Jump to content

Menu

Calculus 1 vs Calculus 2


lewelma
 Share

Recommended Posts

Is it typical to count calc 1,  calc 2, and multivariate as three separate classes?  If so, which topics belong in calc 1 vs calc 2?

 

DS completed the AoPS book in addition to the first 10 chapters of Anton so that he got both the theoretical and applied approaches, which is why I want to give him 2 credits as I think it is both typical in the USA (I think) and represents his extra effort. 

 

This is the AoPS website's description of their book: This course covers limits, continuity, derivatives and their applications, definite and indefinite integrals, infinite sequences and series, plane curves, polar coordinates, and basic differential equations. (this is for both calc 1 and calc 2 I think. My understanding is that the book covers more topics than a standard high school calculus 1 course)

 

For Anton's text, the local university covers these chapters in its first course: limits and continuity, derivatives, implicit differentiations, graphing, integration.

 

And these Anton Chapters in its second course: applications of the definite integral in geometry, science and engineering; principles of integral evaluation, mathematical modeling with differential equations, infinite series, and parametric and polar curves and conic sections, and a bit of partial differentials.

 

How is calc 1 and calc 2 typically broken up in the USA?

 

Thanks,

 

Ruth in NZ

Link to comment
Share on other sites

Calc I usually corresponds to AP Calc AB. 

 

Calc II usually corresponds to AP Calc BC.  AoPS textbook covers the material on the BC exam.

 

Calc III usually corresponds to multivariable calculus.

 

This with a minor rearrangement.

 

AP Calc I usually corresponds to Calc I.

 

AP Calc BC usually corresponds to Calc I + II.

Link to comment
Share on other sites

AB: limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus.

 

BC: polar, parametric, vector-valued equations, and new topics (such as Euler's method, integration by parts, partial fraction decomposition, and improper integrals), and introduces the topic of sequences and series.

 

This is what I found.  Sound about right?

  • Like 2
Link to comment
Share on other sites

Calc I is usually differential calculus and about one chapter of integration. Calc II is usually integration techniques and sequences and series. 

 

On looking at Anton TOC, ch. 1-4 would be Calc I, ch. 5-7 and 9 would be Calc II, and most of ch. 8 would be covered in a diffeq class or possibly in an honors Calc II. Calc II might do separable equations at most (an engineering calculus class might be a bit different, my experience is with "standard" Calc I-II)

 

For AOPS, ch. 1-4 and part of ch. 5 would be Calc I -- probably through 5.3.3, and then Calc II would be the rest of the book, with ch. 8 and 9 getting skimpy coverage at best. 

 

Calc AB is rather odd as it doesn't line up precisely with Calc I -- it covers two quarters of a three-quarter sequence (Calc A, B, C, with the same coverage as Calc I-II), so universities that are on semesters (the majority of them by now) will grant credit for Calc I but not II. Calc BC lines up well in coverage with Calc I-II or with Calc A/B/C, providing one full year of university calculus if the student has thoroughly grokked the content. 

 

Frankly I would give him credit for Honors Calc I and Honors Calc II because of all the extra topics, but you can at least thoroughly justify Calc I and Calc II, or if you'd prefer, Calc AB and Calc BC. He has definitely covered everything that would be in there. 

 

 

  • Like 1
Link to comment
Share on other sites

The university told him that he had to self study ch 6-10 and the beginning of 13 from Anton to cover their calc 2 class and be ready for multivariate. (So in addition to your list: ch 10 is parametric and polar curves and conic sections, and the beginning of 13 is partial derivatives).  So that is what he did in addition to doing the entire AoPS calc book.

 

These are my course descriptions, second one is choppy still as I'm mixing and matching 2 different books topics.  I don't know this material, so not sure if it makes sense what I wrote:

 

Calculus 1: 1.0 credit.

The properties of functions of one variable and their use for modelling continuous phenomena, including ideas and applications of differential and integral calculus.

Textbooks: Patrick, David. Calculus. Art of Problem Solving Inc. 2012

Te Kura exams: Distinction in Differentiation and Integration.

 

Calculus 2: 1.0 credit.

Further topics in differential and integral calculus: the Riemann integral, techniques of integration, l’Hopital’s Rule, differential equations, Taylor polynomials, implicit, parametric and polar representation of curves, functions of two variables and their properties, introduction to sequences and series, and applications of the definite integral in geometry, science, and engineering. A theoretical and practical approach was studied concurrently using the two different textbooks.

Textbooks: Patrick, David. Calculus. Art of Problem Solving Inc. 2012

Anton, Bivens, and Davis. Calculus 10th ed. Wiley and Sons Inc. 2012.

 

 

 

 

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

 Share

×
×
  • Create New...