![]() The presentation is geared towards students who enjoy learning mathematics for its own sake. ![]() As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. This book covers the standard material for a one-semester course in multivariable calculus. Our functional goals describe the attitudes and behaviors we hope our students will adopt in using calculus to approach scientific and mathematical questions. Our curricular goals are what we aim to convey about the subject in the course. Our starting points are thus our summary of what calculus is really about. We began our work with a "clean slate," not by asking what parts of the traditional course to include or discard. The mathematical questions that arise are compelling in part because the answers matter to other disciplines. We also believe that much of the mathematical depth and vitality of calculus lies in connections to other sciences. Smith College Open Educational Resources: TextbooksÄesigning the curriculum We believe that calculus can be for students what it was for Euler and the Bernoullis: a language and a tool for exploring the whole fabric of science.
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