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微積分 版權(quán)信息
- ISBN：9787562966531
- 條形碼：9787562966531 ; 978-7-5629-6653-1
- 裝幀：一般膠版紙
- 冊(cè)數(shù)：暫無(wú)
- 重量：暫無(wú)
- 所屬分類：>
微積分 內(nèi)容簡(jiǎn)介
數(shù)學(xué)是自然學(xué)科的基礎(chǔ)，我們幾乎所有的工作都與數(shù)學(xué)相關(guān)，追求科學(xué)的、可持續(xù)發(fā)展的工作目標(biāo)，越來(lái)越多地需要數(shù)學(xué)的描述，需要使用數(shù)學(xué)工具進(jìn)行定量分析。高等數(shù)學(xué)課程因其在培養(yǎng)大學(xué)生理性思維、計(jì)算能力、創(chuàng)新意識(shí)等方面具有不可替代的作用，成為非數(shù)學(xué)專業(yè)開(kāi)設(shè)的一門(mén)重要的公共必修課。高等數(shù)學(xué)不僅是學(xué)好其他專業(yè)課程的前提和保障，也是后續(xù)很多課程的基礎(chǔ)和工具。 本書(shū)按照“工科類本科數(shù)學(xué)基礎(chǔ)課程教學(xué)基本要求”，按照突出數(shù)學(xué)思想和方法、淡化運(yùn)算技巧、強(qiáng)調(diào)實(shí)際應(yīng)用的原則，在經(jīng)典教材的理論框架下編寫(xiě)而成。 本書(shū)的特色主要體現(xiàn)在以下三個(gè)方面： 1. 結(jié)構(gòu)優(yōu)化。適當(dāng)精簡(jiǎn)初等數(shù)學(xué)的內(nèi)容，淡化不定積分的計(jì)算技巧，整合高階微分方程的知識(shí)等等。 2. 結(jié)合原版英文教材的優(yōu)點(diǎn)，敘述清晰完整； 3. 突出數(shù)學(xué)建模的思想和方法。 本書(shū)分上、下兩冊(cè)，全書(shū)由吳傳生教授、王衛(wèi)華教授審核，并提出了寶貴的意見(jiàn)。
微積分 目錄
Chapter 1 Functions and Limits
1.1 Functions
1.1.1 Sets
1.1.2 Intervals and Neighborhood
1.1.3 Function
1.1.4 Properties of Function
1.1.5 Inverse Function
1.1.6 Composite Function
1.1.7 Elementary Functions
Problem Set 1.1
1.2 The Limit of a Function
1.2.1 Intuitive Meaning of Limit
1.2.2 The Precise Definition of a Limit
1.2.3 One-Sided Limits
1.2.4 The Limit at Infinity
1.2.5 The Properties of Limits
Problem Set 1.2
1.3 Limit of a Sequence
Problem Set 1.3
1.4 Infinitesimals and Infinity
1.4.1 Infinitesimal
1.4.2 Infinite Limit
1.4.3 The Relationship between Infinitesimal and Infinite Limit
Problem Set 1.4
1.5 The Limit Theorems
Problem Set 1.5
1.6 Two Remarkable Limits
1.6.1 The Squeeze Theorem
1.6.2 Remarkable Limit □（數(shù)學(xué)公式）
1.6.3 Monotonic Sequence Theorem
1.6.4 Remarkable Limit Limit □（數(shù)學(xué)公式）
Problem Set 1.6
1.7 Comparison of Infinitesimals
Problem Set 1.7
1.8 Continuity
1.8.1 Continuity at a Point
1.8.2 Continuity on an Interval
1.8.3 Discontinuous Points
1.8.4 Operations on Continuous Functions
Problem Set 1.8
1.9 Properties of Continuous Functions on Closed Intervals
Problem Set 1.9
Chapter Exercise 1
Chapter 2 Derivatives and Differentials
2.1 Concept of Derivatives
2.1.1 Two Examples with the Same Theme
2.1.2 Definition of Derivatives
2.1.3 Left-hand Derivatives and Right-hand Derivatives
2.1.4 The Relationship between Differentiability and Continuity
Problem Set 2.1
2.2 Rules of Finding Derivatives
2.2.1 Four Arithmetic Operation Rules of Derivatives
2.2.2 The Derivative Rule for Inverse Functions
2.2.3 The Derivative Rule for Composite Functions
2.2.4 The Summary of Derivative Formulas and Rules
Problem Set 2.2
2.3 Higher-Order Derivatives
Problem Set 2.3
2.4 Implicit Differentiation and Parametric Equations
2.4.1 Implicit Differentiation
2.4.2 Parametric Equations
……
Chapter 3 The Mean Value Theorems and the Applications of Derivatives
Chapter 4 Indefinite Integrals
Chapter 5 Definite Integrals
Chapter 6 Applications of Definite Integral
Chapter 7 Differential Equations
Chapter 8 Space Analytic Geometry
Chapter 9 Derivatives of Multi-variable Functions
Chapter 10 Integrals in Space
Chapter 11 Line Integrals and Surface Integrals
Chapter 12 Infinite Series
1.1 Functions
1.1.1 Sets
1.1.2 Intervals and Neighborhood
1.1.3 Function
1.1.4 Properties of Function
1.1.5 Inverse Function
1.1.6 Composite Function
1.1.7 Elementary Functions
Problem Set 1.1
1.2 The Limit of a Function
1.2.1 Intuitive Meaning of Limit
1.2.2 The Precise Definition of a Limit
1.2.3 One-Sided Limits
1.2.4 The Limit at Infinity
1.2.5 The Properties of Limits
Problem Set 1.2
1.3 Limit of a Sequence
Problem Set 1.3
1.4 Infinitesimals and Infinity
1.4.1 Infinitesimal
1.4.2 Infinite Limit
1.4.3 The Relationship between Infinitesimal and Infinite Limit
Problem Set 1.4
1.5 The Limit Theorems
Problem Set 1.5
1.6 Two Remarkable Limits
1.6.1 The Squeeze Theorem
1.6.2 Remarkable Limit □（數(shù)學(xué)公式）
1.6.3 Monotonic Sequence Theorem
1.6.4 Remarkable Limit Limit □（數(shù)學(xué)公式）
Problem Set 1.6
1.7 Comparison of Infinitesimals
Problem Set 1.7
1.8 Continuity
1.8.1 Continuity at a Point
1.8.2 Continuity on an Interval
1.8.3 Discontinuous Points
1.8.4 Operations on Continuous Functions
Problem Set 1.8
1.9 Properties of Continuous Functions on Closed Intervals
Problem Set 1.9
Chapter Exercise 1
Chapter 2 Derivatives and Differentials
2.1 Concept of Derivatives
2.1.1 Two Examples with the Same Theme
2.1.2 Definition of Derivatives
2.1.3 Left-hand Derivatives and Right-hand Derivatives
2.1.4 The Relationship between Differentiability and Continuity
Problem Set 2.1
2.2 Rules of Finding Derivatives
2.2.1 Four Arithmetic Operation Rules of Derivatives
2.2.2 The Derivative Rule for Inverse Functions
2.2.3 The Derivative Rule for Composite Functions
2.2.4 The Summary of Derivative Formulas and Rules
Problem Set 2.2
2.3 Higher-Order Derivatives
Problem Set 2.3
2.4 Implicit Differentiation and Parametric Equations
2.4.1 Implicit Differentiation
2.4.2 Parametric Equations
……
Chapter 3 The Mean Value Theorems and the Applications of Derivatives
Chapter 4 Indefinite Integrals
Chapter 5 Definite Integrals
Chapter 6 Applications of Definite Integral
Chapter 7 Differential Equations
Chapter 8 Space Analytic Geometry
Chapter 9 Derivatives of Multi-variable Functions
Chapter 10 Integrals in Space
Chapter 11 Line Integrals and Surface Integrals
Chapter 12 Infinite Series
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