Fundamental Ideas of Analysis
暫譯: 分析的基本概念

Michael Reed

Fundamental Ideas of Analysis

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商品描述

The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that results are true and provides techniques to estimate the errors in approximate calculations. The ideas and methods of analysis play a fundamental role in ordinary differential equations, probability theory, differential geometry, numerical analysis, complex analysis, partial differential equations, as well as in most areas of applied mathematics.

Table of Contents

Preliminaries.

Sequences.

The Riemann Integral.

Differentiation.

Sequences of Functions.

Series of Functions.

Differential Equations.

Complex Analysis.

Fourier Series.

Probability Theory.

Bibliography.

Indexes.

商品描述(中文翻譯)

數學的思想和方法，長期以來一直是物理科學的核心，現在在各種學科中扮演著越來越重要的角色。分析提供了證明結果真實性的定理，並提供了估算近似計算誤差的技術。分析的思想和方法在常微分方程、機率論、微分幾何、數值分析、複變分析、偏微分方程以及大多數應用數學領域中都扮演著基本角色。

目錄

前言

數列

黎曼積分

微分

函數序列

函數級數

微分方程

複變分析

傅立葉級數

機率論

參考文獻

索引

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