The best (in your opinion) books for various math.

[misogynisticfeminist]

I am looking for good books regarding

Linear Algebra, ODEs, calculus with one variable, many variable and vector calculus, PDEs, and finally, Tensor Analysis. I am looking for books suitable for self-studying.

 

[lurflurf]

I am looking for good books regarding

Linear Algebra, ODEs, calculus with one variable, many variable and vector calculus, PDEs, and finally, Tensor Analysis. I am looking for books suitable for self-studying.

Personal preference is a big factor as well as level of rigor, topics covered ect. Also many good books are out of print.
As far as calculus books most of the modern ones are either bad or rather bland. For linear algebra I like linear algebra done right by Sheldon Axler, but a more concrete book might be helpful for some. For ode's Rainville is great. Vectors, tensors, and basic equations of fluid mechanics is a nice book by Rutherford Aris. It covers tensors, but it starts by covering vector calculus which it does not assume.Generalized Vector and dyadic analysis by Chen-to Tai is a nice book, but it is way over priced. For PDEs there are 4 approches Numerical Techniques, Separation of Variables, Transform Methods and Asymptotic Analysis. Different books focus on different things. Transform Methods for Solving Partial Differential Equations by Dean Duffy is a good book that is almost entirely about transform methods. Duffy also has written a book on PDEs in general and one on applied math that covers PDEs, but I have not read those. These are just books that come to mind I have not performed a comparative analysis. There are no doubt other good choices.

 

[tacman]

1. Linear Algebra: "Linear Algebra Done Right" by Sheldon Axler is a highly recommended book for self-study. It covers the fundamentals of linear algebra with a clear and concise approach, making it suitable for beginners.

2. ODEs: "Ordinary Differential Equations" by Morris Tenenbaum and Harry Pollard is a classic textbook that covers all the essential topics in ODEs. It has a comprehensive approach and includes many examples and exercises for self-study.

3. Calculus with One Variable: "Calculus" by Michael Spivak is considered one of the best books on single-variable calculus. It has a rigorous and intuitive approach, making it suitable for self-study.

4. Calculus with Many Variables and Vector Calculus: "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba is a popular textbook that covers multivariable calculus and vector calculus in a clear and concise manner. It also includes many exercises for self-study.

5. PDEs: "Partial Differential Equations for Scientists and Engineers" by Stanley J. Farlow is a highly recommended book for self-study on PDEs. It covers the basics of PDEs and includes many real-world applications.

6. Tensor Analysis: "Tensor Analysis" by Edward Nelson is a comprehensive textbook that covers the fundamentals of tensor analysis. It has a clear and concise approach, making it suitable for self-study.

Overall, these books are highly recommended for self-study on various math topics. However, it is always best to consult with a math professor or tutor for personalized recommendations and to ensure proper understanding of the concepts.