The main difference between "Vector Calculus by Marsden and Tromba" and "Vector Analysis by Brand" is the level of mathematical rigor. "Vector Calculus" is geared towards advanced undergraduate and graduate students, while "Vector Analysis" is more suitable for introductory courses. "Vector Calculus" also covers more advanced topics, such as differential forms and manifolds, while "Vector Analysis" focuses on the fundamentals of vector calculus.
For self-study, it really depends on the individual's mathematical background and goals. If you have a strong foundation in calculus and linear algebra, "Vector Calculus" may be a better choice as it covers more advanced topics in vector calculus. However, if you are new to the subject and are looking for a more accessible introduction, "Vector Analysis" may be a better option.
Both books have clear explanations and illustrations, but some readers may prefer the style and approach of one over the other. It is best to preview both books to see which one resonates with you more.
Both books have a variety of practice problems and exercises, but the level of difficulty may vary. "Vector Calculus" may have more challenging problems, while "Vector Analysis" may have more introductory level exercises. It is recommended to use both books for a well-rounded understanding of the subject.
Yes, using both books simultaneously can be beneficial for a deeper understanding of the subject. The books cover similar topics but with different approaches and levels of rigor, which can complement each other. It is also a good idea to consult with your instructor or a tutor to guide you in using both books effectively.