# Which book I should get to learn mathematics?

• Applied
My question is:What is the mathematics necessary for, and which book(or books) i should read to understand graduate-texts like Jackson, Sakurai, Goldstein?? i'm already reading the Boas' book, i'm asking because some people says that for Jackson you need to understand very much of Green Functions and other fancy things about PDEs, and others says thats not to difficult, and i'm confused, so, what book i should read to really understand these texts?

Dr. Courtney
Gold Member
2020 Award
I'm not sure reading alone will get you there. You need to work lots of problems. Boas is a good place to start.

Jackson is taught lots of different ways. Very few courses cover every section of every chapter.

Can you get syllabi for the graduate courses you'll be taking? Can you get advice from the instructors who have taught these courses?

When I learned E&M from Jackson, the instructor emphasized material that required knowing spherical harmonics a lot more than Green's functions.

DEvens
i'm self-studying, what i need to do for a better understanding even than read? i don't have access to a university because i'm in the highschool right now...

SteamKing
Staff Emeritus
Homework Helper
i'm self-studying, what i need to do for a better understanding even than read? i don't have access to a university because i'm in the highschool right now...
Perhaps if you gave us an idea of the math you've already studied, it might help produce some useful suggested reading.

At the minimum, university math for physics or engineering is going to involve courses in:

Integral and differential calculus of a single variable.
Vector Calculus and multi-variable calculus
Ordinary Differential equations
Introduction to partial differential equations, usually of the separable type
linear algebra
numerical analysis
statistics

You won't find all of this material covered in a single text, at least not one you would be capable of lifting and carrying with you.

"Integral and differential calculus of a single variable.
Vector Calculus and multi-variable calculus
Ordinary Differential equations
Introduction to partial differential equations, usually of the separable type"
These i have already seen, i have heard that some textbooks teaches the math necessary to understand the phenomena, this is true?

SteamKing
Staff Emeritus
Homework Helper
"Integral and differential calculus of a single variable.
Vector Calculus and multi-variable calculus
Ordinary Differential equations
Introduction to partial differential equations, usually of the separable type"
These i have already seen, i have heard that some textbooks teaches the math necessary to understand the phenomena, this is true?
It's not clear what you mean by "phenomena" here. I thought we were talking about learning mathematics.

Yes, some textbooks teach these subjects, but not all at once (at least not in any great detail.) Even Math Handbooks which usually cover the breadth of this subject can only devote short articles to each topic, in order to fit into a book which isn't the size of a household appliance. Even so, the articles are written for people who have studied the subject in detail previously, and need a handy source of math facts, important theorems, identities, etc., to save from having to search through multiple volumes to find what they need. A math handbook is definitely not suitable for one to first learn the subject.

I should mention that each of the math topics I listed in my previous post is generally covered in a one semester course, sometimes two or three. All told, there is about three years of university math study on that one list (and I omitted the calculus of complex variables).

"Integral and differential calculus of a single variable.
Vector Calculus and multi-variable calculus
Ordinary Differential equations
Introduction to partial differential equations, usually of the separable type"
These i have already seen, i have heard that some textbooks teaches the math necessary to understand the phenomena, this is true?
Are these from high school calculus, or? I'm not sure where these would have come from, and how "knowledgeable" you really are in them, or if you're just trying to make something look "familiar" more than anything.

No, isn't highschool calculus, i have begin study calculus since 2 years ago, i have already read some books on these, i have seen the complete courses of MIT OCW, NPTEL, and some others of my country, i'm very familiar with derivatives and integrals, what i'm really worried about it's some most difficult mathematical courses(Functional Analysis, PDEs, Differential Geometry, Tensor Analysis) that some people say that's necessary a fully understanding to some more advanced areas in physics(QFT, GR, Nuclear, Laser , Condensed Matter Physics), after i finish the Boas' book, what book should i get to learn more of the mathematical methods for these more advanced areas?

Student100
Gold Member
My question is:What is the mathematics necessary for, and which book(or books) i should read to understand graduate-texts like Jackson, Sakurai, Goldstein?? i'm already reading the Boas' book, i'm asking because some people says that for Jackson you need to understand very much of Green Functions and other fancy things about PDEs, and others says thats not to difficult, and i'm confused, so, what book i should read to really understand these texts?

Goldstein is more of an undergraduate text, and you can garner more physical insights by using Jackson as a paperweight in lieu of actually reading it. I would never, ever, in a million years try to read Jackson as a self-study text.

No, isn't highschool calculus, i have begin study calculus since 2 years ago, i have already read some books on these, i have seen the complete courses of MIT OCW, NPTEL, and some others of my country, i'm very familiar with derivatives and integrals, what i'm really worried about it's some most difficult mathematical courses(Functional Analysis, PDEs, Differential Geometry, Tensor Analysis) that some people say that's necessary a fully understanding to some more advanced areas in physics(QFT, GR, Nuclear, Laser , Condensed Matter Physics), after i finish the Boas' book, what book should i get to learn more of the mathematical methods for these more advanced areas?

You should get the physics texts. So you aren't in university? Have you already self studied the introductory physics texts to a level you feel comfortable? Why are you in a hurry to get to graduate texts?

Dr Transport
Gold Member
Goldstein in not an undergraduate text, you need to know a significant amount of mechanics to get through it.

I you want to learn the mathematics for Jackson, etc.... Arfken is a reasonable choice. After slogging through graduate school, I found that Jackson by itself is a reasonably decent math methods text in its own. I learned more Green's function applications from it than any other text/course I ever did.

Thank you all for your replies, i'm very grateful,Student100, i'm reading the Griffiths' E&M , and i'm very confortable with the book, i can do the exercices from the chapters, and i'm already in the end of the chapter of Electric Fields in Matter, i have for some time studied the Quantum Mechanics Griffiths book, the integrals, differential equations, in 3D, Spherical Coordinates and so on i can do very well in this book, but the Linear Algebra formalism made me quit the book, so now i'm studying the Boas' Mathematical Methods to reinforce my mathematics.Dr Transport, i have seen that in the comments of this book, many people recommends the Byron's "Mathematics for Classical and Quantum Physics", what do you think?

Student100
Gold Member
Goldstein in not an undergraduate text, you need to know a significant amount of mechanics to get through it.

Shrug just going off my experience, we used it as the third quarter in mechanics just after Taylor- all required pre-grad classes.

Dr Transport