Vector Calculus, Linear Algebra, and Differential Forms by Hubbard

[micromass]

• Author: John Hubbard, Barbara Hubbard
• Title: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach
• Amazon Link: https://www.amazon.com/dp/0971576653/?tag=pfamazon01-20

 

[slider142]

This is an excellent companion to Spivak's "Calculus on Manifolds", as it provides lots of applied and numerical problems while Spivak provides theoretical problems. Both texts give excellent motivations and proofs.

 

[deluks917]

Hubbard does everything the hard way in my opinion. He covers suprisingly little in a huge number of large pages. Spivak is a much better read that gives a much better perspective. Each page/problem of Spivak is harder but there are less then a quarter as many.

 

[dustbin]

I kind of agree with deluks, but this text is FAR better than a normal multivariable text. Also, the author writes pretty well. I actually enjoyed reading the book. However, towards the end of the book, I started acquiring enough of the elusive "mathematical maturity" that I constantly wish he'd choose brevity in his writing. I just wanted him to get to the point... a bit too wordy.

I wish he talked about pullback when covering integration and differential forms, but I digress. Thankfully my instructor did. By the end of the text, I was helping people with their differential geometry homework (despite never taking the course)... so that was cool :-) Overall, I highly recommend the book, but another reference would be ideal (I used Spivak's CoM and Rosenlicht's Intro Analysis).

 

[wreckemtech]

Question for anyone who's used this book:

Is there a detailed step-by-step solutions manual available online or in print?

 

[deluks917]

Did you try google?

hint: this is a good idea

 

[JPKelly6]

I just ordered a solutions manual from Amazon. It was a bit expensive.

JPK

 

[QuantumCurt]

Would this book be a good choice as a supplemental text for my Calculus III class? This fall I'm taking both Differential Equations, and Linear Algebra. Followed by Calculus III in the spring. Given that I'll have already had plenty of exposure to both Diff EQ and Linear Algebra, would this still be a good choice?

 

[micromass]

Would this book be a good choice as a supplemental text for my Calculus III class? This fall I'm taking both Differential Equations, and Linear Algebra. Followed by Calculus III in the spring. Given that I'll have already had plenty of exposure to both Diff EQ and Linear Algebra, would this still be a good choice?

Sure, it's still a good choice. But I think there are better choices out there such as Spivak's calculus on manifolds or the second volume of Apostol's calculus.

 

[QuantumCurt]

Sure, it's still a good choice. But I think there are better choices out there such as Spivak's calculus on manifolds or the second volume of Apostol's calculus.

Thanks for the suggestions. I just checked both of those out, and I'm going to keep them in mind. I like the looks of Spivak's book. I know Spivak's 'Calculus' is a legend...I plan to pick it up sometime down the line.

I'm comparing reviews and 'Calculus on Manifolds' seems to be a bit better received than Hubbard's book.

 

[micromass]

Thanks for the suggestions. I just checked both of those out, and I'm going to keep them in mind. I like the looks of Spivak's book. I know Spivak's 'Calculus' is a legend...I plan to pick it up sometime down the line.

I'm comparing reviews and 'Calculus on Manifolds' seems to be a bit better received than Hubbard's book.

Both books are good. I wouldn't base myself too much on amazon reviews. Finding the right math book is something really personal. Read the first few pages of both books and see what you like most. You can't go wrong with either book.

 

[tridianprime]

It is brilliant. I have found it very easy to read, and the relaxed style of the writer makes it an enjoyable and motivating read. I would recommend it to anyone who likes Spivak.