摘抄preface第一段:This book is particularly intended for the student with one year of calculus who wants to develop, in a short time, a basic competence in each of the many areas of mathematics needed in junior to senior-graduate courses in physics, chemistry, and engineering. Thus it is intended to be accessible to sophomores. It may also be used effectively by a more advanced student to review half-forgotten topics and learn new ones, either in independent study or in a class. Although the book was written especially for students of the physical sciences, students in any field(say, mathematics or mathematics for teaching) may find it useful to survey many topics or to obtain some knowledge of areas they do not have time to study in depth. Since theorems are stated carefully, such students should not have to unlearn anything in their later work.
作者在To The Student中写到,You can obtain a certain superficial knowledge of mathematics by listening to lectures, but you cannot obtain skill this way.所以他在本书中加入大量习题来develop skill。很适合励志成为quant的金融数学专业同学自学!
目录:内容太多,我就只列章目的内容了。
1.Infinite series, power series
2.Complex numbers
3.Linear equations;vectors,matrices,and determinants
4.Partial differentiation
5.Multiple integrals;applications of integration
6.Vector analysis
7.Fourier series
8.Ordinary differential equations
9.Calculus of variations
10.Coordinate transformations;tensor analysis
11.Gamma,Beta,and error functions;asymptotic series;stirling's formula;elliptic integrals and functions
12.Series solutions of differential equations;legendre polynomials;bessel functions;sets of orthogonal functions
13.Partial differential equations
14.Functions of a complex variable
15.Integral transforms
16.Probability