Calculus and Analytic Geometry 5th Revised edition [Kietas viršelis]

Calculus and Analytic Geometry1. An Overview of Calculus. 1.1 The Derivative1.2 The Integral1.3 Survey of the Text2. Functions, Limits, and Continuity. 2.1 Functions2.2 Composite Functions2.3 The Limit of a Function2.4 Computations of Limits2.5 Some Tools for Graphing2.6 A Review of Trigonometry2.7 The Limit of (sin Ø)/Ø as Ø Approaches 02.8 Continuous Functions2.9 Precise Definitions of lim(x->infinity)f(x)=infinity and lim(x->infinity)f(x)=L2.10 Precise Definition of lim(x->a)f(x)=L2.S Summary3. The Derivative.3.1 Four Problems with One Theme3.2 The Derivative3.3 The Derivative and Continuity3.4 The Derivative of the Sum, Difference, Product, and Quotient3.5 The Derivatives of the Trigonometric Functions3.6 The Derivative of a Composite Function3.S Summary4. Applications of the Derivative.4.1 Three Theorems about the Derivative4.2 The First Derivative and Graphing4.3 Motion and the Second Derivative4.4 Related Rates4.5 The Second Derivative and Graphing4.6 Newtons Method for Solving an Equation4.7 Applied Maximum and Minimum Problems4.9 The Differential and Linearization4.10 The Second Derivative and Growth of a Function4.S Summary5. The Definite Integral.5.1 Estimates in Four Problems5.2 Summation Notation and Approximating Sums5.3 The Definite Integral5.4 Estimating the Definite Integral5.5 Properties of the Antiderivative and the Definite Integral5.6 Background for the Fundamental Theorems of Calculus5.7 The Fundamental Theorems of Calculus5.S Summary6. Topics in Differential Calculus. 6.1 Logarithms6.2 The Number e6.3 The Derivative of a Logarithmic Function6.4 One-to-One Functions and Their Inverses6.5 The Derivative of b^x6.6 The Derivatives of the Inverse Trigonometric Functions6.7 The Differential Equation of Natural Growth and Decay6.8 lHopitals Rule6.9 The Hyperbolic Functions and Their Inverses6.S Summary7. Computing Antiderivatives.7.1 Shortcuts, Integral Tables, and Machines7.2 The Substitution Method7.3 Integration by Parts7.4 How to Integrate Certain Rational Functions7.5 Integration of Rational Functions by Partial Fractions7.6 Special Techniques7.7 What to Do in the Face of an Integral7.S Summary8. Applications of the Definite Integral.8.1 Computing Area by Parallel Cross Sections8.2 Some Pointers on Drawing8.3 Setting Up a Definite Integral8.4 Computing Volumes8.5 The Shell Method8.6 The Centroid of a Plane Region8.7 Work8.8 Improper Integrals8.S Summary9. Plane Curves and Polar Coordinates.9.1 Polar Coordinates9.2 Area in Polar Coordinates9.3 Parametric Equations9.4 Arc Length and Speed on a Curve9.5 The Area of a Surface of Revolution9.6 Curvature9.7 The Reflection Properties of the Conic Sections9.S Summary10. Series.10.1 An Informal Introduction to Series10.2 Sequences10.3 Series10.4 The Integral Test10.5 Comparison Tests10.6 Ratio Tests10.7 Tests for Series with Both Positive and Negative Terms10.S Summary
11. Power Series and Complex Numbers.11.1 Taylor Series11.2 The Error in Taylor Series11.3 Why the Error in Taylor Series Is Controlled by a Derivative11.4 Power Series and Radius of Convergence11.5 Manipulating Power Series11.6 Complex Numbers11.7 The Relation between the Exponential and the Trigonometric Functions11.S Summary12. Vectors.12.1 The Algebra of Vectors12.2 Projections12.3 The Dot Product of Two Vectors12.4 Lines and Planes12.5 Determinants12.6 The Cross Product of Two Vectors12.7 More on Lines and Planes12.S Summary13. The Derivative of a Vector Function.13.1 The Derivative of a Vector Function13.2 Properties of the Derivative of a Vector Function13.3 The Acceleration Vector13.4 The Components of Acceleration13.5 Newtons Law Implies Keplers Laws13.S Summary14. Partial Derivatives.14.1 Graphs14.2 Quadratic Surfaces14.3 Functions and Their Level Curves14.4 Limits and Continuity14.5 Partial Derivatives14.6 The Chain Rule14.7 Directional Derivatives and the Gradient14.8 Normals and the Tangent Plane14.9 Critical Points and Extrema14.10 Lagrange Multipliers14.11 The Chain Rule Revisited14.S Summary15. Definite Integrals over Plane and Solid Regions. 15.1 The Definite Integral of a Function over a Region in the Plane15.2 Computing |R f(P) dA Using Rectangular Coordinates15.3 Moments and Centers of Mass15.4 Computing |R f(P) dA Using Polar Coordinates15.5 The Definite Integral of a Function over a Region in Space15.6 Computing |R f(P) dV Using Cylindrical Coordinates15.7 Computing |R f(P) dV Using Spherical Coordinates15.S Summary16. Greens Theorem.16.1 Vector and Scalar Fields16.2 Line Integrals16.3 Four Applications of Line Integrals16.4 Greens Theorem16.5 Applications of Greens Theorem16.6 Conservative Vector Fields16.S Summary17. The Divergence Theorem and Stokes Theorem.17.1 Surface Integrals17.2 The Divergence Theorem17.3 Stokes Theorem17.4 Applications of Stokes Theorem17.S SummaryAppendices:A. Real Numbers. B. Graphs and Lines.C. Topics in Algebra. D. Exponents. E. Mathematical Induction. F. The Converse of a Statement. G. Conic Sections. H. Logarithms and Exponentials Defined through Calculus.I. The Taylor Series for f(x,y). J. Theory of Limits. K. The Interchange of Limits. L. The Jacobian. M. Linear Differential Equations with Constant Coefficients.Answers to Selected Odd-Numbered Problems and to Guide QuizzesList of SymbolsIndex

Sherman Stein, received his Ph.D. from Columbia University. After a one-year instructorship at Princeton University, he joined the faculty at the University of California, Davis, where he taught until 1993. His main mathematical interests are in algebra, combinatorics, and pedagogy. He has been the recipient of two MAA awards; the Lester R. Ford Award for Mathematical Exposition, and the Beckenbach Book Prize for Algebra and Tiling (with Sandor Szabo). He also received The Distinguished Teaching Award from the University of California, Davis, and an honorary Doctor of Humane Letters from Marietta College.