Which is the best mathematics textbook dealing with all major topics on mathematics?

Rhydo

Hi!

I would like to revise my Mathematics from the high school to the Engineering level. I have been on the look out for a book that deals with the major fields of mathematics such as calculus, probability, complex numbers, linear equations etc. on an easy to understand manner.

Is there any such text book that bridges the gap between high school and Engineering Mathematics? I'am just looking to get a physical interpretation of the mathematics while I do it.

I dont have a satisfactory access to a library to collect the books on individual topics so I might as well start with gaining a working knowledge of the basics before specializing on individual fields.

I hope there are authors who have felt the same need as I do! From where I belong to, any help I get here would be greatly valued!!

MrAnchovy

First of all, if your interest is engineering a book covering all major topics in maths (if such a thing exists) would not be very relevant - algebra, geometry, topology, combinatorics, logic and number theory are all intersting topics, but won't help you bulid things/make things/design circuits/produce substances or whatever your field of engineering is.

When I was an undergraduate this was the book used on the physics course and I think that was a pretty good course, although the fact that it was given by the author probably helped. Of course that was 30 years ago (last edition published 1973) and it was geared towards physics rather than engineering so someone else might have something better.

solve

I like Engineering Math by K.A. Stroud and Dexter J. Booth

It's actually two books, second being Advanced Engineering Math which is the title of the textbook.

The textbooks are geared towards getting students become technically proficient problem solvers so there's very little in the way of proofs and such. Very concise and (super)straight to the point. There are more problems in them than your worst nightmare.

The first one starts out with Foundation Topics: Arithmetic; Intro to Algebra; Linear, Simultaneous, Polynomial Equations; Partial Fractions; Trig; Binomial Series; Functions; Differentiation; Integration...

Then goes the main part: Complex Numbers, Hyperbolic Functions, Determinants, Matrices, Vectors, Differentiation and its Applications, Partial Differentiation, Curves and Curve Fitting, Integration and its Applications, Reduction Formulas, Approximate Integration, Polar Coordinate Systems, Multiple Integrals, First/Second Order Differential Equations, Intro To Laplace Transforms, Statistics, Probability...

SECOND BOOK covers: Numerical Solutions of Equations and Interpolation, Laplace Transforms, Z-Transforms, Fourier Series, Intro To Fourier Transform, Power Series Solutions of Ordinary Differential Equations, Numerical Solutions Of Ordinary Differential Equations, Partial Differentiation, Partial Differentiation Equations, Matrix Algebra, Numerical Solutions of Partial Differential Equations, Multiple Integration, Integral Functions, Vector Analyses, Complex Analyses, Optimization and Linear Programming.

alan2

If it's engineering math I much prefer Kreyszig's "Advanced Engineering Mathematics" to Stroud's books. I think it's a bit more rigorous and contains a handful of extra topics but if you can find either one in a good used copy for cheap you'll be fine. I think you can find Stroud in one volume.

Jamma

It may not be relevant, but to get a good overview of some pure maths concepts I really recommend the Princeton companion to mathematics, edited by Timothy Gowers (it does cover the things you mentioned, complex numbers, linear equations etc. and a lot more).

It's more like a book you can "dip into" - it doesn't cover everything in huge detail, but explains new concepts that you might not have seen before really well (and covers a huge range of topics). I got it for about £40 which I think is excellent given how much information it has and the quality (written and physical) of the book is excellent.

MrAnchovy

Thanks Jamma, it seems that The Princeton Companion to Mathematics is that book, I had not seen it (or anything like it) before.

Jamma

http://press.princeton.edu/TOCs/c8350.html

Here is the table of contents, which should give you a better picture. It's a great thing, as I said, to look things up in first to give you a really good feel for some concept before you undertake actually studying it deeply. There are also some really nice introductions to the ideas of mathematics, and "perspectives", which are a nice read:

Part I Introduction
I.1 What Is Mathematics About? 1
I.2 The Language and Grammar of Mathematics 8
I.3 Some Fundamental Mathematical Definitions 16
I.4 The General Goals of Mathematical Research 48

Part VIII Final Perspectives
VIII.1 The Art of Problem Solving 955
VIII.2 "Why Mathematics?" You Might Ask 966
VIII.3 The Ubiquity of Mathematics 977
VIII.4 Numeracy 983
VIII.5 Mathematics: An Experimental Science 991
VIII.6 Advice to a Young Mathematician 1000
VIII.7 A Chronology of Mathematical Events 1010

mal4mac

Gullberg's "Mathematics from the Birth of Numbers" is worth a look, for high school to first year.

For harder material, Stroud looks good. Even harder? Look at "Mathematical methods" books like Boas and Arfken - Boas first...

Arfken is tough, but it's useful for starting you off on many advanced topics. It has good references to books with more hand-holding!

mathwonk

what is the meaning of life?

mathwonk

another good general book is "what is mathematics?" by courant and robbins.

n10Newton

Basic Mathematics by Lang. + What is Mathematics by Courant. + Cambridge Undergraduate Campanion to Mathematics.

n10Newton

mathwonk, can you give name of the writer,there are many of the same title.

mathwonk

the name is unspeakable.

Bipolarity

A good textbook for EE math would be something that covers all of the following:

- Calculus of single and multiple variables
- Vector calculus
- Linear Algebra
- Differential Equations
- Function of a complex variable
- Some boolean and abstract algebra (equivalence relations, homomorphisms, injections, surjections, bitwise operators, sequential logic, finite state machines, Quine-McCluskey reduction methods)
- Some Fourier analysis
- Probability models and stochastic processes

I am doubtful that such a book exists. There are of course, general mathematical encyclopedias that can give an overview of all these concepts, but an in-depth treatment of all of them in one 1000 page book is unthinkable.

BiP

n10Newton

For all try/buy the Series "International Series in Pure and Applied Mathematics" by McGraw Hill and bound them together, you will get whole mathematics in one book.

clope023

Mary Boas Mathematical Methods for Physical Sciences

Erwin Kriezig Advanced Engineering Mathematics