具體描述
基本信息
書名:單變量微積分
定價：80.00元
售價：60.0元,便宜20.0元,摺扣75
作者:鄒雲誌
齣版社：世界圖書齣版公司
齣版日期：2015-05-01
ISBN：9787510094903
字數：
頁碼：350
版次：1
裝幀：平裝
開本：16開
商品重量：0.4kg
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內容提要
Irecently years, more and more Chinese students are going overseas, either as exchange students, or to pursue degrees. At the same time, more and more students are ing from other countries to Chinese universities to further their studies. We've noticed that iterms of both knowledge transfer and intercultural munication, the English language has played aindispensable role. Furthermore, it is the interest of these students to have a smooth transitiofrom one system to another, for their credits to transfer, and for them to immerse themselves ithe new environment as quickly as possible. To this end, more and more Chinese schools are offering courses delivered bilingually or iEnglish to enhance students' international outlook.
One of the greatest challenges ioffering Chinese students a course iEnglish is finding a suitable textbook: the textbook must seriously consider what students have done itheir high schools; it must meet the national and local official course standards; and it should resonate with significant international flavors so as to benefit students.
目錄
CHAPTER 1 Prereqrusites for Calculus
1.1 Overview ofCalculus
1.2 Sets and Numbers
1.2.1 Sets
1.2.2 Numbers
1.2.3 The Least Upper Bound Property
1.2.4 The Extended Real Number System
1.2.5 1ntervals
1.3 Functions
1.3.1 Definitioofa Function
1.3.2 Graph ofa Function
1.3.3 Some Basic Functions and Their Graphs
1.3.4 Building New Functions
1.3.5 Fundamental Elementary Functions
1.3.6 Properties ofFunctions
1.4 Exercises
CHAPTER 2 Limits and Continruty
2.1 Rates ofChange and Derivatives
2.2 Limits of a Function
2.2.1 Definitioof a Limit
2.2.2 Properties of Limits of Functions
2.2.3 Limit Laws
2.2.4 One-sided Liruits
2.2.5 Limits Involving Infinity and Asymptotes
2.3 Limits of Sequences
2.3.1 Definitions and Properties
2.3.2 Subsequences
2.4 Squeeze Theorem and Cauchy's Theorem
2.5 Infinitesimal Functions and Asymptotic Functions
2.6 Continuous and Discontinuous Functions
2.6.1 Continuity and Discontinuity
2.6.2 Continuous Functions
2.6.3 Theorems oContinuous Functions
2.6.4 Uniform Continuity
2.7 Some Proofs iChapter
2.8 Exercises
CHAPTER 3 I'he Derivative
3.1 Derivative ofa Functioat a Point
3.1.1 Instantaneous Rates of Change and Derivatives Revisited
3.1.2 One-sided Derivatives
3.1.3 A FunctioMay Fail to Have a Derivative at a Point
3.2 Derivative as a Function
3.2.1 Graphing the Derivative of a Function
3.2.2 Derivatives of Some Basic Functions
3 .3 Derivative Laws
3.4 Derivative of aJnverse Function
3.5 Differentiating a Composite Functio- The ChaiRule
3.6 Derivatives ofHigher Orders
3.7 Implicit Differentiation
3.8 Functions Defined by Parametric and Polar Equations
3.8.1 Functions Defined by Parametric Equations
3.8.2 Polar Curves
3.9 Related Rates ofChange
3.10 The Tangent Line Approximatioand the Differentia
3.10.1 Linearization
3.10.2 Differentials
3.11 Derivative Rules-Summary
3.12 Exercises
CHAPTER 4 Applications of the Derivative
4.1 Extreme Values and The Candidate Theorem
4.2 The MeaValue Theore
4.3 Monotonic Functions and The First Derivative Test
4.3.1 Monotonic Functions
4.3.2 The First Derivative Test
4.4 Extended MeaValue Theorem and the L'Hopital's Rules
4.4.1 Extended MeaValue Theorem
……
CHAPTER 5 The Definite Integral
CHAPTER 6 Techniques for Integratioand Improper Integrals
CHAPTER 7 Applications of the Definite Integral
CHAPTER 8 Infinite Series, Sequences, and Approximations
作者介紹
文摘
序言
CHAPTER 1 Prereqrusites for Calculus
1.1 Overview ofCalculus
1.2 Sets and Numbers
1.2.1 Sets
1.2.2 Numbers
1.2.3 The Least Upper Bound Property
1.2.4 The Extended Real Number System
1.2.5 1ntervals
1.3 Functions
1.3.1 Definitioofa Function
1.3.2 Graph ofa Function
1.3.3 Some Basic Functions and Their Graphs
1.3.4 Building New Functions
1.3.5 Fundamental Elementary Functions
1.3.6 Properties ofFunctions
1.4 Exercises
CHAPTER 2 Limits and Continruty
2.1 Rates ofChange and Derivatives
2.2 Limits of a Function
2.2.1 Definitioof a Limit
2.2.2 Properties of Limits of Functions
2.2.3 Limit Laws
2.2.4 One-sided Liruits
2.2.5 Limits Involving Infinity and Asymptotes
2.3 Limits of Sequences
2.3.1 Definitions and Properties
2.3.2 Subsequences
2.4 Squeeze Theorem and Cauchy's Theorem
2.5 Infinitesimal Functions and Asymptotic Functions
2.6 Continuous and Discontinuous Functions
2.6.1 Continuity and Discontinuity
2.6.2 Continuous Functions
2.6.3 Theorems oContinuous Functions
2.6.4 Uniform Continuity
2.7 Some Proofs iChapter
2.8 Exercises
CHAPTER 3 I'he Derivative
3.1 Derivative ofa Functioat a Point
3.1.1 Instantaneous Rates of Change and Derivatives Revisited
3.1.2 One-sided Derivatives
3.1.3 A FunctioMay Fail to Have a Derivative at a Point
3.2 Derivative as a Function
3.2.1 Graphing the Derivative of a Function
3.2.2 Derivatives of Some Basic Functions
3 .3 Derivative Laws
3.4 Derivative of aJnverse Function
3.5 Differentiating a Composite Functio- The ChaiRule
3.6 Derivatives ofHigher Orders
3.7 Implicit Differentiation
3.8 Functions Defined by Parametric and Polar Equations
3.8.1 Functions Defined by Parametric Equations
3.8.2 Polar Curves
3.9 Related Rates ofChange
3.10 The Tangent Line Approximatioand the Differentia
3.10.1 Linearization
3.10.2 Differentials
3.11 Derivative Rules-Summary
3.12 Exercises
CHAPTER 4 Applications of the Derivative
4.1 Extreme Values and The Candidate Theorem
4.2 The MeaValue Theore
4.3 Monotonic Functions and The First Derivative Test
4.3.1 Monotonic Functions
4.3.2 The First Derivative Test
4.4 Extended MeaValue Theorem and the L'Hopital's Rules
4.4.1 Extended MeaValue Theorem
……
CHAPTER 5 The Definite Integral
CHAPTER 6 Techniques for Integratioand Improper Integrals
CHAPTER 7 Applications of the Definite Integral
CHAPTER 8 Infinite Series, Sequences, and Approximations
用戶評價
這本書的裝幀設計簡直是藝術品，那種沉甸甸的質感，封麵選用的啞光紙張，觸摸起來細膩又高級，讓人愛不釋手。內頁的排版也看得齣是用心瞭，字體選擇的襯綫體，閱讀起來非常舒適，長篇的公式推導也不會讓人感到視覺疲勞。不過，我得說，第一遍翻閱時，我幾乎被那些密密麻麻的符號陣仗給‘震懾’住瞭。它不像我以前看過的那些入門教材那樣，上來就用大量的日常例子來‘軟化’讀者。這本書是直接亮劍，毫不客氣地把最核心、最抽象的概念就擺在你麵前。比如，介紹極限的時候，那種嚴謹的$epsilon-delta$定義，讀起來簡直像在啃一塊堅硬的花崗岩，需要反復咀嚼纔能體會到其中蘊含的數學美感。我花瞭很長時間纔適應這種‘高冷’的敘事風格，但一旦跨過那道門檻，你會發現，這種開門見山的直擊本質，反而建立瞭一種極其紮實的數學直覺。它不屑於用太多拐彎抹角的比喻，而是用最精煉的語言，構建起一個邏輯自洽的體係。對於那些追求深度和純粹性的讀者來說，這無疑是一本寶藏，但對於初學者，可能需要一個非常耐心的引導者陪伴。
評分這本書的‘跨界’參考價值也是一個亮點，它在某些章節的討論中，會不自覺地引入一些其他學科的術語和概念，使得讀者能夠跳齣純數學的象牙塔，看到微積分在現實世界中的巨大影響力。例如，在涉及級數收斂性的討論中，作者巧妙地引用瞭物理學中關於量子態疊加的某些思想來輔助理解，雖然沒有深入展開，但這種‘點到為止’的暗示，極大地激發瞭我的好奇心，促使我主動去查閱相關的交叉學科資料。在我看來，一本好的教材，不應該隻是一門學科的聖經，更應該是一座橋梁，連接著不同的知識領域。這本書在這方麵做得非常齣色，它讓你在學習如何求導、如何積分的同時，也在潛移默化地拓寬你的知識邊界。它就像一個經驗豐富的老者，在教你基礎技藝的同時，不斷嚮你描繪更廣闊的江湖風光，讓人心馳神往，迫不及待想去探索。
評分這本書的習題設計是其精髓，也是我個人感覺最‘摺磨人’但也最有收獲的部分。它沒有采用那種‘一題多變’的重復訓練模式，而是更側重於‘一題多解’和‘概念應用深度’的考察。我做完第三章後麵那些關於麯綫麯率和弧長計算的題目後，感覺自己對空間想象力的要求達到瞭一個新的高度。很多題目都不是直接套用公式就能解決的，它要求你必須先在腦海中構建一個清晰的物理模型或者幾何場景，然後將微積分工具恰當地‘嵌入’進去。更妙的是，在書的末尾，它附帶瞭一個非常精簡的‘解題思路提示’部分，但這個提示往往隻給齣一個方嚮性的引導，而不是具體的步驟，這極大地鍛煉瞭我們獨立解決問題的能力。我有一個習慣，就是把那些花瞭我超過一小時纔解齣來的題目，標記齣來，然後過一段時間再重新做一遍，每一次重做，似乎都能發現新的角度和更優雅的解法。這套習題集，是真正意義上的‘試金石’。
評分我必須承認，這本書在定理的證明環節展現齣的深度和廣度，遠超我預期的任何一本微積分教材。它沒有將證明過程‘降維打擊’成幾個簡單的步驟，而是將每一步邏輯的跳躍都進行瞭詳盡的、近乎於‘吹毛求疵’的論證。特彆是關於反導數的存在性以及中值定理的推導部分，作者似乎特意花瞭大量的篇幅去探討那些在普通教材中常常被‘一筆帶過’的邊界情況和特殊條件。我記得有一個關於泰勒級數餘項錶達式的討論，它詳細對比瞭四種不同餘項形式的適用場景和收斂速度的差異，這簡直是為那些準備考研或者打算深入研究數學分析的同學量身定做的‘秘籍’。我甚至懷疑作者是不是偷偷地在嚮更高階的分析學課程‘輸送’知識點。唯一讓我感到略微頭疼的是，一些高級的證明過程需要讀者對集閤論和拓撲學的基礎概念有非常清晰的認識，否則，當你看到諸如‘緊緻集’或者‘完備性’這類詞匯在證明中自然齣現時，會有一種掉隊的感覺。它要求你不僅要知道‘怎麼做’，更要知道‘為什麼能這麼做’。
評分從教學法革新的角度來看，這本書的敘事結構非常獨特，它似乎顛覆瞭傳統的‘定義-定理-例題’的綫性流程。作者更傾嚮於以‘問題驅動’的方式展開章節內容。比如，在講解定積分與不定積分的關係時，它不是先給齣微積分基本定理，而是先提齣一個‘如何計算不規則形狀的麵積’的古老難題，然後層層剝筍地引入黎曼和、上積分、下積分的概念，最終纔水到渠成地引齣那個偉大的定理。這種‘曆史重演’式的教學方法，雖然在初次閱讀時會顯得有點慢熱，但它極大地增強瞭知識的‘源頭活水’感，讓你真切地感受到數學是如何一步步發展和完善起來的。這種敘事策略，讓那些原本可能枯燥的理論推導，瞬間充滿瞭曆史的厚重感和探索的激動。它培養的不是一個公式的搬運工，而是一個數學思想的追隨者。
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