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I am a graduate Engineer looking to qualify a post graduate entrance examination (for Master's degree) where I have 'Engineering Mathematics' as one of my Subjects.I hereby paste my course syllabus:

ENGINEERING MATHEMATICS

Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.

Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.

Complex variables: Analytic functions, Cauchy’s integral theorem, Taylor and Laurent series.

Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson,Normal and Binomial distributions.

Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson’s rule, single and multi-step methods for differential equations.

Hence, I am actually looking for some standard textbooks to cover up the syllabus very well.I would actually prefer to refer to some proper textbooks for each of the portions separately instead of following a general textbook covering up all the topics.

I went through 'Advanced Engineering Mathematics' by Erwin Kreszig and also the book with the exact same title by Michael Greeberg.To be honest I found both of them quite satisfactory but not thrilling to learn the subject with a solid foundation and in depth understanding that would make me feel comfortable enough.I am precisely looking for books that would be quite easy to follow as some self teaching guides yet complete with regards to both the content and concepts.Any suggestions?

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My background is in algebra primarily, but I do have a few favourite books in some of these areas:

For probability I would recommend Probability by Grimmet and Welsh. It starts from the very basics and develops a rigorous theory of probability, and you only need some basic analysis to follow (which based on your syllabus you seem to have).

The standard textbook in calculus, that covers everything you mentioned, is Stewart's Calculus. It's standard for a reason, and you've probably come across it in a calculus class before. If you want to develop an even more rigorous foundation in calculus, I recommend Rudin's Principles of Mathematical Analysis (roughly the first half). It's again a classic for a reason.

A good book for some complex analysis is Howie's Complex Analysis. I found it very useful as an undergraduate.

There are a lot of good linear algebra books, but the most comprehensive and well-written one I've come across is Friedberg, Insel and Spence's Linear Algebra.

I won't recommend any books in the other areas, since I've barely studied them. Good luck with your exam!

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    $\begingroup$ It seems to me that the reason Stewart is standard is that it plays to the needs of people organizing huge calculus courses, not, as you seem to imply, that it's a great book. Spivak's calculus is a nice option in between Stewart and Rudin. $\endgroup$
    – Kevin Arlin
    Nov 18, 2014 at 6:02
  • $\begingroup$ @KevinCarlson My main reason for recommending it is that it is extremely comprehensive, has a lot of good exercises and is generally very clear and easy to understand. I like it for reviewing because it covers basically everything. I'm sure there are better ones out there though :) $\endgroup$
    – user141592
    Nov 18, 2014 at 6:13
  • $\begingroup$ I really appreciate your suggestions @Johanna.I went through Grimmet and Welsh in a preview on Google Books and found it to be very nearly the exact kind of book I was looking for.The same holds true for Complex Analysis by Howie.The Book "Linear Algebra" by Friedberg, Insel and Spence seems quite easy to follow as well and in perfect agreement with the content I needed.For Calculus I have had experience with Stewart earlier and it's no doubt a decent work.The thing you when it comes to calculus you really have plenty of options to choose from! :) $\endgroup$
    – Milo
    Nov 19, 2014 at 6:57
  • $\begingroup$ @KevinCarlson I would definitely have a look at Spivak's Calculus :) $\endgroup$
    – Milo
    Nov 19, 2014 at 6:59
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I am just going through 'Advanced Engineering Mathematics' (K A Stroud, Fourth Edition) currently.

It has a lot of Pure and Applied mathematics and one Operational Research topic (on optimisation and linear programming). Nice additions are the numerical methods.

The book doesn't include statistics topics.

I would recommend it.

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