标题：海外优秀数学类教材系列丛书·托马斯微积分
图书信息
出版社: 高等教育出版社; 第1版 (2004年7月1日)
外文书名: Thomas' Calculus (10th Edition)
平装: 606页
正文语种: 简体中文, 英语
开本: 16
ISBN: 7040144247
条形码: 9787040144246
尺寸: 25.2 x 21.4 x 3 cm
重量: 1.1 Kg
作者简介
作者：（美国）吉尔当诺 编者：（美国）芬尼
内容简介
《托马斯微积分》(上)(第10版影印版)从Pearson出版公司引进，是一本颇具影响的教材。50多年来，该书平均每4至5年就有一个新版面世，每版较之先前版本都有不少改进之处，体现了这是一部锐意革新的教材；与此同时，该书的一些基本特色始终注意保持且有所增强，说明它又是一部重视继承传统的教材。
目录
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