Beginning Calculus

[Jesus]

Hey everyone, I come yet again seeking assistance and advice. I am planning on going back to school next summer and taking some engineering courses. Now, my math skills are very rusty and I am aware there will be several calculus course I will have to take.

I would like to know of there are any books that teach the basics of calculus, and perhaps also contain example problems. I used to be quite good at math, but faltered in high school, and I haven't taken any such classes since a statistics course in college.

 

[Jorghnassen]

OK, first thing, all calculus books are mediocre (especially the ones written in English). Second, if you want a calculus book, go to your local college/university. Go visit the undergraduate math society. If they're having a book sale, you can talk to them but don't buy anything. Come back when they are not having a book sale. They should have tons of calculus books they can't get rid of and use as expensive doorstops and bookshelf support. Graciously offer to relieve them of a few for free. They will likely gladly accept. The only drawback is that you probably won't get a brand new book (which they will likely have sold at a technical discount to silly unsuspecting undergrads).

/it's possible to get brand new calculus books for free but you need to know the calculus prof well...

 

[Dylab]

Is it really neccesary to get a calculus book? I always heard that people really tend to have troubles with the stuff they were supposed to learn before they start. I would brush up on your algebra and trignometry.

 

[DanishDynamite]

During my early university days I came across a big, fat (English/American) book on calculus which started at the very basics and ended at very advanced stuff, but was extremely pedagogical throughout. It was one of the best books on a technical subject I've read.

Unfortunately, it is standing on my bookshelf in Denmark (I'm in Brazil) and for the life of me I can't remember the title. Can I get back to you in December when I'll probably go home for Christmas?

 

[sir drinks-a-lot]

Make sure you know your precalculus before you even get started. For example:

-Can you graph y=2x^3+2?
-Do you remember all of the trigonometric functions like, sin, cos, sec, etc.
-Can you write an equation for a circle of radius 3 with its origin at (0,0)?
-Can you give the limit of x^4/(x^3+1) as x -> infinity?

Even though you were good at math, sometimes it takes a bit of actually doing math to get back into the swing of things. I would go to a used book store and buy any precalculus workbook they have with exercises and the answers in the back, and start working some problems. The reason I say any precalculus book will do is that the stuff hasn't changed in years. As long as you have a bunch of problems, and the answers so you can check yourself you should be OK.

Good luck!

 

[Jesus]

Make sure you know your precalculus before you even get started. For example:

-Can you graph y=2x^3+2?
-Do you remember all of the trigonometric functions like, sin, cos, sec, etc.
-Can you write an equation for a circle of radius 3 with its origin at (0,0)?
-Can you give the limit of x^4/(x^3+1) as x -> infinity?

Even though you were good at math, sometimes it takes a bit of actually doing math to get back into the swing of things. I would go to a used book store and buy any precalculus workbook they have with exercises and the answers in the back, and start working some problems. The reason I say any precalculus book will do is that the stuff hasn't changed in years. As long as you have a bunch of problems, and the answers so you can check yourself you should be OK.

Good luck!

That's probably the best thing to do. I need to cover a lot of old ground, because I don't remember nearly enough of it.

DanishDynamite, if you remember in December, I'd greatly appreciate it!

 

[Beth]

Hey everyone, I come yet again seeking assistance and advice. I am planning on going back to school next summer and taking some engineering courses. Now, my math skills are very rusty and I am aware there will be several calculus course I will have to take.

I would like to know of there are any books that teach the basics of calculus, and perhaps also contain example problems. I used to be quite good at math, but faltered in high school, and I haven't taken any such classes since a statistics course in college.

Here are a couple of titles I like with links to Amazon. Both are more readible than the typical text book. They do a good job of explaining the basic ideas and giving you a head's up on some of the most common types of errors/tough problems that students will encounter. I think you might find them useful supplement to lectures.

How to Ace Calculus and Calculus made easy

You may want to audit an algebra class before beginning calculus. When I teach calc or precalc, I warn my students the hardest part of calculus is the algebra and trig. You really need to have those skills well in hand or calculus will be much much harder. You'll spend hours working through the detailed algebra and trig of the homework problems.

I have a bunch of math text books I'm looking to get rid of. I changed jobs a few weeks ago and am no longer teaching. The books are fine, but I lack storage space yet hate to throw out perfectly good math books. If you're interested, PM me.

Beth

 

[Jorghnassen]

Re: Re: Beginning Calculus

You may want to audit an algebra class before beginning calculus.

You don't need group or ring theory to do calculus . (No really, be sure to read the course description. So many non-math students register for Basic Algebra thinking it's going to be an easy course).

 

[Brown]

Make sure you know your precalculus before you even get started.

This is good advice. When I started engineering school, there were a lot of math subjects that were as important as calculus:

(1) Trigonometry. As you start drawing freebody diagrams with forces acting in particular directions, you need to know how to break these forces into horizontal and vertical components. And that means knowing your sines, cosines and tangents. Trig identities also play a major role in linear systems and basic signal analysis. You will also need trig for manipulation of imaginary numbers, which are typically introduced in an introductory circuits class.

(2) Geometry. You will need to know the basics of various shapes and curves, and how to graph them. Review congruence and similarity.

(3) Algebra. Cripes, there's more algebra than anything else. You need to memorize the formula for roots of quadratic equations (if you haven't already) and you need to be able to solve multiple equations having an equal number of unknowns. The ability to simultaneously solve multiple equations is one that gives a lot of beginning engineering students trouble. You should also practice multiplying polynomials, as there is a lot of this in engineering, too.

And then there's calculus.

Now, depending on your field of study, you may advance into areas of mathematics that are really interesting: convolution, Laplace transforms, Fourier series, Fourier transforms, differential equations, advanced linear algebra, wave functions, Maxwell's equations and so on.

 

[ernon]

<snip> I would like to know of there are any books that teach the basics of calculus, and perhaps also contain example problems. I used to be quite good at math, but faltered in high school, and I haven't taken any such classes since a statistics course in college.

I liked this one, here's a short review of it from Amazon.com:

"Calculus For Dummies" is intended for three groups of readers:

Students taking their first calculus course – If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.

Students who need to brush up on their calculus to prepare for other studies – If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course.

Adults of all ages who'd like a good introduction to the subject –

Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth.

This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. Calculus For Dummies covers the following topics and more:

Real-world examples of calculus
The two big ideas of calculus: differentiation and integration
Why calculus works
Pre-algebra and algebra review
Common functions and their graphs
Limits and continuity
Integration and approximating area
Sequences and series

 

[LostAngeles]

My book is pretty decent, but my current Calc teacher gripes about how they present some of the material.

"They do not show this in American books, but they do it this way in European books. I will show."

And he does.

And it's so much better and we can see where some of the stuff comes from.

(He's from the Ukraine where he used to teach, so he talks just like I posted.)

Generally, I feel that anything that shows you where the stuff comes from instead of constantly saying, "This is," is the best way to go. Sometimes if I can't remember something, if I can remember some of how it's gotten, I can rebuild it myself.

 

[Diamond]

I would recommend three books:

"How to Ace Calculus - the Streetwise Guide"
"How to Ace the Rest of Calculus"
"Forgotten Calculus"

The rest are just commentary. No, I'm not kidding.

 

[Dr Adequate]

Generally, I feel that anything that shows you where the stuff comes from instead of constantly saying, "This is," is the best way to go. Sometimes if I can't remember something, if I can remember some of how it's gotten, I can rebuild it myself.

It was years before I worked out why the product rule for differentiation is what it is. It makes such perfect sense... now.

It would have taken five minutes just to tell me.

 

[JamesM]

I would recommend three books:

"How to Ace Calculus - the Streetwise Guide"
"How to Ace the Rest of Calculus"

I concur with Diamond and Beth in recommending these books. Often, these sorts of publications are overburdened with "wacky" humour, but here it was never too annoying.

 

[LostAngeles]

It was years before I worked out why the product rule for differentiation is what it is. It makes such perfect sense... now.

It would have taken five minutes just to tell me.

You're kidding me. In high school calculus, the teacher taught us all the product, the chain, and the quotient rule by showing it to us with the delta-x and then followed it up by saying, "Never ever do that, just do this."