جزییات کتاب
کتاب “حساب دیفرانسیل و انتگرال” نوشته Tom Apostol، یک معرفی حساب دیفرانسیل و انتگرال میباشد که تعادلی عالی میان تئوری و تکنیکها ایجاد کرده است.
در این کتاب، انتگرالگیری قبل از مشتقگیری انجام شده است که برگرفته از مدرنترین متون میباشد اما از لحاظ تاریخی نیز صحیح است و بهترین روش برای ایجاد ارتباط صحیح میان انتگرال و مشتق میباشد. اثبات تمام قضایای مهم ارائه شده است و قبل از آن مباحث شهودی و هندسی، به طور کلی مطرح شده اند.
ویرایش دوم کتاب، برهانهای با ارزش متوسط را معرفی میکند و کاربردهای آنها را بیان میکند. همچنین شامل مباحث جبر خطی و تعداد زیادی از تمرینهای جدید و آسان میباشد.این نسخه نیز همانند نسخه اول، هر مفهوم جدید و مهم را در ابتدا از لحاظ تاریخی معرفی میکند.
Perhaps my love of this text is because I was one of those students who only wanted to know how to use a derivative or integral to solve a physical problem when I took my first calculus class in 1973. Years later when I was visiting MIT looking for economic texts, I came across Calculus by Apostol and after briefly skimming the index, decided to purchase it. It was three years later that I actually began studying the material in the text and honestly, I felt as though blinders had been removed from my eyes. From the opening chapters on step functions and integration, the material on diffferentiation and limits and proceeding into the topics of differential equations, sequences and series, complex numbers, differential equations and linear algebra, I was excited to be studying mathematics and finally understanding the material versus memorizing formulas. This text motivated me to purchase Apostol's second and third books on multivariable calculus and analysis. Today I am studying Royden's real Analysis text to prepare me for my next topic - probability. Is this book for everyone? Probably not. But if you ever felt that you had shortchanged yourself in college mathematics and are in a career where you can benefit from starting over and learning calculus the right way, I recommend the Apostol text. (And I firmly believe that all of us can benefit in our jobs from studying the logic of mathematics!)