Vector/multivariable calculus textbook

In summary: It provides a rigorous and detailed approach to the subject, with challenging problems that can aid in effective revision. The book also includes lecture notes, videos, and recitations, providing a comprehensive learning experience. Other recommended resources include MIT OCW's multivariable course, which offers lecture notes, videos, and challenging problem sets, as well as Griffiths' textbook on electrodynamics, which builds upon the foundation of vector calculus. Overall, these resources are highly beneficial for gaining a deep understanding of multivariable and vector calculus concepts.
  • #1
lizzie96'
26
5
Hello,

I’m looking for a good book on multivariable and vector calculus for a first/second year undergrad course. I’ve been using Stewart’s Early Transcendentals so far, but probably because I haven’t attended any of the lectures I don’t feel like I have a very deep understanding of the ideas. I’m looking for a (slightly) more rigorous, detailed textbook (or lecture notes) with lots of challenging problems for effective revision.

Thanks for any recommendations!
 
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  • #2
lizzie96' said:
Hello,

I’m looking for a good book on multivariable and vector calculus for a first/second year undergrad course. I’ve been using Stewart’s Early Transcendentals so far, but probably because I haven’t attended any of the lectures I don’t feel like I have a very deep understanding of the ideas. I’m looking for a (slightly) more rigorous, detailed textbook (or lecture notes) with lots of challenging problems for effective revision.

Thanks for any recommendations!
I personally went through MIT OCW's multivariable course from beginning to end and found it extremely useful. It includes lecture notes, videos, recitations and full problem sets with solutions. The problems on part B of their problem sets can be quite challenging and rewarding. I'm not sure how to classify its rigour but I can vouch for its effectiveness - I went on to study electrodynamics from Griffiths' textbook immediately after finishing this course and am having no problem with its level of vector calculus.
Good luck!
 
  • #3
Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, 4th edition, MatrixEditions.com
 

1. What is vector/multivariable calculus?

Vector/multivariable calculus is a branch of mathematics that deals with functions of multiple variables, such as those in three-dimensional space. It extends the concepts of single-variable calculus to functions with more than one independent variable, and involves the use of vectors to represent quantities that have both magnitude and direction.

2. What topics are typically covered in a vector/multivariable calculus textbook?

A vector/multivariable calculus textbook typically covers topics such as vector algebra, multivariable functions, partial derivatives, multiple integrals, line and surface integrals, and vector fields. It may also include applications of these concepts in physics, engineering, and other fields.

3. What are some benefits of studying vector/multivariable calculus?

Studying vector/multivariable calculus can improve one's understanding of three-dimensional space and the behavior of functions with multiple variables. It is also essential for advanced topics in mathematics, physics, and engineering, and can improve problem-solving skills and critical thinking abilities.

4. Are there any prerequisites for studying vector/multivariable calculus?

Yes, it is recommended to have a strong understanding of single-variable calculus, including topics such as limits, derivatives, and integrals. Some knowledge of linear algebra and basic trigonometry may also be helpful.

5. How can I choose the best vector/multivariable calculus textbook for my needs?

When choosing a textbook, consider your level of understanding and your specific needs. Look for textbooks with clear explanations, relevant examples and exercises, and a good balance between theory and applications. You may also want to read reviews and consult with your instructor or peers for recommendations.

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