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Best Mathematics Text Book (for 1st year university)

  • #1

Main Question or Discussion Point

I'm going to Uni in October and want to get a head with maths for physics NOW so its not so daunting when I am there.

What textbooks/resources are an excelent introduction to physical mathematics?

Thanks

Nathan
 

Answers and Replies

  • #2
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I think calculus and linear algebra are the keywords here. You can have a look on the books on OpenStax , e.g. Calculus I or higher in case you already know the content. However, I would concentrate on linear algebra, as I think it's the bigger step from school to university. Matrices and vector spaces are usually taught only very basically at school, if at all, whereas in physics you use them all the time. So it might be helpful to get used to the concepts and terms.

However, there is always a risk to learn wrong, i.e. to interpret the subtleties of a subject in a wrong way: e.g. the difference between a linear transformation or vector and its representation by coordinates, the concept of continuity, i.e. confusing the ##\varepsilon - \delta## definition.
 
  • #3
Thanks. Openstax is a decent resource I hadn't heard of before. I'll definitely be using it.
 
  • #4
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Alonso and Finn University Physics. A book forgotten in the US, but used in other parts of the world. Concise explanations and diagrams are meaningful. Ie., the pages are not cluttered with pictures like most of todays physics book. Diagrams are drawn clearly and well explained. Everything is derived from first principle. Problems can be challenging. Derivations are clear. The real gem is part 2 and part 3. Topics are introduced that are usually covered in upper division courses. This book is below Klepner and Kolenkow, but can prepare you for upper division books of the that ilk. Calculus is highly emphasized at the beginning. Majority of intro physics books in mechanics, do not use calculus extensively.
https://www.amazon.com/dp/B0006BNQDG/?tag=pfamazon01-20

Also purchase another introductory book to reference. Maybe Giancoli Physics for Scienties and Engineers or Serway Physics. Always choose the older editions. Much cheaper, and practically the same.

Edwin E. Moise : Calculus. Much easier than Spivak/Apostol/Courant. Everything is motivated carefully. Great precise, clear, and informative writing. Explains things like the well ordering principle, the power and motivation behind the Mean Value Theorem. Fields and their axioms are explained. Explains what a parabolic sector is, and how Archimedes approached the area of a curve. Logirithmic functions and their integrals are constructed and well defined.
Explains sequences and series very well.Mathematically correct derivation of arc length, most modern calculus book that have a proof of this are incorrect. Great place to learn to think mathematically. Great balance between theory and application. Reminds of a gentler Courant Calculus.
https://www.amazon.com/dp/B000L3UO2A/?tag=pfamazon01-20

Stewart Calculus. It's more towards engineers and very generic. Use it as a problems book.
https://www.amazon.com/dp/0538497815/?tag=pfamazon01-20

Thomas Calculus 3rd ed. Mathwonk wrote a great summary of the books strengths. More of an applied approach, but a goody. I learned Calculus from this book.
https://www.amazon.com/dp/B00GMPZBGA/?tag=pfamazon01-20


I recommend that you read Moise as the main book, and supplement it with Thomas. If Moise is too hard, you can use Thomas, and later do Moise.

This should be enough for now.
 
  • #5
I would say Apostol's Calculus, vols 1 and 2. It has sequences, series, single variable calculus, vector algebra, linear algebra, vector calculus, multivariable calculus, differential equations, (and some probability and numerical analysis). The book is excelent at ballancing between intuition and formalism. It is not overly formal or pedantic, and contains many computational exercises. But it is a rigorous textbook with clear explanations of the material.

Be careful with the edition, though. There are many bad reviews that criticize the international edition.
 
  • #6
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I'd concentrate on first-year calculus and differential equations. It's more important at this point to learn how to do calculations efficiently than get bogged down in knowing how to prove everything. Don't discount getting better at algebra and trig.

The OpenStax physics book, University Physics, isn't great. My students largely don't care for it. You'd be better off buying an old edition of Young and Freedman.
 

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