Vector Calculus

by Susan Jane Colley

This text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. Accessible to anyone with a good background in single-variable calculus, it presents more linear algebra than usually found in a multivariable calculus book. Colley balances this with very clear and expansive exposition, many figures, and numerous, wide-ranging exercises. Instructors will appreciate Colley’s writing style, mathematical precision, level of rigor, and full selection of topics treated. Vectors in Two and Three Dimensions. More About Vectors. The Dot Product. The Cross Product. Equations for Planes; Distance Problems. Some n -Dimensional Geometry. New Coordinate Systems. Differentiation in Several Functions of Several Variables; Graphing Surfaces. Limits. The Derivative. Properties; Higher-Order Partial Derivatives; Newton’s Method. The Chain Rule. Directional Derivatives and the Gradient. Vector-Valued Parametrized Curves and Kepler's Laws. Arclength and Differential Geometry. Vector An Introduction. Gradient, Divergence, Curl, and the Del Operator. Maxima and Minima in Several Differentials and Taylor's Theorem. Extrema of Functions. Lagrange Multipliers. Some Applications of Extrema. Multiple Areas and Volumes. Double Integrals. Changing the Order of Integration. Triple Integrals. Change of Variables. Applications of Integration. Line Scalar and Vector Line Integrals. Green's Theorem. Conservative Vector Fields. Surface Integrals and Vector Parametrized Surfaces. Surface Integrals. Stokes's and Gauss's Theorems. Further Vector Analysis; Maxwell's Equations. Vector Analysis in Higher An Introduction to Differential Forms. Manifolds and Integrals of k -forms. The Generalized Stokes's Theorem.
For all readers interested in multivariable calculus.

Genres: Mathematics, Textbooks, Reference

Hardcover

First published July 17, 1997

Reviews

[Nick · Rating 3 out of 5]

This is adequate. The emphasis, as usual, is on proof of concepts rather than demonstration. I am only a little sorry to see my nights spent with Susan come to an end...

[Kaung Si Thu · Rating 5 out of 5]

For those who will be first introduced to multi-dimensions, this might be first confusing due to concise notations. But, I enjoyed my time reading this just for that reason. Fewer examples than your usual math textbooks, more about notations and nice graphs. I give this five stars because this book introduces u how some area of math should be written (in my opinion) especially in the last chapter: e.g. differential k-forms.

[Musfiqur Pavel · Rating 5 out of 5]

loved it!

[Mirzuis Alinus · Rating 5 out of 5]

Fantastic book
Explain everything in simple manner
But could use more tough problem
And another book for solution to problem

[Jake · Rating 5 out of 5]

I used this book as a supplement for the vector calculus textbook (Hughes Hallett) used at my school. The explanations are thorough and three times longer with diagrams that are much more illustrative. The theorems are more rigorous, requiring linear algebra, and I appreciated that. To other students in my class this book would likely be intimidating to them at my level but I found it much better allowing me to properly challenge myself and prepare myself for what my instructor would throw at me. The book, while challenging, is also straightforward. Hughes Hallett often wast much of the students time with the qualitative question of what is going on, without giving the student the tools to properly explore those questions. Colley's approach asks fewer qualitative questions but that is covered extensively in the copious examples. I plan on going further with this textbook than what was covered in our course. Highly recommended text on vector calculus.

[Adam Lantos · Rating 5 out of 5]

I can only compare it with Marsden and Tromba's book as I have little experience with other book on Vector Calculus of this type (although I have experience with books like Schey's "Div, Grad, Curl and All That"). The only thing I can say is this: It's insightful, clear, detailed, has nice explanations and gives nice discussions on the geometric nature of the material presented here. It has a lot of exercises and I found them to be much better than those found in the book by Marsden. It also contains proofs at the end of each chapters for those who want to learn the material in a rigorous way or for those who are just curious of how some results are obtained.
In conclusion, this is a great book!

[Kate Lane · Rating 4 out of 5]

Great textbook; proofs were clear and helpful, other discussions were insightful and engaging. Tons of exercises.

[Vishnuram Leonardodavinci · Rating 5 out of 5]

The book was wonderful and covers theory as well a broad range of applications from physics to economics. The problems were easy to compute to challenging.

It is a very good book for transition from vector calculus to higher mathematics.

[Brandon Meredith]

Everyone needs to pick up a Calculus book at some point, right?