Single Variable Calculus: Early Transcendentals (International Metric Edition) 英文原版 [精裝] pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

James Stewart 著

圖書標籤:

• 微積分
• 單變量微積分
• 高等數學
• 國際版
• 英文原版
• 精裝
• 數學
• 理工科
• 大學教材
• 微積分教材

齣版社： Cengage Learning

ISBN：9780538498883

版次：7

商品編碼：19172452

包裝：精裝

齣版時間：2011-01-01

頁數：936

正文語種：英文

商品尺寸：26.2x22.3x3.4cm;1.789kg

內容簡介

James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are widely renowned for their mathematical precision and accuracy, clarity of exposition, and outstanding examples and problem sets. Millions of students worldwide have explored calculus through Stewart's trademark style, while instructors have turned to his approach time and time again. In the Seventh Edition of SINGLE VARIABLE CALCULUS: EARLY TRANSCENDENTALS, Stewart continues to set the standard for the course while adding carefully revised content. The patient explanations, superb exercises, focus on problem solving, and carefully graded problem sets that have made Stewart's texts best-sellers continue to provide a strong foundation for the Seventh Edition. From the most unprepared student to the most mathematically gifted, Stewart's writing and presentation serve to enhance understanding and build confidence.
CourseSmart goes beyond traditional expectations–providing instant, online access to the textbooks and course materials you need and at a lower cost to your students. To request an electronic sample of this Cengage Learning title, go to: www.coursesmart.com/instructors.

目錄

Diagnostic Tests.
A Preview of Calculus.
1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving.

2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus.

3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus.

4. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and L'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Newton's Method. Antiderivatives. Review. Problems Plus.

5. INTEGRALS.
Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus.

6. APPLICATIONS OF INTEGRATION.
Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Where to Sit at the Movies. Review. Problems Plus.

7. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus.

8. FURTHER APPLICATIONS OF INTEGRATION.
Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus.

9. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Applied Project: Calculus and Baseball. Linear Equations. Predator-Prey Systems. Review. Problems Plus.

10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.
Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bezier Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus.

11. INFINITE SEQUENCES AND SERIES.
Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the . Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus.

APPENDIXES.
A. Numbers, Inequalities, and Absolute Values.
B. Coordinate Geometry and Lines.
C. Graphs of Second-Degree Equations.
D. Trigonometry.
E. Sigma Notation.
F. Proofs of Theorems.
G. The Logarithm Defined as an Integral.
H. Complex Numbers.
I. Answers to Odd-Numbered Exercises.

精彩書摘

Diagnostic Tests. A Preview of Calculus. 1. FUNCTIONS AND MODELS. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Review. Principles of Problem Solving. 2. LIMITS AND DERIVATIVES. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Problems Plus. 3. DIFFERENTIATION RULES. Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions. Review. Problems Plus. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and L'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Newton's Method. Antiderivatives. Review. Problems Plus. 5. INTEGRALS. Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus. 6. APPLICATIONS OF INTEGRATION. Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Where to Sit at the Movies. Review. Problems Plus. 7. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Problems Plus. 8. FURTHER APPLICATIONS OF INTEGRATION. Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Problems Plus. 9. DIFFERENTIAL EQUATIONS. Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Applied Project: Calculus and Baseball. Linear Equations. Predator-Prey Systems. Review. Problems Plus. 10. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bezier Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. Problems Plus. 11. INFINITE SEQUENCES AND SERIES. Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the . Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus. APPENDIXES. A. Numbers, Inequalities, and Absolute Values. B. Coordinate Geometry and Lines. C. Graphs of Second-Degree Equations. D. Trigonometry. E. Sigma Notation. F. Proofs of Theorems. G. The Logarithm Defined as an Integral. H. Complex Numbers. I. Answers to Odd-Numbered Exercises.,

前言/序言

深入微積分的基石：探索極限、導數與積分的奧秘 《多變量微積分導論：早期超越函數（國際公製版）》 是一本專為全球數學、工程學和科學領域的學生精心打造的權威教材。它以嚴謹的邏輯結構、清晰的教學方法，引導讀者係統地掌握多變量微積分的核心概念、技術和應用。本書建立在堅實的單變量微積分基礎之上，將微積分的強大工具擴展到三維及更高維度的空間，為理解復雜係統的建模和分析奠定瞭不可或缺的理論框架。 本書的核心目標是培養學生對空間幾何直覺的深刻理解，並熟練運用嚮量運算、偏導數、多重積分以及嚮量場理論來解決實際問題。全書內容編排匠心獨運，力求在概念的深度與計算的實用性之間取得完美的平衡。 第一部分：嚮量與空間幾何的基石 教材伊始，我們首先將焦點從二維平麵擴展到三維空間。嚮量代數是理解多變量微積分的語言。本部分詳盡闡述瞭三維笛卡爾坐標係、嚮量的錶示法、加法、標量乘法以及至關重要的點積（內積） 和叉積（外積）。通過對點積與角度、投影關係的深入探討，讀者能夠直觀地理解嚮量在物理學和幾何學中的作用。叉積則被係統地引入，用於計算平行四邊形或三角形的麵積，並確定垂直於平麵的法嚮量——這是後續麯麵分析的基礎。 隨後，章節轉嚮空間麯綫和麯麵的描述。參數方程在描述三維運動軌跡方麵的優勢被充分挖掘。我們詳細分析瞭麯綫的切綫嚮量、法嚮量、麯率等幾何量。對於麯麵的研究，我們引入瞭二次麯麵（如球麵、橢球麵、拋物麵、雙麯麵等）的分類和標準方程，使讀者能夠熟練地在幾何直覺和代數錶示之間進行轉換。 第二部分：偏導數的威力與梯度場 當函數依賴於多個變量時，我們如何衡量其變化率？偏導數應運而生。本部分是多變量微積分的第一個關鍵飛躍。我們定義瞭偏導數，並探討瞭它們如何描述函數沿著特定方嚮的變化。 對偏導數的深入理解自然引嚮可微性的概念，並在此基礎上推導齣至關重要的鏈式法則（Chain Rule）在多變量環境下的擴展形式。通過大量的實例，讀者將掌握如何處理復閤函數鏈條中的復雜依賴關係。 梯度（Gradient）是衡量函數最大增長率和方嚮的矢量工具。本書詳細解釋瞭梯度嚮量場的性質，以及它與等值麵（Level Surfaces）的垂直關係。接著，我們引入瞭方嚮導數（Directional Derivative），它將偏導數的概念推廣到任意指定方嚮，是連接幾何與分析的橋梁。 本部分的高潮在於極值理論。通過應用偏導數，我們學習如何尋找多元函數的局部最大值和最小值。這包括對駐點（Critical Points）的識彆，並運用二階偏導數檢驗（Hessian 矩陣） 來區分鞍點、局部極大值和局部極小值。此外，拉格朗日乘數法（Lagrange Multipliers） 作為一種強大的約束優化技術，被係統地介紹，它在經濟學、物理學約束優化問題中具有不可替代的價值。 第三部分：多重積分——體積與質量的計算 將單變量積分的概念擴展到二維和三維區域，是計算纍積量的關鍵。本部分專注於二重積分和三重積分。 對於二重積分，我們從黎曼和的定義齣發，精確地解釋瞭它如何用來計算平麵區域上的體積。我們詳細分析瞭直角坐標係下積分區域的描述與積分次序的互換（Fubini's Theorem）。為瞭應對更復雜的幾何形狀，本書投入瞭大量篇幅介紹極坐標係（Polar Coordinates） 及其雅可比行列式，極大地簡化瞭涉及圓形或扇形區域的積分計算。 進入三維空間，三重積分成為計算實體體積、密度函數下的總質量、質心和轉動慣量的核心工具。同樣，我們引入瞭柱坐標係（Cylindrical Coordinates） 和球坐標係（Spherical Coordinates），展示瞭這些坐標變換如何根據問題的幾何對稱性，將原本繁復的積分轉化為易於求解的形式。 第四部分：嚮量微積分與場論 本部分是多變量微積分中最精妙也最具挑戰性的部分，它連接瞭矢量分析與微分方程的基礎。 我們首先定義瞭嚮量場（Vector Fields），如流體力學中的速度場或電磁場，並介紹瞭嚮量場上的綫積分。綫積分不僅用於計算粒子在力場中移動所做的功，也是理解流量（Flux）的先導概念。 接著，我們深入探討瞭保守場的概念，以及判斷一個嚮量場是否保守的關鍵工具——鏇度（Curl）。鏇度的幾何意義在於衡量嚮量場在某點鏇轉的趨勢。 本部分的核心理論是格林公式（Green's Theorem），它建立瞭平麵區域上雙重積分與該區域邊界上的綫積分之間的深刻聯係。 在進入三維空間後，我們推廣瞭格林公式，引齣瞭微積分的“終極”定理：斯托剋斯定理（Stokes' Theorem） 和散度定理（Divergence Theorem，也稱高斯定理）。 斯托剋斯定理將麯麵上鏇度的麵積分與該麯麵邊界上的綫積分聯係起來，是經典物理學中處理鏇轉流體的強大工具。 散度定理則建立瞭穿過閉閤麯麵的通量（Flux）與麯麵內部散度（Divergence）的三重積分之間的關係，是理解流體源匯問題的基礎。 教材特色與教學優勢 本書的國際公製版本確保瞭所有示例和練習都采用國際單位製（SI units），更貼閤全球工程和科學教育的實踐需求。全書的講解風格注重直觀性和幾何解釋，確保讀者不僅學會“如何做”，更能理解“為什麼”這樣做。 豐富且精心設計的習題貫穿始終，從基礎的代數操作到復雜的應用問題，為鞏固和檢驗學習成果提供瞭充足的資源。關鍵概念配有詳細的圖形和圖示，幫助學生可視化抽象的四維和多維概念。通過對這些核心概念的係統學習，讀者將為後續的微分方程、高等物理、流體力學和復雜係統建模課程打下堅實、無可動搖的數學基礎。 本書承諾提供一個全麵、嚴謹且富有啓發性的多變量微積分學習體驗。

評分☆☆☆☆☆

我是在一個時間非常緊張的學期末接觸到這本書的，當時需要快速掌握多變量微積分的基礎，而這本書的章節組織邏輯對我來說簡直是迷宮。它似乎有一種魔力，總能把最關鍵的定理和最需要的例題分隔得非常遙遠。比如，當你剛學完一個抽象的嚮量場概念，緊接著齣現的習題卻要求你用一個半小時前纔草草帶過的錶麵積分技巧去解一個看起來無比復雜的實際問題。這種脫節感讓我感覺自己像在學一門“孤立知識點”的集閤，而不是一門連貫的數學學科。我不得不頻繁地跳躍式閱讀，前後翻閱幾十頁纔能把一個概念的來龍去脈串起來，這無疑極大地拖慢瞭我的學習進度，尤其是在期末復習階段，效率低下帶來的焦慮感是難以言喻的。

評分☆☆☆☆☆

這本書的國際公製版本，說實話，在某些理論解釋上顯得有些過於“保守”或“剋製”瞭。它似乎更側重於形式化的推導和嚴格的證明，而在直觀的幾何意義或實際應用場景的闡述上略顯不足。舉個例子，當它介紹拉格朗日乘數法時，重點完全放在瞭梯度嚮量的共綫性證明上，但對於“沿著約束麯麵尋找極值點”這種幾何直覺的描述，卻是寥寥數語帶過。我發現，我不得不去翻閱其他更側重於工程應用的教材或在綫資源，來彌補這種在“理解其為何如此”上的空缺。一本好的微積分教材，理應在嚴謹性與直觀性之間找到完美的平衡點，但這本書顯然更偏嚮於前者，使得那些希望將數學知識應用於物理或工程領域的讀者，會感到理論和實踐之間存在一道鴻溝。

評分☆☆☆☆☆

這本書的國際度量衡版本在定價上顯得極其不閤理。考慮到其印刷質量的粗糙程度，以及其內容在某些關鍵概念解釋上的不足，它所要求的價格實在高得離譜。我清楚地知道齣版行業的成本構成，但麵對一本在國際市場上流通，且在許多大學課程中被強製要求購買的教材，其性價比之低，令人咋舌。每一次翻開它，我總會想到那些為瞭湊齊教材費而省吃儉用的同學。更諷刺的是，這本書的許多核心內容，在許多更新的、排版更精良的替代品中都能找到，而且價格可能隻是其三分之一。這種定價策略，讓學習過程本身就充滿壓力的學生群體，又增添瞭一份不必要的經濟負擔，這對於一本旨在普及高等數學知識的工具書來說，實在是一種商業上的不負責任。

評分☆☆☆☆☆

這本教材的排版和印刷質量簡直是一場災難，紙張薄得像蟬翼，油墨總是洇開，尤其是那些復雜的積分符號和希臘字母，看得人頭疼欲裂。我記得有一次嘗試在圖書館裏對著強光看那些微分方程的推導過程，結果眼花瞭，硬是沒看清一個公式的上下標。更彆提它的國際公製版本，有些單位的標注方式和我在課堂上習慣的完全不同，讓人在做習題時總要多花幾秒鍾去適應這種“國際化”的錶達。說實話，作為一個需要反復查閱和做筆記的學習者來說，這種低劣的物理實體體驗，極大地削弱瞭學習微積分本身的挑戰性。我真希望齣版商能在這方麵多投入一點成本，畢竟這是一本核心的數學參考書，不該如此敷衍瞭事。我的書架上放著一堆高階物理和工程學的書，它們的印刷質量都遠超此書，讓人不禁懷疑這本被寄予厚望的微積分教材，到底經曆瞭怎樣的成本控製環節纔以這種麵貌示人。

評分☆☆☆☆☆

這本書的習題設計實在過於“精英化”瞭，充滿瞭各種反直覺和需要靈光一現纔能解決的怪題。我理解數學學習需要挑戰，但挑戰和摺磨之間隻有一綫之隔。很多基礎練習題的步驟跳躍得非常快，仿佛作者默認讀者已經對每一步中間的代數操作瞭如指掌，完全沒有提供足夠的“腳手架”。我記得有一道關於泰勒展開式的題目，解答過程直接從一個復雜的函數形式跳躍到瞭一個簡化的連分式，中間缺失瞭至少五六步關鍵的因式分解和配方，我花瞭整整一個下午去逆嚮推導，纔勉強還原齣完整的路徑。對於那些初次接觸微積分，或者數學基礎相對薄弱的同學來說，這本書帶來的挫敗感可能會遠大於啓發。它更像是為已經掌握瞭紮實預備知識的“學霸”準備的“挑戰手冊”，而不是一本普適性的入門教材。