《海外優秀數學類教材系列叢書·托馬斯微積分》一書從Pearson出版公司引進，是一本頗具影響的教材。50多年來，該書平均每4至5年就有一個新版面世，每版較之先前版本都有不少改進之處，體現了這是一部銳意革新的教材；與此同時，該書的一些基本特色始終注意保持且有所增強，說明它又是一部重視繼承傳統的教材。
基本介紹
- 書名：海外優秀數學類教材系列叢書·托馬斯微積分
- 出版社：高等教育出版社
- 出版時間：2004年7月1日
- 版次：第1版
圖書信息,作者簡介,目錄,
圖書信息
外文書名: Thomas' Calculus (10th Edition)
平裝: 606頁
正文語種: 簡體中文, 英語
開本: 16
ISBN: 7040144247
條形碼: 9787040144246
尺寸: 25.2 x 21.4 x 3 cm
重量: 1.1 Kg
作者簡介
作者：（美國）吉爾當諾 編者：（美國）芬尼
目錄
Preliminaries
1 Lines 1
2 Functions and Graphs 1 0
3 Exponential Functions 24
4 Inverse Functions and Logarithms 3 1
5 Trigonometric Functions and Their lnverses 44
6 Parametric Equations 60
7 Modeling Change 67
QUESTIONS TO GUIDE YOUR REVIEW 76
PRACTICE EXERCISES 77
ADDITIONAL EXERCISES：THEORY．EXAMPS．APPUCATIONS 80
1 Limits and Continuity
1．1 Rates of Change and Limi85
1．2 Finding Limiand One-Sided Limits 99
1．3 LimiInvolving Infinity 11 2
1．4 Continuity 123
1．5 Tangent Lines 134
QUESTIONS TO GUIDE YOUR REVIEW 1 41
PRACTICE EXERCISES 1 42
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 1 43
2 DeriVatives
2．1 The Derivative as a Function 147
2．2 The Derivative as a Rate of Change 1 60
2．3 Derivatives of Products．Quotients．and Negative Powers 173
2．4 Derivatives of Trigonometric Functions 1 79
2．5 The Chain Rule and Parametric Equations 1 87
2．6 Implicit Difierentiation 1 98
2．7 Related Rates 207
QUESTIONS TO GUIDE YOUR REVIEW 21 6
PRACTICE EXERCISES 21 7
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPUCATIONS 221
3 Applications of Derivatives
3．1 Extreme Values of Functions 225
3．2 The Mcan Value Theorem and Difierential Equations 237
3．3 The Shape of a Graph 245
3．4 Graphical Solutions of Autonomous Differential Equations 257
3．5 Modeling and Optimization 266
3．6 Linearization and Differentials 283
3．7 Newton’S Method 297
QUESTIONS TO GUIDE YOUR REVIEW 305
PRACTICE EXERCISES 305
ADDITIONAL EXERCISES：THEORY,EXAMPLES．APPLICATIONS 309
4 Integration
4．1 Indefinite Integrals,Differential Equations．and Modeling 3 1 3
4．2 Integral Rules；Integration by Substitution 322
4．3 Estimating with Finite Sums 329
4．4 Ricmann Sums and Definite Integrals 340
4．5 The Mcan Value and FundamentaI Theorems 351
4．6 SubStitution in Definite Integrals 364
4．7 NumericalIntegration 373
QUESTIONS TO GUIDE YOUR REVIEW 384
PRACTICE EXERCISES 385
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 389
5 Applications of Integrals
5．1 Volumes by Slicing and Rotation About an Axis 393
5．2 Modeling Volume Using Cylindrical Shells 406
5．3 Lengths of Plane Curves 41 3
5．4 Springs．Pumping．and Lifting 421
5．5 Fluid Forces 432
5．6 Moments and Centers of Mass 439
QUESTIONS TO GUIDE YOUR REVIEW 451
PRACTICE EXERCISES 45 1
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 454
6 Transcendental Functions and Differential Equations
6．1 Logarithms 457
6．2 Exponential Functions 466
6．3 D——e|rivatives of Inverse Trigonometric Functions；Integrals 477
6．4 First．Order Separable Differential Equations 485
6．5 Linear FirSt．Order Differential Equations 499
6．6 Euler‘S Method；Poplulation Models 507
6．7 Hyperbolic Functions 520
QUESTIONS TO GUIDE YOUR REVIEW 530
PRACTICE EXERCISES 531
ADDmONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 535
7 Integration Techniques，L'H6pital’s Rule,and Improper Integrals
7．1 Basic Integration Formulas 539
7．2 Integration by Parts 546
7．3 Partial Fractions 555
7,4 Trigonometric Substitutions 565
7．5 Integral Tables．Computer Algebra Systems．and
Monte Cario Integration 570
7．6 L'HSpitarS Rule 578
7．7 Improper Integrals 586
QUESTIONS TO GUIDE YOUR REVIEW 600
PRACTICE EXERCISES 601
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 603
8 Infinite Series
8．1 Limis of Sequences of Numbers 608
8．2 Subsequences．Bounded Sequences．and Picard'S Method 61 9
8．3 Infinite Series 627
8．4 Series of Nonnegative Terms 1639
8．5 Alternating Series。Absolute and Conditional Convergence 651
8．6 Power Series 660
8．7 Taylor and Maclaurin Series 669
8．8 Applications of Power Series 683
8．9 Fourier Series 691
8．10 Fourier Cosine and Sine Series 698
QUESTIONS TO GUIDE YOUR REVIEW 707
PRACTICE EXERCISES 708
ADDITIONAL EXERCISES：THEORY,EXAMPS．APPLICATIONS 7 11
9 Vectors in the Plane and Polar Functions
9．1 Vectors in the Plane 71 7
9．2 Dot Products 728
9．3 Vector-Valued Functions 738
9．4 Modeling Projectile Motion 749
9．5 Polar Coordinates and Graphs 761
9．6 Calculus of Polar Curyes 770
QUESTIONS TO GUIDE YOUR REVIEW 780
PRACTICE EXERCISES 780
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPUCATIONS 784
10 Vectors and M0tion in Space
1O．1 Cartesian(Rectangular)Coordinates and Vectors in Space 787
10．2 Dot and Cross Products 796
10．3 Lines and Planes in Space 807
10．4 cylinders and Ouadric SurfaCes 816
10．5 Vector-Valued Functions and Space Curves 825
10．6 Arc Length and the Unit Tangent Vector T 838
10．7 The TNB Frame；Tangential and Normal Components of Acceleration
10．8 Planetary Motion and Satellites 857
QUESTIONS TO GUIDE YOUR REVIEW 866
PRACTICE EXERCISES 867
ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 870
11 Multivariable Functions and 111eir Derivatives
1 1．1 Functions of SeveraI Variables 873
11．2 Limits and Continuity in Higher Dimensions 882
11．3 PartiaI Derivatives 890
11．4 The Chain Rule 902
11．5 DirectionaI Derivatives．Gradient Vectors．and Tangent Planes 91 1
11．6 Linearization and Difierentials 925
11．7 Extreme Values and Saddle Points 936
……
12 Multiple Integrals
13 Integration in Vector Fields
Appendices
