Difference Between "Engineering Math" and "Mathematical Methods"

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What really is the difference between a book for Engineering Math and a Math methods book for, say, Physics? They all look very similar to me. Also, a math method book may significantly differ from another math method book depending on the level covered and a math method book may be very similar to an engineering math book depending on the book. How does this classification make sense? Won't the following book be useful to a Physicist as well?
https://www.amazon.com/dp/0133214311/?tag=pfamazon01-20
 

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  • #2
Ssnow
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I don't know precise but Engineering problems are of different nature respect physics problem, so it is possible that math techniques are similar but I think the applications will be different ...
 
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I don't know precise but Engineering problems are of different nature respect physics problem, so it is possible that math techniques are similar but I think the applications will be different ...
So, are you saying that the nature of problems and exercises are different between mathematical methods for science and and engineering mathematics book and and the theory is the same?
 
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What really is the difference between a book for Engineering Math and a Math methods book for, say, Physics? They all look very similar to me. Also, a math method book may significantly differ from another math method book depending on the level covered and a math method book may be very similar to an engineering math book depending on the book. How does this classification make sense? Won't the following book be useful to a Physicist as well?
https://www.amazon.com/dp/0133214311/?tag=pfamazon01-20
Advanced engineering math texts are generally used for advanced calculus courses in engineering programs to teach multivariable and vector calculus and complex analysis. Other topics may include an introduction to PDEs and harmonic functions. A lot of the topics taught in these texts are useful for physics students.

Math methods, on the other hand, will tend to focus on using and applying numerical techniques to solve various physics problems. Mathematical Methods in the Physical Sciences by Mary Boas is one of the better known titles for this type of text. Its primary focus is on problem solving techniques, rather than advancing your knowledge of higher math.
 
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Thanks. So, physics is more application (problem solving) based and engineering is more theory? I would have thought just the opposite.
Advanced engineering math texts are generally used for advanced calculus courses in engineering programs to teach multivariable and vector calculus and complex analysis. Other topics may include an introduction to PDEs and harmonic functions. A lot of the topics taught in these texts are useful for physics students.

Math methods, on the other hand, will tend to focus on using and applying numerical techniques to solve various physics problems. Mathematical Methods in the Physical Sciences by Mary Boas is one of the better known titles for this type of text. Its primary focus is on problem solving techniques, rather than advancing your knowledge of higher math.
 
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I can't agree with SteamKing in general. A math methods class I took in the early 2000s covered complex analysis, Fourier series, partial differential equations, and special functions. We didn't do any numerical methods, and most of our time was spent on complex analysis, contour integrals, applications of the residue theorem and Cauchy's integral formula, etc.
 
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SteamKing
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Thanks. So, physics is more application (problem solving) based and engineering is more theory? I would have thought just the opposite.
No, you were asking about textbooks.

The comments I provided about textbooks are not intended to distinguish the study of physics from the study of engineering.

If you want to discuss that topic, start a different thread.

The way undergraduate math is taught in the engineering schools is you start out with single variable calculus and then move on to more advanced math topics, usually in the second year. These advanced topics would include a course in ODEs followed by multivariable calculus, the latter topic being taught as "Advanced Engineering Math" or some such description.

Physics majors and engineering majors are both going to take similar math sequences as undergrads. Some of the math texts in the two undergrad programs may even overlap.
 
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No I was talking about Textbooks only. But Textbooks are modeled after courses and vice - versa. It just seems strange that math methods books may be more application based than engineering math textbooks. But your explanation below makes sense. Thanks.


No, you were asking about textbooks.

The comments I provided about textbooks are not intended to distinguish the study of physics from the study of engineering.

If you want to discuss that topic, start a different thread.

The way undergraduate math is taught in the engineering schools is you start out with single variable calculus and then move on to more advanced math topics, usually in the second year. These advanced topics would include a course in ODEs followed by multivariable calculus, the latter topic being taught as "Advanced Engineering Math" or some such description.

Physics majors and engineering majors are both going to take similar math sequences as undergrads. Some of the math texts in the two undergrad programs may even overlap.
 
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No I was talking about Textbooks only. But Textbooks are modeled after courses and vice - versa. It just seems strange that math methods books may be more application based than engineering math textbooks. But your explanation below makes sense. Thanks.

You seem to labor under the impression that there is one thing called "engineering" math and something else called "physics" math.

It's all the same math. Engineering students learn complex analysis just like the physics students do. Which group will wind up using complex analysis more after graduation? Probably the newly minted physicists, unless the engineering students decide on post graduate work.

In the engineering courses, which are taught separately from the math courses, there will be some focus on the application of math to solving particular problems in a given field of engineering. Each brand of engineering has some core calculations which must be understood by the student and applied in his work after he graduates and starts practicing as an engineer. There will also be some overlap, but usually not too much, which is why civil engineers are different from mechanical engineers are different from electrical engineers, etc.
 
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Precisely my point. If you read my OP, you will see that that is exactly what I observed. There is virtually no difference between 'engineering' and 'science' math books in general, so, why stereotype them as such?

You seem to labor under the impression that there is one thing called "engineering" math and something else called "physics" math.

It's all the same math. Engineering students learn complex analysis just like the physics students do. Which group will wind up using complex analysis more after graduation? Probably the newly minted physicists, unless the engineering students decide on post graduate work.

In the engineering courses, which are taught separately from the math courses, there will be some focus on the application of math to solving particular problems in a given field of engineering. Each brand of engineering has some core calculations which must be understood by the student and applied in his work after he graduates and starts practicing as an engineer. There will also be some overlap, but usually not too much, which is why civil engineers are different from mechanical engineers are different from electrical engineers, etc.
 
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Precisely my point. If you read my OP, you will see that that is exactly what I observed. There is virtually no difference between 'engineering' and 'science' math books in general, so, why stereotype them as such?
The textbook market is a very lucrative one for the big publishing houses. They can take the same basic material and repackage it for use in different courses by making a few cosmetic changes, slapping on a different title, whatever. It's 90% perception, 10% reality.
 
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The textbook market is a very lucrative one for the big publishing houses. They can take the same basic material and repackage it for use in different courses by making a few cosmetic changes, slapping on a different title, whatever. It's 90% perception, 10% reality.
I hear you.
 
  • #13
Thanks. So, physics is more application (problem solving) based and engineering is more theory? I would have thought just the opposite.
There is a reason why engineering is called applied physics, and in engineering, besides other techniques, a hell lot of numerical analysis is also used.........back to the original question, I have read both engineering math and math methods for physics and I have found them quite similar, in fact, math methods books often put exercises from engineering background.
 
  • #14
Ssnow
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So, are you saying that the nature of problems and exercises are different between mathematical methods for science and and engineering mathematics book and and the theory is the same?

mathematical methods for science and engineering mathematics book sometimes can have similar topics in common (not exactly the same ... )
 
  • #15
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As an engineer who is greatly interested in maths methods in physics, I will leave some comments.

Both are anyway intended to provide students with sufficient mathematical background for learning their majors. So the greatest difference should come from the applications. Different emphases on applications make huge differences in the writing styles.

I guess the core topics for physics undergrads start with electrodynamics and go onto quantum mechanics. (Let's not talk about classical mechanics and statistical mechanics for now.) So the goal of maths methods classes should be to understand vector calculus and linear algebra. To be more specific, the ultimate goal is to be able to apply Gauss's and Stokes' theorem, and to be able to solve eigenvalue equations. Also, a lot of special functions are there to be used in solving physics problems.

I will have to make clear that what's typically called engineering maths, in comparison to maths methods for physics, is about the maths used in pure engineering subjects - which hardly depend on knowledge of physics. It's basically (a) what electrical and information engineers do, (b) what industrial engineers do, and (c) what computer and data scientists do.

(a) includes circuit analysis, digital electronics, signal processing, control theory, etc. Such subjects apply differential equations, Laplace transforms, Z transform and Fourier transform. However, you know, DE theory has really extensive applications, hence is used throughout engineering. So this is a core topic of a typical engineering maths book.

(b) includes linear programming, production process analysis, financial engineering, etc. All of such subjects direct towards the optimisation methods. Note that both (a) and (b) use a lot of specialised diagrams - unrelated to physics - to model various real-world phenomena and processes.

(c) includes algorithms, data structure, some other subjects common with information engineering, software production theory, machine learning, etc. In doing these, the knowledge of discrete mathematics is essential. The latter requires linear algebra, multivariable calculus and statistics.

So, a good engineering maths book, at least as a reference, should include most of the topics mentioned above. But note that, unlike physics majors in which some hard maths methods books really provide all maths you will ever encounter in an undergrad course, an engineering maths book usually touches the minimum.

To talk about the philosophical aspects, this is because physics has an ultimate goal of explaining the world in unified and concise mathematical laws, whereas engineering is much broader and thus it's impossible to set a single goal. So the maths used depends on a sub-field of study, and specific mathematical techniques are usually taught within engineering courses themselves.

To be honest, there are two aspects of engineering - an applied maths aspect and an applied physics aspect. All of the things I mentioned so far are the applied maths aspect. It looks fair to teach applied maths only in a separate applied maths class, not in a single engineering maths class. For example, ocean engineers needn't really learn about the maths of signal processing. It's like maths methods for physics courses not really going deep into the details of variational calculus and perturbation theory, tensor analysis and differential geometry, group and representation theory, etc.

But the applied and experimental physics aspect is also a huge part of engineering. Actually, it has a closer meaning to what engineering is classically and originally supposed to be - like civil engineering which has originated from constructing scientific ways of building housings and facilities, or like chemical engineering that was essential for large-scale production of various useful substances and drugs.

Such subjects require a deep enough understanding of physical principles. Electrical engineers must know how electrodynamics works, mechanical engineers must know how fluid dynamics works, chemical engineers must know how thermodynamics works, materials engineers must know how quantum mechanics works. Obviously, they have to learn the maths needed for individual physics subjects. In that case, maths methods for physics books will be really good references for engineers.

I think a good engineer is someone who has a solid and fundamental understanding of at least one and ideally two or more sub-fields of engineering. That means he knows the basic mathematical and physical principles and understands how engineering works in industries. Then whatever new problem comes to the front of him, he may quickly learn, adapt and eventually resolve the problem.

Finally, the reason why I am talking about all these is that I don't think it's not a simple matter of distinguishing between books. Like all other things, engineering is a very broad and complexly interrelated subject, so it's quite meaningless to talk about the curriculum of the discipline as a whole.

But I can guarantee that a typical engineering maths book should prepare you for the bare minimum of mathematical techniques. Actually, if it's the first time that you are learning university maths - especially ODE - then I would strongly recommend using an engineering maths book, whether you are an engineer, a physicist, or a chemist.
 
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  • #16
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The difference is that physics math has a chapter on group theory, while engineering math has a chapter on Laplace transform. :oldbiggrin:

Now seriously, there is no big difference, but engineering math books are often written at a slightly simpler level, meaning that a few more intermediate steps of calculation are written down explicitly.
 
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  • #17
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Physicists usually prefer the Fourier transformation, although the Laplace transformation is sometimes more convenient when it comes to initial-value problems. At the end it's anyway equivalent. As it should be the same math formulated in different ways leads to the same conclusions ;-)).

Group theory is however not sufficiently treated in the standard (physics) textbooks, because it's considered a difficult subject. IMHO that's a mistake, because the understanding of the foundations of physics is much facilitated by the use of group theory, and it's highly aesthetic too, because it describes the Laws of Nature in terms of symmetry principles of all kinds (most obviously the symmetry properties of space-time models, but also abstract (gauge) symmetries underlying the dynamics of classical and quantum fields).

I guess for engineers group theory is not of such important use, because they are not so much interested in the foundations of physics but just in applications of the findings of physicists for engineering.
 
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