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Summary:
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: 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 Variables: 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 Functions: Parametrized Curves and Kepler's Laws. Arclength and Differential Geometry. Vector Fields: An Introduction. Gradient, Divergence, Curl, and the Del Operator. Maxima and Minima in Several Variables: Differentials and Taylor's Theorem. Extrema of Functions. Lagrange Multipliers. Some Applications of Extrema. Multiple Integration: Introduction: Areas and Volumes. Double Integrals. Changing the Order of Integration. Triple Integrals. Change of Variables. Applications of Integration. Line Integrals: Scalar and Vector Line Integrals. Green's Theorem. Conservative Vector Fields. Surface Integrals and Vector Analysis: Parametrized Surfaces. Surface Integrals. Stokes's and Gauss's Theorems. Further Vector Analysis; Maxwell's Equations. Vector Analysis in Higher Dimensions: An Introduction to Differential Forms. Manifolds and Integrals of k-forms. The Generalized Stokes's Theorem.
For all readers interested in multivariable calculus.
Customer Reviews:
Average Customer Rating:
Vector Calculus Solutions Manual
Customer Rating:
The manual is not at all detailed. It in no way supplemented my learning. She does not offer detailed explanation, something I think is necessary when first learning a concept.
May or may not help.
Customer Rating:
I ordered the solutions manual to help explain the homework problems assigned to me in class from the textbook (since my professor doesn't go over homework at all and has horrible lectures), but it only has certain odd problem solutions. This only helps for those certain problems and can't help me understand what to do for the others...
So it's good if you're lucky enough to get those problems listed in the solutions manual.
Student's Perspective: Ineffective Textbook
Customer Rating:
One positive note, this book covers what you would expect in a vector calculus class or multivariable calculus class in the U.S. It starts with a brief background in vectors and covers through Stokes' and Gauss' Theorems.
This textbook is terrible for mainstream vector calculus students. Even some of the simplest material is covered in an odd, obscure fashion for students new to vector calculus. Important material, formulas, and concepts tended to be written without emphasis. The individual sections in the book were long, but don't let that fool you as each example was confusing the first time around because the author decided we knew the "obvious" steps in an example before being taught them. The author also conveniently avoided any difficult integrals thus leaving the student to devise methods of solving the integrals in the exercises. Some of these problems required prior coursework knowledge which is understandable, but some required a table of integrals, which is conveniently not on the front or back covers of the book. In fact, there are no formulas on the inside of the covers of the book. No trigonometric identities, which were needed for most integrals...
The exercise problems at the end of the sections were sometimes incredibly difficult to complete even though they may have been numbered low. If you are hoping the book will help in solving some of its hard exercises, find another book. Some exercise problems' instructions were written so badly, I did the problem incorrect the first time only to realize it was only asking for something simple.
I often keep my mathematics textbook after the course, but I did not even think twice about keeping this one. Avoid buying this textbook unless you understand vector calculus already, in which case you would only need this book to do exercise problems.
The Bane of My Mathematical Existence
Customer Rating:
If you are in charge of designing curricula for your Place of Higher Learning, please don't force your students to use this book as anything more than a doorstop. It's full of text, 70% of which is unnecessary filler. One of the author's favorite pedantic methods is using the phrase "convince yourself that [some mathematical idea is true]" instead of actually proving it. This might be acceptable if the author had balanced out the massive seas of empty text with massive seas of examples. But keeping with the theme of the book ("useless"), there are few examples, which are what usually makes a textbook valuable.
The one bright spot is reading the uncomfortably forced praise on the back cover.
Good condition, but wrong book.
Customer Rating:
The book was in great condition and arrived speedily. However, what I got in the mail was the second edition. I needed the third edition for my class, which I then had to get from a school bookstore at a very high price.
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