 1 question?
A person is standing next to a hot air balloon. At the same time, the person starts moving away from the balloon at 5 ft/sec and the balloon rises straight into the air at a rate of 12 ft/sec. Is the ...
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Why not think of derivatives as fractions?
Back in high school—back in the 1900s, as my sons say—when our calculus teacher was introducing the chain rule...
$\frac{dy}{dx} = \frac{dy}{dt} \cdot \frac{dt}{dx}$
...he made a special point of ...
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"Real life" examples of limits of functions at finite points
This is more specific than this similar question on math.SE, since I'm not satisfied with the answers there.
Question:
Can you provide an interesting, natural and simple example of some physical/...
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Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs
Background
I'm informally helping a few students with college Calc 1. This isn't the first time I've aided people with calculus, and so they've sought me for help, though I don't consider myself to ...
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What would be a good pacing for teaching this calculus 2 course?
Next semester I'm going to lecture calculus 2 in an institution I just joined. However, when I had calculus 2 back then the syllabus was very different, it mainly covered several variable calculus up ...
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