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As with his other texts, Larson approaches subjects from an analytical perspective AND from a graphic/geometric perspective.
This allows students who despise the Xs, Ys, and Zs of algebra to "see" what might otherwise escape them if approached only analytically.
Excellent text.
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Chapter 11 on vectors and geometry of space offer a solid foundation for understanding basic vector functions and operations (dot and cross product, projection and components, etc.), 3-D geometrical shapes (paraboloid, hyperboloids of 1 or 2 sheets, etc.), as well as applications for both, also cylindrical and spherical coordinates.
Chapter 12 on vector-valued functions initiates the idea of rate, velocity, and acceleration vectors and their relationship including vector differentiation, tangent and normal vectors, and arc length and curvature.
Chapter 13 does a wonderful job introducing functions of several variables, using limits, differentials, partial differentiation rules, gradients, max/minimization, and applications.
Chapter 14 on multiple integration is much easier to understand using this text than others. Lots of physics applications using area, volume, center of mass, moment of inertia, and change of variables.
Chapter 15 returns to vectors with topics such as curl (with physical interpretation), divergence, line and surface integrals, Green's thm, Stoke's thm, flux, and parametric surfaces.
Chapter 16 concludes the text by introducing differential equations. Basic concepts, separation of variables, exactness, homogenous equations, and power series solutions offer both as a learning tool and as somewhat of a refresher course.
Overall, the book is very well-written, from the introduction which illustrates the many advantages of calculus over algebra, the insight into careers using mathematics, to the appendices with proofs of theorems, basic differentian rules and answers to odd-numbered exercises (even exercises for the first 10 chapters), this book is a work of art for any math and/or science student.
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University of Northern Iowa. He has always written pretty much what he wanted to write.
His books are a pleasure to read, as they take the reader through all the twists and turns of life.
Ordinary Ghosts tells the story of a small town in Iowa, where Ron Roberts grew up. By the time you are
done reading this book you will know some of the people, a few of the ghosts, and a lot
more than you ever wanted to know about such a place. Then again, as the book is so much fun to read,
my bet is you will sell your home in the city and move your family to Iowa. Ordinary Ghosts grabs you and
will not let go.
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If you are going to selfstudy calculus, i have some advices:
1 Not every section is necessary. Some sections are mainly about applications in mechanical engineerings(actually, most applications). If you are not interested in ME, just skip them.
2 Don't go too fast. If you don't have time, just skip some sections of the end of each chapters. Especially at the end of the book. Chapter 14 is quite confusing. Read them slowly, understand piece by piece.
If you are a math major, particularly pure math, this is not a book for you. You need a book that talks more about theory.
The exercise problems at the end of each section are never huge surprises. As for their difficulty, they tend to start out easy and end with the more challenging word problems. When I was confused or frustrated, it helped to go back and re-read the examples. The Thomas text's examples were extremely difficult (for us non-MIT level math students) and unrelated/inconsistent with the exercises.
The editing of Larson's text is fantastic, because there are relatively few errors (whereas Thomas' was full of them). And I especially liked the photographs and brief biographies of the famous mathematicians sprinkled throughout each chapter, because they humanize this mysterious and feared subject.
I'd say that this book made calculus less scary and much more manageable. I still had to study really hard to ace the class, but at least it wasn't because the book was overly confusing.
Larson's approach is practical, logical, thorough, and most importantly, CLEAR!!!!
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PS: I am still searching for an errata sheet.