海外优秀数学类教材系列丛书·托马斯微积分（上）（第10版）（影印版）（附光盘1张）

《托马斯微积分》（上）（第10版影印版）与我国现行通用高等数学教材相比，其基本内容和结构框架有着许多近似之处，但在题材选取和处理上又有更多不同特色，尤其是，突出应用和数学建模，重视数值计算和程序应用。在适时引进现代数学和新学科知识等方面，更有不少精彩之处。

《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。

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，LH6pital’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 LHSpitarS 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 PicardS 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

在我国已经加入WTO、经济全球化的今天，为适应当前我国高校各类创新人才培养的需要，大力推进教育部倡导的双语教学，配合教育部实施的“高等学校教学质量与教学改革工程”和“精品课程”建设的需要，高等教育出版社有计划、大规模地开展了海外优秀数学类系列教材的引进工作。 高等教育出版社和Pearson Education，John Wiley & Sons，McGraw-Hill，Thomson Learning等国外出版公司进行了广泛接触，经国外出版公司的推荐并在国内专家的协助下，提交引进版权总数100余种。收到样书后，我们聘请了国内高校一线教师、专家、学者参与这些原版教材的评介工作，并参考国内相关专业的课程设置和教学实际情况。