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Difference Between "Engineering Math" and "Mathematical Methods"

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Main Question or Discussion Point

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
 

Answers and Replies

  • #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 ...
 
  • #3
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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?
 
  • #4
SteamKing
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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.
 
  • #6
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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.
 
  • #8
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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.
 
  • #9
SteamKing
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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.
 
  • #10
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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.
 
  • #11
SteamKing
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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.
 
  • #12
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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 ... )
 

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