دانلود کتاب مبانی حساب دیفرانسیل و انتگرال چند متغیره

Our age is revolutionary. Just as the appearance of hand-held calculators buried the art of mental arithmetic and logarithmic slide rules, without which a century ago one could scarcely imagine a practicing engineer, we can expect many other arts to recede. These may include cumbersome algebraic and trigonometric transformations, evaluation of complicated integrals, or the analytic solution of differential equations. A good portion of modern mathematical textbooks is repetition from 19th century textbooks, despite the inclusion of modern pseudo-applications. But computers have already taken over the tasks of solving various equations — both algebraic and differential — and provide numerical, analytic, and graphical results. The study of tricks required to evaluate awkward integrals, and so on, will be left to professional mathematicians and theoretical physicists who need to develop new mathematical studies. One of the authors of this book asked a masters-degreed civil engineer “What kinds of mathematics do you use in your practice?” The answer was, “A calculator!” With the continued development of handheld electronics, this answer will surely become more and more typical. What should the modern engineering or science student learn? Certainly not how to solve artificial exercises they will never apply. Rather they should come to understand what is done in various parts of mathematics, and why. Students can be given tools, but without understanding their proper use is impossible. We cannot say how the mathematical curriculum for engineering or science students should be changed, except that (a) it should include a good portion of numerical methods, and (b) the cumbersome tricks of the 18th and 19th centuries should be eliminated. It is not clear how to achieve the main goal of education in anything, which is understanding of the matter, but it should be done. This book is an introduction to multivariable calculus (or “vector calculus”). The prerequisites are limited to single-variable calculus, linear algebra, and analytic geometry. So what should a student know about multivariable calculus, and how is this knowledge to be acquired? The second question is by far the easier one: the presentation must be clear and well motivated, and exercises must be worked. Real conceptual grasp cannot come without problem solving activity, though the exercises themselves need not be technically burdensome. Our list of topics is also quite conventional: limits, continuity, partial derivatives, extrema, the nabla operator, multiple integrals, line integrals, and surface integrals. However, our classroom experience with engineering students has led to certain choices regarding emphasis and approach. Reasons for a few of these are noted in the following list.