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Reddit mentions of Mathematical Methods in the Physical Sciences

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Reddit mentions: 31

We found 31 Reddit mentions of Mathematical Methods in the Physical Sciences. Here are the top ones.

Mathematical Methods in the Physical Sciences
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Found 31 comments on Mathematical Methods in the Physical Sciences:

u/ThroughTheForests · 5 pointsr/math

Khan Academy and Professor Leonard on YouTube will cover up to Calculus 3. From there you can use this Mathematical Methods book to cover the rest of what you would need for an undergraduate physics major. Then you can start learning the physics.

For a brief overview of the scope of math and physics, look at these two videos.

I want to emphasize that learning the math and the physics up to and especially including the theory of relativity is very difficult and time consuming. General Relativity itself is quite beyond undergraduate level physics.

I suggest if you are curious about topics like relativity that you check out Paul Sutter's Ask a Spaceman! podcast. He breaks down what the math says and explains complex subjects in a way that is easy to understand.

I also recommend watching Richard A. Muller's physics for presidents course, which is another great resource for learning about physics without the math getting in the way of understanding the concepts.

u/ShanksLeftArm · 5 pointsr/Physics

For Calculus:

Calculus Early Transcendentals by James Stewart

^ Link to Amazon

Khan Academy Calculus Youtube Playlist

For Physics:

Introductory Physics by Giancoli

^ Link to Amazon

Crash Course Physics Youtube Playlist

Here are additional reading materials when you're a bit farther along:

Mathematical Methods in the Physical Sciences by Mary Boas

Modern Physics by Randy Harris

Classical Mechanics by John Taylor

Introduction to Electrodynamics by Griffiths

Introduction to Quantum Mechanics by Griffiths

Introduction to Particle Physics by Griffiths

The Feynman Lectures

With most of these you will be able to find PDFs of the book and the solutions. Otherwise if you prefer hardcopies you can get them on Amazon. I used to be adigital guy but have switched to physical copies because they are easier to reference in my opinion. Let me know if this helps and if you need more.

u/djimbob · 4 pointsr/askscience

What are you trying to be? Have one book just slightly deeper than Greene's book, or actually learn theoretical physics to say become a theoretical physicist or at least understand it?

If the former, it will be difficult as there's a lot of things that might be tacitly assumed that you know about more basic physics. However, a very good intro to Quantum Mechanics is Shankar. I'd also look into Foster and Nightingale's relativity book for a brief introduction to special (read Appendix A first) and general relativity. Maybe after both try A. Zee intro to QFT if you want to learn more about QFT. If you want to learn about phenomenological particle physics, say look at Perkins. Also it may help to have a book on mathematical physics, such as Boas or Arfken. (Arfken is the more advanced book, but has less examples). Also it may help to get a basic modern physics book that has very little math, though I can't think of any good ones.

If the latter than you will have to learn a lot. Here's advice from Nobel Laureate theoretical physicist Gerardus t'Hooft.

u/nerga · 4 pointsr/Physics

Get a decent book in Mathematical Methods, it will teach you basically everything you need for physics up to a good point. Boas is good.

u/narfarnst · 4 pointsr/matheducation

Math

  • Multivariable Calculus

  • Differential Equations

  • Linear Algebra

    You have to know those three pretty well to start. You pick up some more math along the way as needed, but that's the bulk of it.

    Physics

  • Classical Mechanics (basic, Newtonian)

  • Electrostatics

  • Electrodynamics

  • Basic Quantum maybe. It's not necessiry for Lagrangians/Hamitonians but it's very cool stuff and you get to see Lagrangians/Hamiltonians in more action (oops, I made a pun...).

  • Special Relativity

    More Math

  • "Old school" differential geometry and Reimannian geometry. They both show up a lot, but Reimannian is more common in more advanced stuff. And notation starts to become more important

  • Tensors (which comes with Reimannian geometry, but they're worth mentioning by themselves cuz they're important)

  • Calculus of Variations

  • Misc: Taylor Series, Taylor Series, Taylor Series. Basic Fourier Analysis and complex numbers.
    More physics

  • Analytic Mechanics ("advanced" class mech/Lagrangian & Hamiltonian dynamics)

  • General Relativity

    Some books

  • Class Mech: Kleppner/Kolenkow for Newtonian stuff, Marian&Thornten for more basics and a pretty good intro to calculus of variations and Lagrangians/Hamiltonians. Both these have chapters on Special Relativity too.

  • Griffiths E&M for E&M (first half of book is statics, second half is dynamics)

  • Quantum: J.S. Townsend's A Modern Approach to QM

  • General Relativity: I used Hartle's Gravity. It's good, but I had two or three major beefs with it. I've also heard Sean Carrol's book is good.

  • This series. Fair warning though, those are very advanced and are more of a reference for professors than an actual book to learn by.

  • This Math Methods in physics book is very nice.

    I come from a physics background so I'm familiar with a lot of this stuff. I'll let people better in the know suggest the relevant math books.

    It's a long road but well worth it in my opinion. Good luck.
u/CurvatureTensor · 3 pointsr/Physics

Math, math and more math. If you don't feel comfortable with differential equations, or if you're like I was after freshman year you don't know what a differential equation really is, then that's where you should start. Quantum Mechanics basically starts with an awesome differential equation and then goes from there.

Learning the math of this level of Physics on your own would be challenging to say the least, but if you want to dive in I'd suggest Mathematical Methods in the Physical Sciences by Boas. Pairing that with Introduction to Quantum Mechanics by Griffiths might be fun.

Nuclear theory goes into statistical mechanics, classical mechanics is multivariable calc/linear algebra, quantum field theory combines those two with differential equations and sprinkles in a bunch of "whoa that's weird" just to keep you on your toes. But it's really important that you know the math (or more likely you fake your way through the math enough to gain some insight to the Physics).

u/Mastian91 · 3 pointsr/math

Similarly, McQuarrie Physical Chemistry may be helpful.

At my school, pchem was divided into a first semester which covered the quantum chemistry of individual atoms/molecules, and a second semester which used some of these quantum ideas (but mostly statistics and thermo) to talk about the statistical mechanics of collections of particles. I believe that McQuarrie's Physical Chemistry covers both, but note that the "mathematical review" sections are just brief interludes. For a more thorough treatment of math methods for physical scientists, consider the Mary Boas book. This book mostly focuses on physics applications, but from my experience in pchem, I would argue that it's just a very "applied" or "specific" version of quantum (or thermal, E&M, etc.) physics.

Also, for quantum chem, it is of utmost importance to be familiar with matrices, vectors, and ideally some of the more fancy portions of a first course in linear algebra, like bases and diagonalization. Although the relative importance of calculus/DE vs. linear algebra might depend on whether your course follows a "Schrodinger" vs. "Heisenberg" (not the Walter White one) approach, respectively.

u/ZPilot · 3 pointsr/learnmath

While the AoPS are phenomenal books and should be used instead of the terrible books used in middle and high schools today, I think you may want to look elsewhere if your primary interest for mathematics is to cover engineering mathematics. The topics covered in these textbooks are mostly at a middle to high school level of mathematics.

To give you an idea of how they are written (at least from their algebra book), they are written in a tone of casualness to guide readers, typically younger students, into the concepts, many times having cute examples to go along with them (Captain Hook trying to find buried treasure comes to mind). After each concept is presented, further concepts are explored through problems. You are told to do each of the problems on your own and to check with the provided solutions that come right after each problem set. The idea behind this is to present the reader with different methods to tackle problems as well as to point out common errors and mistakes that a student might make. After every few sections, there is an exercise set with no solutions for you to do. To fully benefit from these problem sets, the authors recommend that you consult the solutions manual (if you order from their website it will come with the textbook) after giving the problems a good attempt or after you finished finding a solution. At the very end of the chapter there will be a large set of problems to do, including what they call "challenge" problems. These challenge problems, unlike the section problems, come from math competitions or are designed to probe more difficult concepts that are usually ignored in the standard curriculum.

For the money they are amazing but, again, you might want to look elsewhere for the level of math you are looking for. There exist mathematical method textbooks specifically aimed at engineers that cover essential topics, usually by the title of "mathematical methods for engineers". One that I know of is Boa's textbook. Google around for what you like. If anything you should be looking to learn calculus, differential equations, and linear algebra as a start.

u/PhysicsFornicator · 3 pointsr/askscience

As a poster mentioned above, Stewart's Multivariable Calculus, and [Boas' Mathematical Physics](http://www.Mathematical.com/ Methods in the Physical Sciences https://www.amazon.com/dp/0471198269/ref=cm_sw_r_cp_apa_6zeYAbQ5R5KB6) are excellent sources for the required math background.

u/SchmittyRexus · 3 pointsr/Physics

Boas Mathematical Methods in the Physical Sciences has a lot of useful math, although it is mostly focused on DEs and complex analysis.

u/PortofNeptune · 3 pointsr/AskEngineers

Linear algebra, calculus, multivariable calculus, differential equations, probability and statistics, complex numbers, Fourier transforms.

This book covers every topic and you can buy the solutions manual as well.

u/KnowsAboutMath · 2 pointsr/math

> then maybe something titled along the lines of “Math Methods for Physics”.

Boas is good.

u/daelin · 2 pointsr/Physics

For introductory physics, I'd recommend Giancoli, Physics for Scientists and Engineers. You may want something in addition to this for deeper math, but Giancoli is fantastic for getting the core ideas and integrating them across different phenomena. After Giancoli, you will understand almost everything a lot better.

After Giancoli, things get a lot rougher. Your next objective is Classical Mechanics. You cannot learn Quantum Mechanics without studying Classical Mechanics in depth. You can try, as I did, but you are in for a world of pain that you won't fully grasp until you take Classical Mechanics seriously. You will especially want to pay attention to periodic and harmonic systems. Giancoli's main disadvantage is a weak treatment of periodic systems. Any Classical Mechanics book will make up for this.

At this point you will also need a companion book to take you through Classical Mechanics and everything that follows (Statistical Mechanics, Electrodynamics, Quantum Mechanics). That book is Mary L. Boas' Mathematical Methods in the Physical Sciences. Frankly, upper level undergraduate physics textbooks assume you have this knowledge. It's a fantastic book and it would have saved me a world of pain if I'd known about it right from the beginning.

Anyhow, after Giancoli you should look at Boas, then you may choose "Classical Mechanics" by Thornton & Marion. This book assumes you have Boas. Then you can plunge into Griffiths' Introduction to Quantum Mechanics, which assumes you have Boas. However, you'll have an easier time of the material if you read Griffiths' E&M book first, which assumes you have Boas. You'll also be well-served with a Statistical Mechanics textbook. Blundell & Blundell (Introduction to Thermal Physics) is a wonderful book conceptually, except that it lacks solutions. The mathematical and conceptual ideas in each of these subjects were fundamental to the development of Quantum Mechanics, and familiarity with the subjects is assumed by QM textbook authors.

u/The_MPC · 2 pointsr/Physics

That's perfect then, don't let me stop you :). When you're ready for the real stuff, the standard books on quantum mechanics are (in roughly increasing order of sophistication)

  • Griffiths (the standard first course, and maybe the best one)
  • Cohen-Tannoudji (another good one, similar to Griffiths and a bit more thorough)
  • Shankar (sometimes used as a first course, sometimes used as graduate text; unless you are really good at linear algebra, you'd get more out of starting with the first two books instead of Shankar)

    By the time you get to Shankar, you'll also need some classical mechanics. The best text, especially for self-learning, is [Taylor's Classical Mechanics.] (http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X/ref=sr_1_1?s=books&ie=UTF8&qid=1372650839&sr=1-1&keywords=classical+mechanics)


    Those books will technically have all the math you need to solve the end-of-chapter problems, but a proper source will make your life easier and your understanding better. It's enough to use any one of

  • Paul's Free Online Notes (the stuff after calculus, but without some of the specialized ways physicists use the material)
  • Boas (the standard, focuses on problem-solving recipes)
  • Nearing (very similar to Boas, but free and online!)
  • Little Hassani (Boas done right, with all the recipes plus real explanations of the math behind them; after my math methods class taught from Boas, I immediately sold Boas and bought this with no regrets)

    When you have a good handle on that, and you really want to learn the language used by researchers like Dr. Greene, check out

  • Sakurai (the standard graduate QM book; any of the other three QM texts will prepare you for this one, and this one will prepare you for your PhD qualifying exams)
  • Big Hassani(this isn't just the tools used in theoretical physics, it's the content of mathematical physics. This is one of two math-for-physics books that I keep at my desk when I do my research, and the other is Little Hassani)
  • Peskin and Schroeder (the standard book on quantum field theory, the relativistic quantum theory of particles and fields; either Sakurai or Shankar will prepare you for this)

    Aside from the above, the most relevant free online sources at this level are

  • Khan Academy
  • Leonard Susskind's Modern Physics lectures
  • MIT's Open CourseWare
u/docmedic · 2 pointsr/mathbooks

Boa's Mathematical Methods for the Physical Sciences will provide you a good foundation in linear algebra and multivariate calculus, completely sufficient math background for a physics student (and a great reference forever). This is the standard math text for physics students at many universities, and it is what people expect physics majors to know when conducting summer research (at least to having the competency to look up and apply without asking). Any high school/intro college calculus text will provide sufficient calculus background to read Boas (Larson; Edwards & Penney; etc.).

u/meshuggggga · 2 pointsr/math

So, you are gonna be an engineer/scientist, rather than a pure math major which, probably, means techniques will take precedence over ideas and rigor. To that end, you might like:

Engineering Mathematics

Advanced Engineering Mathematics

Numerical Methods for Scientists and Engineers

Mathematical Methods in the Physical Sciences

Basically, you need to put yourself through technical boot-camp that involves Calculus, Applied Linear Algebra, some Stats, Diff. Equations.

u/mofo69extreme · 2 pointsr/AskPhysics

Most of the topics you mentioned were what I would call algebra or single-variable calculus. I would start learning some linear algebra and multivariable/vector calculus first - the latter should be available in any good calculus text anyways. Besides these, you should at least know some basic probability and maybe a little about complex numbers. With this amount of math you could probably get through most of a "basic" physics degree, but you'll probably want to learn much more math if that's what you're into.

Many people on Reddit have glowing reviews for Boas' mathematical physics text (haven't read it myself though). Looking at the table of contents, I think it's a good overview of topics useful for an undergrad curriculum.

u/HolidayWaltz · 2 pointsr/learnmath

Read this:

https://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269


The Cambridge Companion to Mathematics is good also.

Here is a path.

Calculus 1,2,3.

Introduction to Proofs.

Real Analysis.

Complex Analysis.

Ordinary Differential Equations.

Partial Differential Equations.

Calculus of Variations.

Linear Algebra.

Fourier Series, Fourier Transforms, Special Functions. Hilbert Space.

Probability and Statistics.

Abstract Algebra/Group Theory.

u/saints400 · 2 pointsr/Physics

Im currently in a mechanics physics course and this is the main text book we use

https://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X

I'd say it's pretty good and an easy read as well

We have also been using a math text book to complement some of the material

https://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269

Hope this helps

u/functor7 · 2 pointsr/Physics

I agree here, they may be a little more "mathy" than what you're looking for but they cover important topics to physics and engineering. Byron and Fuller is pretty good and has already been mentioned, it's less mathy and more focused on how physicists treat the subjects.

Just stay the hell away from Boas, I have a degrees in math and physics, and that book is completely useless and confusing for physicists and extra disrespectful to mathematics

u/Cletus_awreetus · 2 pointsr/astrophys

Square one...

You should have a solid base in math:

Introduction to Calculus and Analysis, Vol. 1 by Courant and John. Gotta have some basic knowledge of calculus.

Mathematical Methods in the Physical Sciences by Mary Boas. This is pretty high-level applied math, but it's the kind of stuff you deal with in serious physics/astrophysics.

You should have a solid base in physics:

They Feynman Lectures on Physics. Might be worth checking out. I think they're available free online.

You should have a solid base in astronomy/astrophysics:

The Physical Universe: An Introduction to Astronomy by Frank Shu. A bit outdated but a good textbook.

An Introduction to Modern Astrophysics by Carroll and Ostlie.

Astrophysics: A Very Short Introduction by James Binney. I haven't read this and there are no reviews, I think it was very recently published, but it looks promising.

It also might be worth checking out something like Coursera. They have free classes on math, physics, astrophysics, etc.

u/chem_deth · 2 pointsr/chemistry

If you understand and are able to work with this material before learning QM, you'll be in excellent position.

For a more in depth and thorough coverage, grab a math for physicists textbook, like Mary Boas'.

u/CommonIon · 2 pointsr/AskPhysics

Most physics undergrads take a class called "Mathematics for Physics" or something similar which uses a book like this. It will help you cut to the chase and is a good reference for the math you haven't studied in detail.

As for where you are right now, you should be okay with ODE, multivariable/vector calc, and linear algebra. Those you probably want to devote considerable time learning.

u/ange1obear · 1 pointr/learnmath

I will give you the same answer I give every one of my students, and that one of my mentors gave me: don't think that there is a logical progression to approaching mathematics. The reason that people think there is such a thing as a logical order to mathematics is due to the school system, which teaches things in a particular order before university, and then structures university classes using prerequisites, making you think that, for example, you need trigonometry before you do calculus. This simply isn't true. I could say more about this, but it won't answer your question.

Here is my suggestion. Go to the mathematics section of a library, yank any book off the shelf, and go to town. Most books aimed at advanced undergrad/grad students (which is the level you're looking for) will say in the introduction something to the effect of "there are no real prerequisites for this book other than mathematical maturity," and this is nearly always true. You probably won't have mathematical maturity starting out, which can be frustrating, but you'll develop it over time. You will encounter things that you don't understand in these books, and the correct response to this is to go find another book on that topic. You can't learn mathematics just by compiling a list of theorems and techniques.

So all you really need is a starting point. Looking at what you're interested in, I'd recommend this book, which is extremely practical. You'll find more computational things in there than mathematical things, but it has a pretty broad spectrum of techniques whose theoretical underpinnings you can pursue. This course of action is the only one I can recommend, because it's the one I took. The only math class I took in college was calculus, and now I do research in mathematics in grad school. The frustrating thing about this approach is that there's no quantitative way to measure your progress. On the other hand, you get a real feeling for why and how people came up with various aspects of mathematics, which is a feeling you can't get from a curriculum.

u/ErmagerdSpace · 1 pointr/Astronomy

First you need Algebra and Trig. From this stage you mainly need to be able to manipulate equations (e.g. take x^2 + y^3 + z^2 = k^2 / n^2 and solve for x, it's one of the easier parts of algebra) and to understand exponents/logarithms. From trig you need to know how to break a vector into components, how to find angles, how sines/cosines/etc are defined, and all those nasty trig identities (e.g 1 - sin^2 = cos^2). You don't need to memorize them (usually, some professors are insane) but it helps to be kinda-sorta familiar with them.

If you've mastered all that, you want to study calculus. If you can take derivatives and solve integrals you're probably good enough to start, but the more you understand the better. It's a lot easier to solve physics problems when you're not struggling with the math you need to solve them.

If you get a book like this and work through it you'll get a lot of what you need, but it's not really necessary to go that far-- that is stuff you won't need until your fourth or fifth semester. Some of it is grad school math.

tl;dr: Trig, Algebra, and basic Calculus for sure. That's what you need for year 1. You can go further if you want, but there is no need to kill yourself to learn advanced math before taking intro physics.

u/TheMightyChodeMonger · 1 pointr/askscience

Just want to mention that pop sci (which everything you mentioned is) and an actual rigorous study of physics are two very very different things. The romantic image of physics you get from those kind of programs is very different then what is actually involved in learning physics.

I would suggest getting more familiar with the mathematics (calculus, statistics, linear algebra) before diving into the actual physics.

Having the math first will make it much easier to see the actual physics behind the equations instead of sitting there trying to figure out the math and physics at the same time.

To that end I would suggest having Boas mathematical methods next to you at all times during your early studies. Its at about a sophomore (college) level but is easily accessible to most anyone with a basic mathematics background.

(http://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269)

Other than that watch Kahn academy or the MIT online courses.

u/ggrieves · -3 pointsr/math

Here's how I was taught, but I was taught in physics not math.
Fourier transforms are more intuitive, so think about how you take a derivative of a FT. You carry the derivative operator into the integral and you just get a factor of 2(pi)ix under the integrand. Logically, if you want a second derivative, just take the FT of the functions transform times x^2 etc. If you want a 1.3^th derivative (yes fractional derivatives exist) then FT the function times x^1.3 etc. This means taking a n^th derivative in real space is the same as multiplying by x^n in transform space. Sounds alot like what logarithms did for multiplication back in the day doesn't it? So now you can turn a differential equation into a polynomial equation if you just take the Fourier transform of it. However, if the diff eq is more complex than just n^th order with constant coefficients, maybe the FT isn't the best transform available for simplifying it? Then use a transform that's tailored for the particular function you have.

If I remember correctly this book has a nice description. I consider this book to be the "readable" version of this one