Questions tagged [calculus]
For questions applying to calculus courses. Topics include derivatives, integrals, limits, continuity, series, application questions, etc.
420 questions
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A different way to assess students' preparation for calculus?
Everyone experienced in teaching calculus in typical state universities in the U.S.A. knows that the overwhelming majority of students' difficulties result from deficiencies in their knowledge and ...
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Teaching calculus vertically!
Let me begin by saying that I am not a scholar of mathematics education, but like many colleagues, I find myself teaching a calculus course for first-year university students. In particular, students ...
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Engineering applications of epsilon-delta?
Epsilon-delta definitions are obviously better than infinitesimal-based definitions because of tradition dating from the heroic era of Weierstrass's disciples.
On the other hand, in an old comment, ...
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Notation $y$ vs $y(x)$ for differential equation
Consider a linear differential equation, say, for the second derivative plus four times the derivative plus three times the "solution" function $x\mapsto y(x)$. Is there any good discussion ...
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Recommendations on number of exercises to do from Thomas Calculus 15th ed
So I wanted to review my calculus (1, 2, and 3) in prep for upcoming classes (starts Aug 2025/Fall since taking 2 gap semesters starting Dec 12th for personal reasons) like stats, diff eq, real ...
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Why are sequences and series typically taught in Calculus 2 and not Calculus 1?
As a current math student, I find the inclusion of sequences and series in Calculus 2 rather odd. Calculus 2 is a course dedicated to integration and its applications (integration techniques, ...
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Engaging students in the beauty of mathematics
I am a teaching assistant for Calculus I, and as a TA, I also take on teaching responsibilities.
My goal as a teaching assistant is to help students appreciate the beauty of mathematics—not just ...
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Why are volumes of revolution typically taught in Calculus 2 and not Calculus 3?
Solids of revolution are typically taught in Calculus II for most undergraduate students or in AP Calculus BC for most high school students. However, it seems to me that this topic is far more ...
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Emphasizing the decreasing condition in the Integral Test or in the AST (in Calculus II): is it worth the time?
The title is basically the question. But I guess I should expand a little. For the background, I'm teaching at a large public university in the US. Out student body is mixed in terms of their ...
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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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