Everything You Need to Know About Calculus 2

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Deviation between Calculus I,II,Three?

• Calculus
• Thread starter ExplosiveGaz
• Start engagement Dec 17, 2014

What is the difference between Calculus I,II,III? Which subjects distinguish them?

Which cocky-written report books would y'all recommend for each of these?

(I already have Calculus by Spivak, but I don't know if that covers Calculus I,2 or 3)

Answers and Replies

If y'all don't know whats in Calculus, then you are not ready for Spivak.

What is the difference between Calculus I,II,3?

It depends on the school. Get to a few academy web sites and look up the grade descriptions.

A common pattern is:

ane - limits and basic differentiation and integration
2 - more than sophisticated integration techniques, and infinite series
three - multivariable calculus a.k.a. vector calculus

If y'all don't know whats in Calculus, then y'all are not gear up for Spivak.

OK, I get it. Cheers.

The book I am currently reading is Technology Mathematics past Yard.A.Stroud. I oasis't seen this one mentioned in the Physics Forums nevertheless then I'm not certain if information technology is proficient or not. What I am trying to figure out is whether it includes all the calculus I will demand. There is a follow up volume called Avant-garde Technology Mathematics by Stroud that I haven't bought and I wondered if that 1 covered Calculus III.

Note that I am self studying and my previous knowledge is roughly A-Level standard (UK) but it was a long time ago when I terminal studied.

Pretty much any introductory (read: one thousand page long) calculus text will cover the textile presented in a three or 4 term calculus sequence. For example, my school uses Stewart'due south volume for four terms. The difference is often professorial preference and how expensive the book the is. Things like Spivak are meant as "advanced" textbooks that ane uses to extend all these things to more complicated mathematical structures (the manifold in Spivak's case).

Think of it similar learning algebra before calculus, or arithmetics earlier algebra, except this fourth dimension the gross field of study affair is still calculus.

Engineering Mathematics by K.A.Stroud

A Google search turned upward the publisher's spider web folio for this book, which includes a table of contents. I see some Calculus III topics (partial differentiation and multiple integrals), only this obviously does not include vector calculus (slope, divergence, whorl, line integrals, divergence theorem, Stokes's theorem).

Advanced Technology Mathematics by Stroud

According to the publisher's page, this includes "Vector Analysis, Parts 1, ii & 3" which I doubtable covers the vector calculus topics I listed above, but of form I tin't say for certain.

If you don't know whats in Calculus, and then you are not ready for Spivak.

^^This.

Spivak is more accurately called an introduction to existent analysis. It's very rigorous, and very abstract. I've completed calc I, calc Two, differential equations, and linear algebra. Next semester is calc III. I've made my way through some of Spivak, and it is a challenging book.

As jtbell pointed out, calc I is all about limits, derivatives, and applications of derivatives (graphing, optimization, related rates etc). The basic forms of integration are introduced at the end of calc I. Calc II is all nearly different methods of integration, and typically ends with infinite series. I found calc I to be a bit more conceptually difficult. Some of the notions that are introduced, such as the Epsilon-Delta definition of a limit are a bit abstract and a little hard to wrap your head around at first. Y'all likewise see the more formal definitions of a derivative and an integral, which can exist complicated and time consuming sometimes. Calc Two was, in my opinion, more than hard. It wasn't as conceptually hard, simply it's much more technically involving. At that place are a TON of methods of integration involved, and they tin can be easily confused and quite complicated.

From my experience:
Calculus I: limits, differentiation and integration
Calculus Two: Integration and it's applications-volume, surface area, arc length, etc.
Calculus Iii: Infinite sequences a series, power series, taylor series, vector spaces
Calcuslus Four: More learning about vector spaces, multivariable calculus, introduction to differential equations and more
I would besides like to recommend getting the Schaum's outline for Calculus.

From my experience:
Calculus I: limits, differentiation and integration
Calculus 2: Integration and it's applications-volume, surface surface area, arc length, etc.
Calculus 3: Infinite sequences a series, power series, taylor series, vector spaces
Calcuslus 4: More than learning well-nigh vector spaces, multivariable calculus, introduction to differential equations and more
I would also similar to recommend getting the Schaum'southward outline for Calculus.

Nonetheless, the Schaum's outline of calculus is dumbed down approach of conveying basic Calculus. I recommend Thomas Calculus with Analytic Geometry 3rd edition used in conjunction with an sometime version of Stewart Calculus.

What is the difference between Calculus I,Two,3? Which subjects distinguish them?

Calculus ane will be focused on the bones concepts of calculus. Limits, differentiation, and integration. Also some applications like linear approximations and optimization issues.

I would say Calculus 2 is both the direct continuation of that into more advanced techniques for those things just also the indicate where the concepts of differential equations are introduced. The main conceptual idea is that calculus bug are actually virtually finding solutions to a differential equation, and some basic methods for solving simple ones. You'll also meet sequences and series. It'due south likewise, from my experience, one of the big weed-out classes for engineering majors.

Calculus 3 is multivariable calculus, which extends the methods you lot learned in the first two semesters to working with vectors, parameterizations, and equations of more than ane independent variable.

Sometimes differential equations (may or may non be combined with linear algebra) is called "calculus 4", but since at that place may exist an "elementary" or "practical" version of these courses meant for engineering and physics majors taken after calculus 2 this is non e'er the case. Linear algebra covers the topics of vectors, vector spaces, and solving linear systems of equations. Differential equations covers methods of dealing with families of equations related by their derivative.

Spivak is a real analysis volume, not an introductory calculus book. Real analysis is much more formal than what you demand right at present. I would go with Stewart'south calculus book. It's what I learned with, and there'south plenty of old editions floating around that are dirt cheap.

However, the Schaum'southward outline of calculus is dumbed down arroyo of conveying basic Calculus. I recommend Thomas Calculus with Analytic Geometry 3rd edition used in conjunction with an sometime version of Stewart Calculus.

Thanks to anybody who answered my questions about the difference between Calculus I,2.III.

I have in fact ordered both of the books MidgetDwarf has recommended (second hand, older editions to keep the cost down. They haven't arrived yet though).

Tin I take it that these two books volition cover all the calculus I volition need to eventually study subjects like Classical Mechanics, Quantum Mechanics, Electrodynamics and Relativity? i.eastward. do they cover Calculus I,II, Iii & IV?

If at that place is indeed more calculus I need tin you lot recommend books across Thomas / Stewart?

(I appreciate that I will probably demand to study other maths bailiwick like more Linear Algebra, but for now I want to ensure I take calculus properly studied.)

As convention, calculus is typically broken up into I, II, and Three. Some schools on quarter systems and the like have a calculus IV, but information technology'due south less typical.

After the calculus sequence, the next courses you lot'll demand for physics are differential equations and linear algebra. With Calc I-III, differential equations, and linear algebra, you'll be pretty well prepared for everything you'd encounter in introductory physics. For the virtually part you really just need Calc I-3 though.

OK, I get it. Thanks.

The book I am currently reading is Engineering Mathematics by G.A.Stroud. I oasis't seen this one mentioned in the Physics Forums nonetheless so I'one thousand not certain if it is skilful or not. What I am trying to figure out is whether it includes all the calculus I volition need. There is a follow upwards book called Avant-garde Engineering Mathematics past Stroud that I haven't bought and I wondered if that 1 covered Calculus 3.

Note that I am self studying and my previous knowledge is roughly A-Level standard (U.k.) merely it was a long time ago when I final studied.

friend, @ZapperZ and @neosoul gave you a straightforward curtailed answer, if you lot desire to show appreciation similar their replies.

Concluding edited: Apr 20, 2015

All the same, the Schaum's outline of calculus is dumbed down arroyo of conveying basic Calculus. I recommend Thomas Calculus with Analytic Geometry tertiary edition used in conjunction with an erstwhile version of Stewart Calculus.

What Schaum's lacks in pedagogical composure, it makes upward in providing a wealth of problems, some solved, on which the reader can practice to hone his skill at solving calculus problems.

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Everything You Need to Know About Calculus 2

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