Beschreibung
This is the text for a two-semester multivariable calculus course specifically designed to meet the needs of liberal arts college science students who are genuinely interested in ideas but who are not math majors and especially technically savvy. The text is a "tweener" book, more advanced than most calculus books, though with conceptual exercises rather than detail-oriented ones, but less technical than most introductory analysis texts. It presumes certain freshman-year preparation that is not normative, and its arrangement of topics does not conform to the standard Calculus I-II-III organization. The textbook's aim is to use multivariable calculus to teach mathematics as a blend of reasoning, computing, and problem-solving, doing justice to the structure, the details, and the scope of the ideas. To this end, the writing is aimed to communicate intent early in the discussion of each topic rather than proceeding coyly from opaque definitions. Also, the exposition occasionally speaks to the pedagogy of mathematics and its effect on the process of learning the subject. Most importantly, the weight of the narrative is spread among figures, formulas, and words to guide the reader to do mathematics resourcefully by marshaling the skills of geometric intuition (the visual cortex being quickly instinctive); algebraic manipulation (symbolpatterns being precise and robust); incisive use of natural language (slogans that encapsulate central ideas enabling a largescale grasp of the subject). Thinking in these ways renders mathematics coherent, inevitable, and fluent. The prerequisite for this book is a proof-based course in one-variable calculus, including sequences and series. Some familiarity with the complex number system and complex mappings is occasionally assumed as well, but the reader can get by without it.
Autorenporträt
Jerry Shurman is professor of mathematics at Reed College, Portland, OR, USA. He is also the co-author of GTM 228 "A First Course in Modular Forms."
Herstellerkennzeichnung:
Springer Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE
E-Mail: juergen.hartmann@springer.com
