首页Calculus 2 - Tom M Apostol
ti Variable Calculus and Linear
Algebra, with Applications to
tial Equations and Probability
John Wiley & Sons
New York London Sydney Toronto
George Springer, Indiana University
1969 BY XEROX CORPORATION.
All rights reserved. No part of the material covered by this copyright
may be produced in any form, or by any means of reproduction.
Previous edition copyright
1962 by Xerox Corporation.
Librar of Congress Catalog Card Number: 67-14605
00007 8 Printed in the United States of America.
Jane and Stephen
This book is a continuation of the author’s Calculus, Volume I, Second Edition. The
present volume has been written with the same underlying philosophy that prevailed in the
first. Sound training in technique is combined with a strong theoretical development.
Every effort has been made to convey the spirit of modern mathematics without undue
emphasis on formalization. As in Volume I, historical remarks are included to give the
student a sense of participation in the evolution of ideas.
The second volume is divided into three parts, entitled Linear Analysis, Nonlinear
and Special Topics. The last two chapters of Volume I have been repeated as the
first two chapters of Volume II so that all the material on linear algebra will be complete
in one volume.
Part 1 contains an introduction to linear algebra, including linear transformations,
matrices, determinants, eigenvalues, and quadratic forms. Applications are given to
analysis, in particular to the study of linear differential equations. Systems of differential
equations are treated with the help of matrix calculus. Existence and uniqueness theorems
are proved by Picard’s method of successive approximations, which is also cast in the
language of contraction operators.
Part 2 discusses the calculus of functions of several variables. Differential calculus is
unified and simplified with the aid of linear algebra. It includes chain rules for scalar and
vector fields, and applications to partial differential equations and extremum problems.
Integral calculus includes line integrals, multiple integrals, and surface integrals, with
applications to vector analysis. Here the treatment is along more or less classical lines and
does not include a formal development of differential forms.
The special topics treated in Part 3 are Probability and Numerical Analysis. The material
on probability is divided into two chapters, one dealing with finite or countably infinite
sample spaces; the other with uncountable sample spaces, random variables, and dis-
tribution functions. The use of the calculus is illustrated in the study of both one- and
two-dimensional random variables.
The last chapter contains an introduction to numerical analysis, the chief emphasis
being on different kinds of polynomial approximation.
Here again the ideas are unified
by the notation and terminology of linear algebra. The book concludes with a treatment of
approximate integration formulas, such as Simpson’s rule, and a discussion of Euler’s
【问题描述】、 马上就要期中考试了，小唐还不会积分，为了帮助她验证积分的正确性，你觉得写一个程序来计算积分，但是在这之前，你需要先得到积分的式子，因此，用c++定义一个Calculus类，数据成员仅为一个字符串str，现告诉你多项式项数，以及每一项的指数和系数，利用构造函数生成一个字符串，存储在数据成员str中，并写一个成员函数输出它。 【输入形式】 第一行一个整数n，接下来n行，每行两个数，第一个数为指数，第二个数为系数 【输出形式】 一个多项式，高次项在前，其中，零次方输出为单个常数，0不输出，乘法用*，次方^。 【样例输入】 4 2 3 3 4 8 0 0 4 【样例输出】 4*x^3+3*x^2+4
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