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Therefore don't expect things as partial diff.eqs techniques in details and such, there are many engineering-type books on that.
This is more about to understand (advanced) vector spaces in general (earlier than you think you need to), calculus, and differential geometry with all its heavy topics.
It's not a book for mathematicians (e.g. rigorous proofs), but it's strict enough for physicists to understand the need of knowing these concepts and topics in order to follow modern physics with math.
No flaws
Ce livre arrive à trouver exactement le juste milieu entre ces 2 approches et par ce fait , il est relativement unique dans son genre. On sent que les auteurs possèdent une expérience pédagogique bien rodée : tout est clair et bien présenté.
Le livre est partagé en 3 sections : algèbre, "calculus" (équivalent à l'analyse réelle et complexe) et enfin analyse vectorielle. Chaque section est composée d'une plusieurs sous-sections (10 pour l'algèbre , 9 pour le calculus et 7 pour l'analyse vectrorielle). Un ordre de progression est proposé au début du libre afin le matériel nécessaire pour aborder un sous-chapitre a déjà été abordé précédement. Une série d'exercice est proposé à la fin de chaque section. Les solutions détaillées des exercices impairs sont disponibles à la fin de l'ouvrage.
En conclusion : EXCELLENTE OUVRAGE !!!
But unless you have some notion of the underlying ideas, how will you ever have confidence you're applying the right procedure to your situation?
Having taught and used this stuff for a long time, this is one of the best introductory books I've come across. And students will be relieved - and helped! to find solutions being provided to some of the problems.
I would highly recommend this text to other physicists, really, any scientist in general that needs a concise brush up or introduction, the reason why is that one is able to relearn their calculus and linear algebra and touch upon some topics within the text that may have never been covered in their university courses, I never recalled learning multilinear algebra, differential geometry, hermiticity & symmetry and various other peculiar/special functions during undergrad calculus and engineering mathematics (with engineering math being just a concise introduction and combination of ordinary differential equations and linear algebra for time purposes). The 3-D diagrams within the textbook are extremely helpful in representing what is going on, also, the various problems within this textbook are helpful as well because they really do make you think (this isn't an exaggeration, some really make you think) and represent the core of the material being taught, no dilly dallying in learning what are the core concepts that one needs to be able work with the mathematics, it also helps out a lot that the text contains solutions to half of the problems.
Now for the bad news. One major thing that irks me a lot is that there is no table/list of symbols/greek alphabet which displays in english the mathematical notations/symbols used (pic related), this also isn't helped by the fact that some of the symbology isn't named? Maybe this is the only exception but the reason why I said the previous sentence is that in section C6.1 the dirac delta function is introduced but isn't even called the dirac delta function, it's just referred to as "function" no joke. I don't recall this occuring regularly, or maybe it's because it's such a famous function that it just caught me completely off guard, I had to google the function name to see if i wasn't going crazy in not recognizing the dirac delta function.
The very first section of the linear algebra section L1.1 Sets and maps & L1.2 Groups, is no joke. I would find it very hard to believe that a student who has never taken an introductory course on proofs and group theory would fully understand this section, seeing as how I've taken a proofs course followed by a group theory course with Book of Proof by Hammack and Discovering Group Theory: A Transition to Advanced Mathematics by Barnard (two of the absolute best introductory mathematical analysis texts I've ever used). I really don't see how one who is new to those two subjects would fully digest those two extremely condensed and concise sub sections, and the problems that go along with said sub sections are no joke (bad).
Of course if you already have some mathematical maturity then going through that part of the text would be a complete breeze, a cakewalk even, but i'm talking about this from the theoretical perspective of a brand new undergrad who bought this textbook to learn from scratch calculus, linear algebra, and some various mathematical methods, who has never seen this stuff before, of course they will have problems with such a short introduction to those two sub section, personally I think that the authors should just reform those two subsections into full chapters or just into bigger subsections in general and explain with more detail about sets and groups (maybe like 15-20 pages each), I mean, come on, the entire book is built using said information from those two subsections in order to understand what is going on in the rest of the text, I can see how that can be a problem for the uninitiated. If you're reading this and decide to buy the book, go for it, it's a really great text to do problems in and relearn or for the first time ever, learn CALC and LINALG and other side stuff that's very useful, also one can easily use this as a reference.
But yeah, just expand those two subsections and make a table of symbols used throughout the text.