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托马斯微积分：第11版=Thomas Calculuss（Elecenth Edition）.上册：英文 
定 价：66.2 元
9 7 4 8 5 7 2 0 5 4 3 0 2 
本书是海外优秀数学类教材系列丛书之一，从Pearson出版公司引进。本书在北美地区是微积分课程最畅销教材之一，已是第11版。本书历经多年教学实践检验，内容翔实，叙述准确，对每个重要专题均用语言的、代数的、数值的、图像的方式予以陈述。本书有众多反映应用微积分应用的教学实例，例、习题贴近生活实际。
Preface
Pretiminaries 1.1 Real Numbers and the Real Line 1.2 Lines, Circles, and Parabolas 1.3 Functions and Their Graphs 1.4 Identifying Functions; Mathematical Models 1.5 Combining Functions; Shifting and Scaling Graphs 1.6 Trigonometric Functions 1.7 Graphing with Calculators and Computers QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Limits and Continuity 2.1 Rates of Change and Limits 2.2 Calculating Limits Using the Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits and Limits at Infinity 2.5 Infinite Limits and Vertical Asymptotes 2.6 Continuity 2.7 Tangents and Derivatives QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Differentiation 3.1 The Derivative as a Function 3.2 Differentiation Rules 3.3 The Derivative as a Rate of Change 3.4 Derivatives of Trigonometric Functions 3.5 The Chain Rule and Parametric Equations 3.6 Implicit Differentiation 3.7 Related Rates 3.8 Linearization and Differentials QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES AppticaUons of Derivatives 4.1 Extreme Values of Functions 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Applied Optimization Problems 4.6 Indeterminate Forms and IgH6pital's Rule 4.7 Newton's Method 4.8 Antiderivatives QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Integration 5.1 Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Rule 5.6 Substitution and Area Between Curves QUESTIONS TO GUIDE YoUR REvIEw PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Apptications of Definite Integrats 6.1 Volumes by Slicing and Rotation About an Axis 6.2 Volumes by Cylindrical Shells 6.3 Lengths of Plane Curves 6.4 Moments and Centers of Mass 6.5 Areas of Surfaces of Revolution and the Theorems of Pappus 6.6 Work 6.7 Fluid Pressures and Forces QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Transcendentat Functions 7.1 Inverse Functions and Their Derivatives 7.2 Natural Logarithms 7.3 The Exponential Function 7.4 ax and logax 7.5 Exponential Growth and Decay 7.6 Relative Rates of Growth 7.7 Inverse Trigonometric Functions 7.8 Hyperbolic Functions QUESTIONS TO GLADE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Techniques of Integration 5 8.1 Basic Integration Formulas 8.2 Integration by Parts 8.3 Integration of Rational Functions by Partial Fractions 8.4 Trigonometric Integrals 8.5 Trigonometric Substitutions 8.6 Integral Tables and Comouter Algebra Systems 8.7 Numerical Integration 8.8 Improper Integrals QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Further Applications of Integration 9.1 Slope Fields and Separable Differential Equations 9.2 First-Order Linear Differential Equations 9.3 Euler's Method 9.4 Graphical Solutions of Autonomous Differential Equations 9.5 Applications of First-Order Differential Equations QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Conic Sections and Polar Coordinates 10.1 Conic Sections and Quadratic Equations 10.2 Classifying Conic Sections by Eccentricity 10.3 Quadratic Equations and Rotations 10.4 Conics and Parametric Equations; The Cycloid 10.5 Polar Coordinates 10.6 Graphing in Polar Coordinates 10.7 Areas and Lengths in Polar Coordinates 10.8 Conic Sections in Polar Coordinates QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Infinite Sequences and Series 11.1 Sequences 11.2 Infinite Series 11.3 The Integral Test 11.4 Comparison Tests 11.5 The Ratio and Root Tests _ 11.6 Alternating Series, Absolute and Conditional Convergence 11.7 Power Series 11.8 Taylor and Maclaurin Series 11.9 Convergence of Taylor Series; Error Estimates 11.10 Applications of Power Series 11.11 Fourier Series QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Vectors and the Geometry of Space 12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Lines and Planes in Space 12.6 Cylinders and Quadric Surfaces QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Vector-Va[ued Functions and Motion in Space 13.1 Vector Functions 906 13.2 Modeling Projectile Motion 920 13.3 Arc Length and the Unit Tangent Vector T 931 13.4 Curvature and the Unit Normal Vector N 936 13.5 Torsion and the Unit Binormal Vector B 943 13.6 Planetary Motion and Satellites 950 QUESTIONS TO GUIDE YOUR REVIEW 959 PRACTICE EXERCISES 960 ADDITIONAL AND ADVANCED EXERCISES 962 Partiat Derivatives 14. l Functions of Several Variables 14.2 Limits and Continuity in Higher Dimensions 14.3 Partial Derivatives 14.4 The Chain Rule 14.5 Directional Derivatives and Gradient Vectors 14.6 Tangent Planes and Differentials 14.7 Extreme Values and Saddle Points 14.8 Lagrange Multipliers 14.9 Partial Derivatives with Constrained Variables 14.10 Taylor's Formula for Two Variables QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES MutUpte Integrats 15.1 Double Integrals 15.2 Areas, Moments, and Centers of Mass 15.3 Double Integrals in Polar Form 15.4 Triple Integrals in Rectangular Coordinates 15.5 Masses and Moments in Three Dimensions 15.6 Triple Integrals in Cylindrical and Spherical Coordinates 15.7 Substitutions in Multiple Integrals QUESTIONS TO GUIDE YOUR REVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Integration in Vector Fietds 16.1 Line Integrals 16.2 Vector Fields, Work, Circulation, and Flux 16.3 Path Independence, Potential Functions, and Conservative Fields 16.4 Green's Theorem in the Plane 16.5 Surface Area and Surface Integrals 16.6 Parametrized Surfaces 16.7 Stokes' Theorem 16.8 The Divergence Theorem and a Unified Theory QUESTIONS TO GUIDE YOUR RnVIEW PRACTICE EXERCISES ADDITIONAL AND ADVANCED EXERCISES Appendices A.1 Mathematical Induction A.2 Proofs of Limit Theorems A.3 Commonly Occurring Limits A.4 Theory of the Real Numbers A.5 Complex Numbers A.6 The Distributive Law for Vector Cross Products A.7 The Mixed Derivative Theorem and the Increment Theorem A.8 The Area ofa Parallelogram's Projection on a Plane A.9 Basic Algebra, Geometry, and Trigonometry Formulas Answers Index A Brief TaMe of Integrals Credits
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