主要介紹一元函數的極限(limit)、導數(derivative)、積分(integral)、微分方程(differential equations)和線性算子(linear operator)的基本概念和理論,並給出與這些概念相關的自主招生考試試題的解析與提高練習。
《一元函數微積分與線性算子》由淺入深,並兼顧高中生參加大學自主招生內容研討,編寫方法上結合雙語課程的特點,探索如何組織雙語教材。
《一元函數微積分與線性算子》可供准備參加自主招生考試的高中生、高中教師、大學數學和相關專業方向的大學生以及從事雙語課程學習與教學的高校教師閱讀和參考。
前言
Chapter 1極限(Limits)
1.1極限概念(The Notion of Limits)
1.2極限的性質與運算(Properties and Rules of Limits)
1.3極限的存在性(Existence of Limits)
1.4函數的連續性(Continuity of Functions)
1.5應用(Applications)
1.6習題(Exercises)
Chapter 2導數(Derivatives)
2.1導數概念(The Notion of Derivatives)
2.2求導法則(Rules for Finding Derivatives)
2.3泰勒公式(Taylor』s Formula)
2.4微分中值定理(The Mean Value Theorems for Derivatives)
2.5應用(Applications)
2.6習題(Exercises)
Chapter 3積分(Integrals)
3.1不定積分概念(The Notion of Indefinite Integrals)
3.2求不定積分法則(Rules for Finding Indefinite Integrals)
3.3微積分基本定理(The Eundamental Theorems of Calculus)
3.4求定積分法則(Rules for Finding Definite Integrals)
3.5應用(Applications)
3.6習題(Exercises)
Chapter 4微分方程(Differential Equations)
4.1微分方程概念(The Notion of Differential Equations)
4.2可分離變量的微分方程(Separable Differential Equations)
4.3可降階的高階微分方程(Higher Order Differential Equations Turned to Lower Order Differential Equations)
4.4線性微分方程解的結構(The Structure of the Solutions of the Linear Differential Equations)
4.5習題(Exercises)
Chapter 5線性算子(Linear Operators)
5.1基本概念與性質(The Notions and Properties)
5.2連續算子(Continuous Operators)
5.3應用(Applications)
參考文獻