# Multivariable calculus PDF books

• Calculus
• taylorandrian
In summary, a multivariable calculus book is a book on mathematics that extends the concepts of single variable calculus to functions of multiple variables. In this subject, vectors and partial derivatives are introduced to represent and manipulate multi-dimensional data. The gradient of a function represents the rate of change of a function in a particular direction, while the tangent plane provides a way to approximate the behavior of a function near a specific point. The Jacobian matrix is used to transform coordinate systems, while multiple integrals are used to calculate the volume under a surface. Two important theorems in multivariable calculus are the divergence theorem and Stokes' theorem, which relate the behavior of vector fields to concepts such as line integrals and the flow of

#### taylorandrian

Multivariable calculus is a branch of mathematics that extends the concepts of single-variable calculus to functions of multiple variables. In this subject, vectors and partial derivatives are introduced to represent and manipulate multi-dimensional data. The gradient of a function represents the rate of change of a function in a particular direction, while the tangent plane provides a way to approximate the behavior of a function near a specific point. The Jacobian matrix is used to transform coordinate systems, while multiple integrals are used to calculate the volume under a surface. Two important theorems in multivariable calculus are the divergence theorem and Stokes' theorem, which relate the behavior of vector fields to concepts such as line integrals and the flow of fluids.

i need some pdf books if you can help me in my master degree i need them

In terms of pdf, you are very limited due to copyright laws. From Malawi_Glenn thread, I am only familiar with Paul's Online notes, which are excellent, but these are a supplement.

I would suggest at the minimum, owning a copy of Mardsen Vector Calculus. It is probably the easiest vector calculus book to work through. older editions are extremely cheap. I purchased one recently for \$8 dollars, having donated my previous copy to the math department at my school.

MidgetDwarf said:
Mardsen Vector Calculus
Just to be clear, and to help in a web search, the author is Jerrold Marsden, and the coauthor is Anthony Tromba.

jim mcnamara, vanhees71 and malawi_glenn
I agree that Marsden and Tromba is an excellent choice. I used it to teach a high school class of exceptional students, some of whom are now well known mathematicians. Another excellent book is the one by Ted Shifrin, professor emeritus of University of Georgia, and happily, his lectures on the subject are available free on youtube:

So if you like lectures, or if they can help you, check these out. Ted was famous as an extraordinarily clear lecturer.

edit: The book by Marsden and Tromba I was talking about was the 1976 or 1981 edition, available cheaply from abebooks:
https://www.abebooks.com/servlet/Se...ld&tn=vector calculus&cm_sp=click-_-plp-_-ntb

Last edited:
vanhees71
mathwonk said:
I agree that Marsden and Tromba is an excellent choice. I used it to teach a high school class of exceptional students, some of whom are now well known mathematicians. Another excellent book is the one by Ted Shifrin, professor emeritus of University of Georgia, and happily, his lectures on the subject are available free on youtube:

So if you like lectures, or if they can help you, check these out. Ted was famous as an extraordinarily clear lecturer.

Do you know of a place to get a copy of Shifrin's book? I think I lost my copy during my last move.

Frimus
The link just above is apparently to a different book, by Marsden and Weinstein.

malawi_glenn
mathwonk said:
The link just above is apparently to a different book, by Marsden and Weinstein.
Yes, it's a multivariate calculus book, not a vector calculus book per se.

i could be wrong, but my impression was that the link is to a traditional calculus book, single variable differentiation and integration, and multivariable. The book by Marsden and Tromba is specifically a modern several variables book with intro to linear algebra preceding the vector calculus, with single variables calc assumed.

malawi_glenn

## 1. What is multivariable calculus?

Multivariable calculus is a branch of mathematics that deals with the study of functions of several variables. It involves the use of calculus techniques, such as differentiation and integration, to analyze and solve problems involving multiple variables.

## 2. Why is it important to study multivariable calculus?

Multivariable calculus is important because it allows us to understand and model complex systems that involve multiple variables. It is also used in various fields, such as physics, engineering, economics, and computer science, to solve real-world problems.

## 3. What are some common applications of multivariable calculus?

Multivariable calculus has many applications, including optimization problems, motion and trajectory analysis, and finding volumes and areas of irregular shapes. It is also used in fields such as economics, biology, and statistics to model and analyze complex systems.

## 4. Are there any recommended books for learning multivariable calculus?

Yes, there are many excellent books available for learning multivariable calculus. Some popular options include "Multivariable Calculus" by James Stewart, "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba, and "Calculus: Early Transcendentals" by William L. Briggs and Lyle Cochran.

## 5. Is it necessary to have a strong foundation in single-variable calculus before studying multivariable calculus?

Yes, it is highly recommended to have a solid understanding of single-variable calculus before delving into multivariable calculus. Many of the concepts and techniques used in multivariable calculus build upon those learned in single-variable calculus. It is also important to have a strong grasp of algebra and trigonometry.

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