# Recommendations for Maths textbooks

1. Feb 1, 2006

### zanazzi78

Im reading undergraduate physic at level1.

The suggested reading has been "Anything with Maths for Engineers" in the title!

So ive been to the Uni library and found only 2 books,and they dont appear to be very good.

i intend to buy myself some books but would greatly appreciate some suggestions.

Below is a list of topics to be covered.

Mathematical modelling: How to set up differential equations.
First order differential equations.
Separation of variables.
Population growth, the logistic equation, radioactive decay.
Integrating factor method.
Second order equations with constant coefficients.
Homogeneous and non-homogeneous equations.
Damping and resonance.
Complementary functions and particular integrals.
Taylor series, and series solutions of differential equations.
Special cases of series solutions.
Nonlinear differential equations and equations with several dependent variables, e.g. the predator-prey equations or enzymemediated chemical reactions

The Sinh and Cosh functions. Some trig identities. Functions of two and three variables. Partial derivativesand the chain rule for partial derivatives.
Exact differentials and their physical significance (2 dimensions only). The gradient, divergence and curl of avector field. Polynomials: Roots, factors and the remainder theorem. Finding approximate roots from graphs.
Matrices and matrix arithmetic, determinants and inverses.
Solving systems of linear equations.
Matrices acting on vectors, eigenvectors and eigenvalues.
Fourier series.
Partial differential equations and separation of variables.
The heat and wave equations.

Do you know of any books that would cover some/most of this
Cost isnt an issue so if you know of several books your recommendations would be very welcomed.

Thanks

2. Feb 2, 2006

### mathwonk

thats a lot of stuff, but i recommend courant volumes 1 and 2 for calculus, and perhaps martin braun for differential equations.

look, on the used book website abebooks.com for cheap copies.

when you go up another level (you asked mainly about undergraduate stuff), try courant - hilbert: methods of mathematical physics.

3. Feb 4, 2006

### Pseudo Statistic

Looks like a combination of differential equations, linear algebra and a bit of trig/hyp stuff to me..
If you want the rough-and-ready hands-on read for all of these, might I recommend you to Schaum's Differential Equations, Linear Algebra and Advanced Calculus. :)
For the polynomial root stuff and seperable partial differential equations... err... don't think they're worth buying a whole book over.

Last edited: Feb 4, 2006
4. Feb 4, 2006

### George Jones

Staff Emeritus
You might try going to amazon.com, clicking on books, clicking on advanced search, and entering advanced engineering mathematics (no quotes) in the title field. Many books have a Look Inside feature that allow you to view the Table of Contents.

A couple of the things that come up are books by Kreyszig and Greenberg.

Kreyszig's book covers most of the topics you list, but not for example, partial differentiation. Kreyszig was a mathematician who was a prolific book writer, and is the author of a wonderfully pedagogical book on functional analysis. He wrote the book above from the point of view of a mathematician who has an eye on what engineering students need to know.

Greenberg's book gets a higher reader rating than does Kreyszig's, and does cover partial differentiation, but I don't know anything about the author.

Regards,
George

PS When my father was a small boy, (I think) he lived in Swansea.

5. Feb 7, 2006

### franznietzsche

I highly recommend Stewart as a general calculus book, it only goes up through Multi-variable and vector calculus, the lower end of your list of topics, but it does a very good job. However, its a bit pricey, I would recommend getting it from the library rather than buying it if you can. Or I think you can get the multivariable portion of the book seperately for a much lower price. The sections you may want to look at are:

Ch 10 : Differential Equations -Seperable Equations, Exponential Growth and Decay, the Logistic Equation, etc. All the joyful 1st order stuff

Ch 12: Infinitie Series and Sequences

Ch 13 Vectors and the Geometry of Space (Good for review if the material isn't new)

Ch 14: Vector Functions (Also good for review, important for the later stuff)

Ch15 Partial Derivatives

Ch16 Multiple Integrals

Ch 17 Vector Calculus - Conservative functions, gradients, divergence, curl, Stokes Theorem, Green's Theorem, etc. All very important.

Ch 18 Second Order Differential Equations

All in all its really a very good book, I know its the standard text in most of the California universities, not sure about elsewhere (hard to find that sort of info without checking from school to school).

6. Feb 10, 2006

### mathwonk

stewart is a book for the average non honors class, not the strong math major. it was a nice book for that pourpose inm the second editiuon but got worse since then.

abebooks.com loists used books, including such old, editions, whicha re mathematically superior and fortunately, also cheaper than the enwer editions:

25. Calculus*(ISBN: 053413212X)
Stewart,James
Bookseller: The Book Stop
(Wheat Ridge, CO, U.S.A.) Price: US$*35.00 [Convert Currency] Shipping within U.S.A.: US$*3.50
[Rates & Speeds]
Book Description: BROOKS-COLE. MM. 2nd. U.S.A.,Brooks / Cole,1991 2nd Edition,Brown HC,NDJ,Clean Pages w/ Slight Creasing,Cover has some scratching w/ worn and Bumped Corners Fair. Bookseller Inventory # 26016

7. Feb 11, 2006

### siddharth

You could also check out Differential and Integral Calculus by N. Piskunov. It covers most of the topics you quoted, but I don't know if the book is available in the US.

\$163.99 seems to be extremely costly. I got my copy for Rs 240 (5.5 USD)

Last edited: Feb 11, 2006
8. Feb 11, 2006

### sid_galt

Check John Baez's website and scroll down for quite a few books on various topics in Maths. Link though it is written for Math books for relativity

For matrices and linear algebra, a very good book is Linear Algebra by Hoffman and Kunze though probably a bit advanced for your level as it is written for juniors in Mathematics but its starts out from the basics.

Then there is Principles of Mathematical Analysis by Walter Rudin. Contains fourier series, gamma functions, etc. though is a bit condensed.

You might also want to check out Vector Calculus by Marsden and Tromba. It has multivariable calculus, partial derivative introduction, constrained extremas and lagrange multipliers, volume and surface integrals, greens stokes and gauss theorems and a few things more. The new edition is pricey so you might wanna get a used one.

Get the Schaum series books for practice. They are very good.

Last edited: Feb 11, 2006
9. Feb 24, 2006

### mathwonk

i repeat, if you read courant's calculus books, you will know more than most people. that is the one book that turned out to contain almost every thing i have ever learned or discovered for myself about calc and de.

it has been in print for over 70 years for good reason.