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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.
- Sales Rank: #268827 in Books
- Published on: 2005-03-26
- Original language: English
- Number of items: 1
- Dimensions: 10.24" h x .95" w x 8.19" l, 2.70 pounds
- Binding: Hardcover
- 576 pages
About the Author
Susan Colley is the Andrew and Pauline Delaney Professor of Mathematics at Oberlin College and currently Chair of the Department, having also previously served as Chair. She received S.B. and Ph.D. degrees in mathematics from the Massachusetts Institute of Technology prior to joining the faculty at Oberlin in 1983. Her research focuses on enumerative problems in algebraic geometry, particularly concerning multiple-point singularities and higher-order contact of plane curves. Professor Colley has published papers on algebraic geometry and commutative algebra, as well as articles on other mathematical subjects. She has lectured internationally on her research and has taught a wide range of subjects in undergraduate mathematics. Professor Colley is a member of several professional and honorary societies, including the American Mathematical Society, the Mathematical Association of America, Phi Beta Kappa, and Sigma Xi.
Most helpful customer reviews
5 of 5 people found the following review helpful.
It's a very good book for what it does
By Joshua E. Hill
I went through most of this text during a 1 quarter vector calculus course aimed at second and third year (US) math and physics undergrads. This book provides a reasonable mid-point between a standard calculus course where calculations are the main thrust of the course, and an analysis course where justifications are the main thrust of the course. This book does not include complete proofs for some of the more technical theorems, but it always includes proofs when the proof is helpful in understanding the theorem. This book also includes a gentle introduction to differential forms, which is very nice.
The aspect of this book that I appreciate the most is that it tries to provide very clear geometric and physical interpretations of the various standard vector calculus theorems. For whatever reason, this is unusual, which is sad. This approach makes these theorems much more accessible to an audience that is more comfortable with envisioning physical systems than with mathematical proof.
4 of 4 people found the following review helpful.
very good entry book for science/engineering students
By NewJersey929
I like this book very much. I took multivariable with the famous Thomas' calculus volume 2 at high school (it was used at Princeton University freshman class, and MIT freshman class). I now take a freshman calculus 2 course with this book. The level is not so much different from Thomas'. Just a bit in more theory oriented discussions. But the book is very well written, and in many respect very similar in tone and style to Thomas'. I am happy to "repeat" multivariable calculus with a minor level-up since I did not wish to jump into real analysis outright. I do not intend to major in math, and for me this is the right level. I also looked upon Buck's advanced calculus book, and it was visibly higher level in theory. I am not sure if I should go through Buck's book after this though since the differential form notation is introduced in the last chapter. I also liked chapter 7, which prepares me for multivariable-based physics 2 (E&M) course I will be taking next semester. The problems seem to be more calculation oriented (at the similar level as Thomas'), but the text discussions are more theory inclined (rather than theory oriented). Overall, I highly recommend this book to students whose background and motivation is like me (science/engineering major student).
11 of 14 people found the following review helpful.
Superlative
By A. Ali
This book covers all the standard vector calculus material. What sets it apart is the pedagogic skill of the author. It is very carefully written and motivated, with clear worked examples for each new concept. A student could work through this book independently.
The author has included a brief section on differential forms in the last chapter and she presents Stokes' theorem in the language of forms. This is a modern formulation and she is to be praised for doing this. It is possible to move from this book on to modern texts on manifolds and differential geometry (such as the books by John Lee and Barrett O'Neill, for example).
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