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Xander Henderson ♦
Xander Henderson ♦
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As noted by other questions on this website (and in other answers), the course names "Calculus I/II/II/A/B/C/whatever" are not well defined: [1], [2], etc. These are course titles, not mathematical terms. This implies that the curriculum for such a class (or sequences of classes) is also not well defined. Instead, you should look carefully at the syllabi or course descriptions of the courses that you are expecting to take or have taken.

Broadly speaking, undergraduate calculus courses tend to cover the following topics:

  • Limits and Continuity: this typically includes a "naive" approach to limits (with, perhaps, some mention of $\varepsilon$ and $\delta$, though these are not typically covered in much detail) and some basic results on continuity, including the intermediate value theorem;

  • Differential Calculus in One Variable: the definition of the derivative, as well as results for computation (the power rule, the chain rule, L'Hospital's rule, etc.);

  • Integral Calculus in One Variable: the definition of the Riemann integral from Riemann sums, the fundamental theorem of calculus (which links integrals and derivatives), and a god-awful long time on techniques of integration, including "$u$-substitution" (the single variable change-of-variables formula), integration by parts, trigonometric substitution, etc.;

  • Sequences and Series: basic definitions and power series are typically covered here, as well as Taylor's theorem and various tests for convergence;

  • Multivariable Calculus: integration and differentiation in multiple variables—the big results are the change of variables formula and the Green/Gauss/Stokes/Divergence theorems (whatever you want to call these theorems, which are all basically corollaries of each other); and

  • "Applications": various "applications" are typically scattered throughout the curriculum, including models of ballistic flight, some simple differential equations, and (wait for it...) volumes of revolution.

In most of the curricula with which I am familiar, volumes of revolution are typically covered with techniques of integration. In a semester system, they often show up about half-way through the second semester of college calculus, after a bunch of trigonometric substitutions. This might be considered "Calculus II", but might also be called "Calculus IB". On the other hand, in a quarter system, volumes of revolution often show up at the beginning of the third quarter, in what might be called "Calculus IC" or "Calculus III" (depending on the institution).

So, again, read the relevant syllabi or course descriptions. If you see anything like "techniques of integration" or "volumes of revolution",

  • applications (or possibly techniques) of integration, or
  • volumes or solids of revolution,

in the description of the course you intend to take, then you are probaby not expected to know the topic going in. On the other hand, if you see these terms in the descriptions of the prerequisites for the course you intend to take, then you will need to bone up before you enroll.

As noted by other questions on this website (and in other answers), the course names "Calculus I/II/II/A/B/C/whatever" are not well defined: [1], [2], etc. These are course titles, not mathematical terms. This implies that the curriculum for such a class (or sequences of classes) is also not well defined. Instead, you should look carefully at the syllabi or course descriptions of the courses that you are expecting to take or have taken.

Broadly speaking, undergraduate calculus courses tend to cover the following topics:

  • Limits and Continuity: this typically includes a "naive" approach to limits (with, perhaps, some mention of $\varepsilon$ and $\delta$, though these are not typically covered in much detail) and some basic results on continuity, including the intermediate value theorem;

  • Differential Calculus in One Variable: the definition of the derivative, as well as results for computation (the power rule, the chain rule, L'Hospital's rule, etc.);

  • Integral Calculus in One Variable: the definition of the Riemann integral from Riemann sums, the fundamental theorem of calculus (which links integrals and derivatives), and a god-awful long time on techniques of integration, including "$u$-substitution" (the single variable change-of-variables formula), integration by parts, trigonometric substitution, etc.;

  • Sequences and Series: basic definitions and power series are typically covered here, as well as Taylor's theorem and various tests for convergence;

  • Multivariable Calculus: integration and differentiation in multiple variables—the big results are the change of variables formula and the Green/Gauss/Stokes/Divergence theorems (whatever you want to call these theorems, which are all basically corollaries of each other); and

  • "Applications": various "applications" are typically scattered throughout the curriculum, including models of ballistic flight, some simple differential equations, and (wait for it...) volumes of revolution.

In most of the curricula with which I am familiar, volumes of revolution are typically covered with techniques of integration. In a semester system, they often show up about half-way through the second semester of college calculus, after a bunch of trigonometric substitutions. This might be considered "Calculus II", but might also be called "Calculus IB". On the other hand, in a quarter system, volumes of revolution often show up at the beginning of the third quarter, in what might be called "Calculus IC" or "Calculus III" (depending on the institution).

So, again, read the relevant syllabi or course descriptions. If you see anything like "techniques of integration" or "volumes of revolution", in the course you intend to take, then you are not expected to know the topic going in. On the other hand, if you see these terms in the descriptions of the prerequisites for the course you intend to take, then you will need to bone up before you enroll.

As noted by other questions on this website (and in other answers), the course names "Calculus I/II/II/A/B/C/whatever" are not well defined: [1], [2], etc. These are course titles, not mathematical terms. This implies that the curriculum for such a class (or sequences of classes) is also not well defined. Instead, you should look carefully at the syllabi or course descriptions of the courses that you are expecting to take or have taken.

Broadly speaking, undergraduate calculus courses tend to cover the following topics:

  • Limits and Continuity: this typically includes a "naive" approach to limits (with, perhaps, some mention of $\varepsilon$ and $\delta$, though these are not typically covered in much detail) and some basic results on continuity, including the intermediate value theorem;

  • Differential Calculus in One Variable: the definition of the derivative, as well as results for computation (the power rule, the chain rule, L'Hospital's rule, etc.);

  • Integral Calculus in One Variable: the definition of the Riemann integral from Riemann sums, the fundamental theorem of calculus (which links integrals and derivatives), and a god-awful long time on techniques of integration, including "$u$-substitution" (the single variable change-of-variables formula), integration by parts, trigonometric substitution, etc.;

  • Sequences and Series: basic definitions and power series are typically covered here, as well as Taylor's theorem and various tests for convergence;

  • Multivariable Calculus: integration and differentiation in multiple variables—the big results are the change of variables formula and the Green/Gauss/Stokes/Divergence theorems (whatever you want to call these theorems, which are all basically corollaries of each other); and

  • "Applications": various "applications" are typically scattered throughout the curriculum, including models of ballistic flight, some simple differential equations, and (wait for it...) volumes of revolution.

In most of the curricula with which I am familiar, volumes of revolution are typically covered with techniques of integration. In a semester system, they often show up about half-way through the second semester of college calculus, after a bunch of trigonometric substitutions. This might be considered "Calculus II", but might also be called "Calculus IB". On the other hand, in a quarter system, volumes of revolution often show up at the beginning of the third quarter, in what might be called "Calculus IC" or "Calculus III" (depending on the institution).

So, again, read the relevant syllabi or course descriptions. If you see anything like

  • applications (or possibly techniques) of integration, or
  • volumes or solids of revolution,

in the description of the course you intend to take, then you are probaby not expected to know the topic going in. On the other hand, if you see these terms in the descriptions of the prerequisites for the course you intend to take, then you will need to bone up before you enroll.

Source Link
Xander Henderson ♦
Xander Henderson ♦
  • 8.7k
  • 1
  • 23
  • 60

As noted by other questions on this website (and in other answers), the course names "Calculus I/II/II/A/B/C/whatever" are not well defined: [1], [2], etc. These are course titles, not mathematical terms. This implies that the curriculum for such a class (or sequences of classes) is also not well defined. Instead, you should look carefully at the syllabi or course descriptions of the courses that you are expecting to take or have taken.

Broadly speaking, undergraduate calculus courses tend to cover the following topics:

  • Limits and Continuity: this typically includes a "naive" approach to limits (with, perhaps, some mention of $\varepsilon$ and $\delta$, though these are not typically covered in much detail) and some basic results on continuity, including the intermediate value theorem;

  • Differential Calculus in One Variable: the definition of the derivative, as well as results for computation (the power rule, the chain rule, L'Hospital's rule, etc.);

  • Integral Calculus in One Variable: the definition of the Riemann integral from Riemann sums, the fundamental theorem of calculus (which links integrals and derivatives), and a god-awful long time on techniques of integration, including "$u$-substitution" (the single variable change-of-variables formula), integration by parts, trigonometric substitution, etc.;

  • Sequences and Series: basic definitions and power series are typically covered here, as well as Taylor's theorem and various tests for convergence;

  • Multivariable Calculus: integration and differentiation in multiple variables—the big results are the change of variables formula and the Green/Gauss/Stokes/Divergence theorems (whatever you want to call these theorems, which are all basically corollaries of each other); and

  • "Applications": various "applications" are typically scattered throughout the curriculum, including models of ballistic flight, some simple differential equations, and (wait for it...) volumes of revolution.

In most of the curricula with which I am familiar, volumes of revolution are typically covered with techniques of integration. In a semester system, they often show up about half-way through the second semester of college calculus, after a bunch of trigonometric substitutions. This might be considered "Calculus II", but might also be called "Calculus IB". On the other hand, in a quarter system, volumes of revolution often show up at the beginning of the third quarter, in what might be called "Calculus IC" or "Calculus III" (depending on the institution).

So, again, read the relevant syllabi or course descriptions. If you see anything like "techniques of integration" or "volumes of revolution", in the course you intend to take, then you are not expected to know the topic going in. On the other hand, if you see these terms in the descriptions of the prerequisites for the course you intend to take, then you will need to bone up before you enroll.