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

Thanks

Nathan

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- Thread starter Nathan Elward
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In summary: It's more towards engineers and very generic. Use it as a problems book.Stewart Calculus. It's more towards engineers and very generic. Use it as a problems book.

- #1

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

Thanks

Nathan

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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.

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Thanks. Openstax is a decent resource I hadn't heard of before. I'll definitely be using it.

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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=pfamazon01-20I 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.

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Be careful with the edition, though. There are many bad reviews that criticize the international edition.

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The OpenStax physics book,

The best mathematics text book for first year university will ultimately depend on the individual student's learning style and the specific course requirements. However, some popular options include "Calculus: Early Transcendentals" by James Stewart, "Linear Algebra and Its Applications" by David C. Lay, and "Discrete Mathematics and Its Applications" by Kenneth H. Rosen.

First, check the level of difficulty and the topics covered in the text book. It should align with the curriculum of a first year university mathematics course. Additionally, read reviews and recommendations from other students or professors to get a better understanding of the book's suitability.

While some universities may provide access to online resources or have copies available in the library, it is generally recommended to purchase a text book for first year mathematics courses. This will allow for better understanding and easier access to the material.

Yes, there are many online resources such as video tutorials, practice problems, and interactive quizzes that can supplement a traditional text book. Some popular options include Khan Academy, Wolfram Alpha, and Mathway.

In some cases, using an older edition of a text book may be acceptable. However, it is important to check with the professor or course syllabus to ensure that the required material is still covered in the older edition. It is also worth considering the potential differences in formatting, examples, and practice problems between editions.

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