Best book for engineering mathematics

1. Jun 15, 2013

judas_priest

What would you recommend as the best book for engineering in mathematics? Something with a great insight and depth, and very well explained. With good exercises too.

Here's the chapter it's required to have:

Partial Differentiation:

Introduction to Partial differentiation, Total derivative, Differentiation of implicit functions,
Geometrical interpretation, Tangent plane and normal to a surface, Change of variables,
Jacobians, Taylor’s theorem for functions of two variables.

Applications Of Partial Differentiation :

Total differential, Maxima and minima of functions of two variables, Lagrange’s method of
undetermined multipliers, Differentiation under the integral sign, Leibnitz’s Rule.

Partial Differential Equations :

Introduction, Formation of partial differential equations, Solutions of a partial differential
equation, Equations solvable by direct integration, Linear equations of the first order, Nonlinear
equations of the first order, Homogeneous linear equations with constant coefficients,
Rules for finding the complementary function, Rules for finding the particular integral.

Linear Algebra-1:

Rank of Matrix, Elementary transformations, Elementary matrices, Inverse, Normal form,
Consistency of linear system of equations, Linear transformations.

Linear Algebra – 2:

Eigen value and eigen vectors of a matrix, Cayley-Hamilton theorem, Reduction to diagonal form,
Quadratic forms and canonical forms, Hermitian and Skew Hermitian matrix, Unitary matrix.

2. Jun 15, 2013

judas_priest

Further required later is :

Fourier Series:

Euler’s formulae, Conditions for a Fourier expansion, Functions having points of discontinuity,
Change of interval, Odd and even functions, Expansions of odd or even periodic
functions, Half range series and practical Harmonic Analysis.

Laplace Transforms:

Transforms of elementary functions, Properties of Laplace transforms, Existence conditions,
Inverse transforms, Transforms of derivatives, Transforms of integrals, Multiplication by tn,
Division by t, Convolution theorem.

Applications Of Laplace Transforms:

Applications to ordinary differential equations and simultaneous linear equations with constant

Vector Calculus (Differentiation) :

Scalar and vector fields, Gradient, Divergence, Curl, Directional derivative, Identities,
Irrotational and Solenoidal fields.

Last edited: Jun 15, 2013
3. Jun 15, 2013

verty

4. Jun 16, 2013

jasonRF

would you mind giving some more context? Are you learning these topics for the first time? Are these books to supplement an existing book you are using but do not like? Is this for a class, or did you pick these topics out yourself? What kind of engineering?

Without this info, all I can say is that most engineers can learn much of the basic math (calc, multivariable/vector calc., linear algebra, odes, pdes, complex variables, Fourier/Laplace) from just a couple math books: 1) a standard calculus book (I learned from Thomas and Finney, but Anton or many others would work too) that includes multivariable and vector calculus, 2) an "advanced engineering mathematics" book by Greenberg, or Kreyzig, or O'Neil, or Wylie. I took a class out of Wylie - it was reasonable. A full-fledged linear algebra book may be preferrable - Anton or Strang (intro to linear algebra) are both reasonable, although most intro books will not cover Cayley-Hamilton theory, even though at least in electrical engineering it does come up from time to time.

By the way, none of the "advanced engineering math" books I am familiar with will cover the 1st order pde topics you listed. You will need a real pde book for that. The most elementary one is by Farlow; if you want something more involved I like "elementary applied partial differential equations" by haberman.

HOpefully you have a library to look at books to find what you like. If you buy them, always buy used copies of old editions unless for some reason you KNOW that the new version is worth the extra \$100+ (US) it will cost. Free online books may be worth a look as well
http://www.e-booksdirectory.com/listing.php?category=3

Good luck,

jason

ps. Make sure that you eventually learn probability theory as well. It is essential.

5. Jun 16, 2013

jasonRF

One addition: engineers typically do not need "depth". None of the books I listed are deep. It is fair to say that I do not have a deep understanding of any branch of mathematics, but have a PhD in electrical engineering and have been in industry for 10+ years. Only worry about "deep" if you are really interested (and have the time!) or if you end up doing graduate work in the mathematical areas of engineering (in EE that is controls, information theory, signal processing, ...).

6. Jun 17, 2013

judas_priest

There are a few things I've already learnt before, and a few that I haven't. The topics I posted, are what my college covers in first semester.

I just recently started with Kreyszig. Should I continue? Or is there something better. G.B Thomas Calculus is a genius of a book. Did it in high school. I doubt it's going to help in engineering though

7. Jun 17, 2013

jasonRF

wow - that is a lot for a one semester class - to me it seems like too much! If I were you I would keep going with Kreyszig, unless for some reason you find it hard to learn from.

By the way, I have found that most of what I learned in Thomas was indeed useful as basic single-variable, multi-variable and vector calculus are standard tools.

good luck,

jason

8. Jun 17, 2013

judas_priest

Haha, I'm from India. The education system here is boring, rigorous and non practical. They make people hate engineering and science with the way they design the syllabus and learning by ourselves is 100x better than being taught. That tells you about the teachers and professors

9. Jun 17, 2013

Natassha

You can take previous year 1st year papers after completing Kreyszig. or ask your Prof. or your seniors who is familiar with that Syllabus. Many Profs. write their own book for their college or University, if that type of book exists then go through it firstly.

10. Jul 12, 2013

judas_priest

Jason, I hope you're still active on PF, and check this post. My course of Electronics and intrumentation engineering has just begun ( I'm a fresher )

And this is the revised syllabus for first semester:

Unit-I: First order Differential Equations (10)
Formation – Variables seperable – Homogeneous, non Homogeneous, Linear and Bernoulli equations. Exact equations - Applications of first order differential equations – Orthogonal Trajectories, Newton’s law of cooling, law of natural growth and decay.
Unit-II: Higher order Differential Equations (12)
Complete solutions - Rules for finding complementary function - Inverse operator - Rules for finding particular integral - Method of variation of parameters - Cauchy’s and Legendre’s linear equations - Simultaneous linear equations with constant coefficients - Applications of linear differential equations to Oscillatory Electrical circuits L-C, LCR – Circuits - Electromechanical Analogy.
Unit-III: Mean Value Theorems (08)
Rolle’s, Lagrange’s and Cauchy’s mean value theorems. Taylor’s and Maclaurin’s theorems and applications (without proofs).
Unit-IV: Infinite Series (12)
Definitions of convergence, divergence and oscillation of a series - General properties of series - Series of positive terms - Comparison tests - Integral test - D’ Alembert’s Ratio test - Raabe’s test - Cauchy’s root test - Alternating series - Leibnitz’s rule - Power series - Convergence of exponential, Logarithmic and binomial series (without proofs).
Unit-V: Linear Algebra (12)
Rank of a Matrix – Elementary Transformations – Echelon form - Normal form (self study). Consistency of Linear system of equations A X = B and A X = 0. Eigen Values and Eigen Vectors – Properties of eigen values(without proofs) – Cayley – Hamilton theorem (Statement only without proof) – Finding inverse and powers of a square matrix using Cayley– Hamiton theorem – Reduction to diagonal form – Quadratic form - Reduction of Quadratic form into canonical form – Nature of quadratic forms.

Also, after reading your posts again, I'd like to ask you, is going deep and understanding maths really not that important for an Electronics engineer? How do you suggest it should be studied? I mean, should it be learnt based on problem solving tricks and all that sort of things that come with rigorous practice, or should the subject be understood, and then solved tactically? I hope this is a valid question and means something, because this the question that keeps running in my head. haha!

Also, if you can now once more suggest a book you think I should do from, it'd be great. You'd know better as an electronics engineer as to what is important and what isn't. I've given Kreyszig a start, and I must say it's a pretty awesome book.

I'm a fresher almost lost with how to approach.

11. Jul 12, 2013

jasonRF

It is crucial to have an understanding of the subject, and not just know how to solve some set of problems that the books/prof happens to emphasize. If this is what you mean by "deep" then yes, you need deep, otherwise you will not know how to use your math in new situations.

On the other hand, when I hear the word "deep" I think of knowing (and being able to prove) why we use the definitions we do and why the theorems you already know really work, which may involve much more advanced math.

Here is an example from Vector calculus. You will learn Stokes' theorem. You will need to understand what it means, situations where it is valid, and how to apply it to solve problems. (EDIT: you will likely see a proof of the theorem for a simple cases, or perhaps just a plausibility argument, which will also help you understand the theorem). When I hear "deep" I think of knowing how to prove the most general form of Stokes' theorem and understand at a fundamental level why it works, which you will likely never need unless you are a mathematician.

Another example: knowing the Cayley-Hamilton theorem and how to use it can be useful. Knowing how to prove it for the most general case and understand why it works at a fundamental level is likely not necessary at this point in your education (it may never be necessary!).

If you like Kreyzig you should stick with it. I am not familiar with it myself, but it is known to be a reasonable book and has plenty of depth for your first time through the topics it covers (and for some topics it may have all the depth you will ever need).

jason