Functions of Several Variables by B. D. Craven


Functions of Several Variables by B. D. Craven

This book is aimed at mathematics students, typically in the second year of a university course. The first chapter, however, is suitable for first-year students. Differentiable functions are treated initially from the standpoint of approximating a curved surface locally by a fiat surface. This enables both geometric intuition, and some elementary matrix algebra, to be put to effective use. In Chapter 2, the required theorems - chain rule, inverse and implicit function theorems, etc- are stated, and proved (for n variables), concisely and rigorously. Chapter 3 deals with maxima and minima, including problems with equality and inequality constraints. The chapter includes criteria for discriminating between maxima, minima and saddlepoints for constrained problems; this material is relevant for applications, but most textbooks omit it. In Chapter 4, integration over areas, volumes, curves and surfaces is developed, and both the change-of-variable formula, and the Gauss-Green-Stokes set of theorems are obtained. The integrals are defined with approximative sums (ex- pressed concisely by using step-functions); this preserves some geometrical (and physical) concept of what is happening. Consequent on this, the main ideas of the 'differential form' approach are presented, in a simple form which avoids much of the usual length and complexity. Many examples and exercises are included.

About the Author

Other Formats

Book Info


138 pages


B. D. Craven
More books by B. D. Craven


Publication date

10th December 1981



I love ‘LoveReading 4 kids’ because they let you read and learn things you’d never dreamed of learning before.

Emily Horncastle – age 11

Lovereading4kids is great, we get books really early never late. We love to read and review, and think you would like it too. The excitement

Jasmine Harris-Hart, age 12

I love Lovereading because I often never know what to read and this helps you find a good book. I have recommended this to many people.

Shannon-Louise Masters – age 15

It’s really exciting to read and review new books, thrilling to see my reviews online and I love finding the final published copies on sale.

Sam Harper – age 10

It’s a community united by a passion for books and promoting the best there is in children’s literature.

Sam Bateman and family

It is THE website to use for narrowing down your search for any book. Definitely knocks the socks off any other book review website.

Nickey and Tomasz Hawryszczuk

I love all the books they recommend & put up for me to review. I also love the fact that they give new authors the chance to share their boo

Daisy Pennock – age 15

LoveReading4Kids is a modern and creative way of emphasising the value and importance of books in this digital age #booksforlife

Amrit Bunet – Teen

Lovereading 4 schools