Calculus Early Transcendentals (Korea Edition)

James Stewart , Daniel Clegg , Saleem Watson 저자(글)

Cengage · 2022년 02월 21일

책 소개

본서는 “Calculus: Early Transcendentals, 9th Edition(제9판)”의 내용을 한국의 교육과정에 맞춰 필요한 부분만을 엄선, 축약하여 출간한 ‘KOREA EDITION’이다.

이에 따라 원서(Calculus: Early Transcendentals, 9th Edition)에 수록된 내용 중 미분방정식(CHAPTER 9. Differential Equations) 등 일부 Chapter 및 Section(sub-Chapter)은 이번 KOREA EDITION에 수록되어 있지 않았음을 참고하기 바란다. 원서의 내용 중 KOREA EDITION에서 수록이 제외된 내용은 다음과 같다.

CHAPTER 1. Functions and Models
1.1. Four Ways to Represent a Function
1.2. Mathematical Models: A Catalog of Essential Functions
1.3. New Functions from Old Functions
1.4. Exponential Functions

CHAPTER 2. Limits and Derivatives
2.1. The Tangent and Velocity Problems

CHAPTER 3. Differentiation Rules
3.7. Rates of Change in the Natural and Social Sciences
3.8. Exponential Growth and Decay
3.9. Related Rates

CHAPTER 4. Applications of Differentiation
4.5. Summary of Curve Sketching
4.6. Graphing with Calculus and Technology
4.8. Newton's Method

CHAPTER 6. Applications of Integration
6.4. Average Value of Function + Applied Projects

CHAPTER 7. Techniques of Integration
7.5. Strategy for Integration
7.6. Integration Using Tables and Technology + Discovery Project
7.7. Approximate Integration

CHAPTER 8. Further Applications of Integration
8.5. Probability

CHAPTER 9. Differential Equations

CHAPTER 10. Parametric Equations and Polar Coordinates
10.6. Conic Sections in Polar Coordinates

CHAPTER 11. Sequences, Series, and Power Series
11.7. Strategy for Testing Series

CHAPTER 16. Vector Calculus
16.10. Summary

Appendixes
A. Numbers, Inequalties, and Absolute Values
B. Coordinate Geometry and Lines
C. Graphs of Second-Degree Equations
E. Sigma Notation
G. The Logarithm Defined as an Integral

작가정보

저자(글) James Stewart

미국 스탠퍼드대학교에서 석사 학위를 받고 토론토 대학교에서 박사 학위를 받았다. 영국 런던대학교에서 연구했는데 스탠퍼드대학교의 저명한 수학자 조지폴리아의 영향을 받았다. 맥마스터 대학교의 수학과 교수로 재직했으며, 연구 분야는 조화해석학이었다. 그는 센게이지러닝을 통해 『PRECALCULUS』 , 『CALCULUS』 , 『CALCULUS : EARLY TRANSCENDENTALS』 , 『CALCULUS : CONCEPTS AND CONTEXTS』 등 다양한 미적분학 교재를 출간한 베스트셀러 저자이다.

저자(글) Daniel Clegg

저자(글) Saleem Watson

목차

• Preface x
  A Tribute to James Stewart xxii
  About the Authors xxiii
  Technology in the Ninth Edition xxiv
  To the Student xxv
  Diagnostic Tests xxvi
  
  A Preview of Calculus
  
  1. Functions and Models
  1.1 Inverse Functions and Logarithms 8
  
  2. Limits and Derivatives
  2.1 The Limit of a Function 32
  2.2 Calculating Limits Using the Limit Laws 44
  2.3 The Precise Definition of a Limit 54
  2.4 Continuity 64
  2.5 Limits at Infinity; Horizontal Asymptotes 76
  2.6 Derivatives and Rates of Change 89
  2.7 The Derivative as a Function 102
  
  3. Differentiation Rules
  3.1 Derivatives of Polynomials and Exponential Functions 124
  3.2 The Product and Quotient Rules 135
  3.3 Derivatives of Trigonometric Functions 141
  3.4 The Chain Rule 149
  3.5 Implicit Differentiation 159
  3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions 167
  3.7 Linear Approximations and Differentials 175
  3.8 Hyperbolic Functions 183
  
  4. Applications of Differentiation
  4.1 Maximum and Minimum Values 202
  4.2 The Mean Value Theorem 212
  4.3 What Derivatives Tell Us about the Shape of a Graph 218
  4.4 Indeterminate Forms and I’Hospital‘s Rule 231
  4.5 Optimization Problems 242
  4.6 Antiderivatives 257
  
  5. Integrals
  5.1 The Area and Distance Problems 274
  5.2 The Definite Integral 286
  5.3 The Fundamental Theorem of Calculus 301
  5.4 Indefinite Integrals and the Net Change Theorem 3 11
  5.5 The Substitution Rule 321
  
  6. Applications of Integration
  6.1 Areas Between Curves 338
  6.2 Volumes 348
  6.3 Volumes by Cylindrical Shells 362
  6.4 Average Value of a Function 369
  
  7. Techniques of Integration
  7.1 Integration by Parts 382
  7.2 Trigonometric Integrals 389
  7.3 Trigonometric Substitution 396
  7.4 Integration of Rational Functions by Partial Fractions 403
  7.5 Improper Integrals 413
  
  8. Further Applications of Integration
  8.1 Arc Length 430
  8.2 Area of a Surface of Revolution 437
  8.3 Applications to Physics and Engineering 446
  8.4 Applications to Economics and Biology 457
  
  9. Parametric Equations and Polar Coordinates
  9.1 Curves Defined by Parametric Equations 468
  9.2 Calculus with Parametric Curves 479
  9.3 Polar Coordinates 490
  9.4 Calculus in Polar Coordinates 500
  9.5 Conic Sections 508
  
  10. Sequences, Series, and Power Series
  10.1 Sequences 524
  10.2 Series 538
  10.3 The Integral Test and Estimates of Sums 551
  10.4 The Comparison Tests 560
  10.5 Alternating Series and Absolute Convergence 565
  10.6 The Ratio and Root Tests 576
  10.7 Power Series 579
  10.8 Representations of Functions as Power Series 584
  10.9 Taylor and Maclaurin Series 593
  10.10 Applications of Taylor Polynomials 610
  
  11. Vectors and the Geometry of Space
  11.1 Three-Dimensional Coordinate Systems 628
  11.2 Vectors 634
  11.3 The Dot Product 645
  11.4 The Cross Product 653
  11.5 Equations of Lines and Planes 662
  11.6 Cylinders and Quadric Surfaces 673
  
  12. Vector Functions
  12.1 Vector Functions and Space Curves 688
  12.2 Derivatives and Integrals of Vector Functions 696
  12.3 Arc Length and Curvature 702
  12.4 Motion in Space: Velocity and Acceleration 714
  
  13. Partial Derivatives
  13.1 Functions of Several Variables 732
  13.2 Limits and Continuity 749
  13.3 Partial Derivatives 759
  13.4 Tangent Planes and Linear Approximations 772
  13.5 The Chain Rule 783
  13.6 Directional Derivatives and the Gradient Vector 792
  13.7 Maximum and Minimum Values 806
  13.8 Lagrange Multipliers 818
  
  14. Multiple Integrals
  14.1 Double Integrals over Rectangles 836
  14.2 Double Integrals over General Regions 849
  14.3 Double Integrals in Polar Coordinates 860
  14.4 Applications of Double Integrals 867
  14.5 Surface Area 877
  14.6 Triple Integrals 880
  14.7 Triple Integrals in Cylindrical Coordinates 893
  14.8 Triple Integrals in Spherical Coordinates 900
  14.9 Change of Variables in Multiple Integrals 907
  
  15. Vector Calculus
  15.1 Vector Fields 922
  15.2 Line Integrals 929
  15.3 The Fundamental Theorem for Line Integrals 942
  15.4 Green’s Theorem 952
  15.5 Curl and Divergence 959
  15.6 Parametric Surfaces and Their Areas 968
  15.7 Surface Integrals 980
  15.8 Stokes' Theorem 993
  15.9 The Divergence Theorem 999
  
  Appendixes
  A Trigonometry A2
  B Proofs of Theorems A14
  C Answers to Odd-Numbered Exercises A26
  
  Index A87

기본정보

ISBN	9788962185300 ( 896218530X )
발행(출시)일자	2022년 02월 21일
쪽수	1116쪽
크기	216 * 253 * 43 mm / 2269 g
총권수	1권
언어	영어

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