Break My Shell

Calculus: Early Transcendentals builds from a foundation of strong exercise sets, then draws you into the narrative through writing that reflects an instructor's voice. Examples are stepped out and thoroughly annotated, and figures are designed carefully to work with the content. The 3rd Edition introduces important advances and refinements while retaining its proven hallmark features. Extensively revised exercise sets are rearranged and relabeled, with some modified and other new ones added. Chapter Review exercises are thoroughly revised to provide more exercises, more intermediate-level problems, and more opportunities to choose a strategy of solution. Cover Calculus_Early_Transcendentals Contents Preface Credits Chapter 1 Functions Chapter Opener 1.1 Review of Functions 1.2 Representing Functions 1.3 Inverse, Exponential, and Logarithmic Functions 1.4 Trigonometric Functions and Their Inverses Review Exercises Chapter 2 Limits Chapter Opener 2.1 The Idea of Limits 2.2 Definitions of Limits 2.3 Techniques for Computing Limits 2.4 Infinite Limits 2.5 Limits at Infinity 2.6 Continuity 2.7 Precise Definitions of Limits Review Exercises Chapter 3 Derivatives Chapter Opener 3.1 Introducing the Derivative 3.2 The Derivative as a Function 3.3 Rules of Differentiation 3.4 The Product and Quotient Rules 3.5 Derivatives of Trigonometric Functions 3.6 Derivatives as Rates of Change 3.7 The Chain Rule 3.8 Implicit Differentiation 3.9 Derivatives of Logarithmic and Exponential Functions 3.10 Derivatives of Inverse Trigonometric Functions 3.11 Related Rates Review Exercises Chapter 4 Applications of the Derivative Chapter Opener 4.1 Maxima and Minima 4.2 Mean Value Theorem 4.3 What Derivatives Tell Us 4.4 Graphing Functions 4.5 Optimization Problems 4.6 Linear Approximation and Differentials 4.7 L ́Hôpital's Rule 4.8 Newton's Method 4.9 Antiderivatives Review Exercises Chapter 5 Integration Chapter Opener 5.1 Approximating Areas under Curves 5.2 Definite Integrals 5.3 Fundamental Theorem of Calculus 5.4 Working with Integrals 5.5 Substitution Rule Review Exercises Chapter 6 Applications of Integration Chapter Opener 6.1 Velocity and Net Change 6.2 Regions Between Curves 6.3 Volume by Slicing 6.4 Volume by Shells 6.5 Length of Curves 6.6 Surface Area 6.7 Physical Applications Review Exercises Chapter 7 Logarithmic, Exponential, and Hyperbolic Functions Chapter Opener 7.1 Logarithmic and Exponential Functions Revisited 7.2 Exponential Models 7.3 Hyperbolic Functions Review Exercises Chapter 8 Integration Techniques Chapter Opener 8.1 Basic Approaches 8.2 Integration by Parts 8.3 Trigonometric Integrals 8.4 Trigonometric Substitutions 8.5 Partial Fractions 8.6 Integration Strategies 8.7 Other Methods of Integration 8.8 Numerical Integration 8.9 Improper Integrals Review Exercises Chapter 9 Differential Equations Chapter Opener 9.1 Basic Ideas 9.2 Direction Fields and Euler’s Method 9.3 Separable Differential Equations 9.4 Special First-Order Linear Differential Equations 9.5 Modeling with Differential Equations Review Exercises Chapter 10 Sequences and Infinite Series Chapter Opener 10.1 An Overview 10.2 Sequences 10.3 Infinite Series 10.4 The Divergence and Integral Tests 10.5 Comparison Tests 10.6 Alternating Series 10.7 The Ratio and Root Tests 10.8 Choosing a Convergence Test Review Exercises Chapter 11 Power Series Chapter Opener 11.1 Approximating Functions with Polynomials 11.2 Properties of Power Series 11.3 Taylor Series 11.4 Working with Taylor Series Review Exercises Chapter 12 Parametric and Polar Curves Chapter Opener 12.1 Parametric Equations 12.2 Polar Coordinates 12.3 Calculus in Polar Coordinates 12.4 Conic Sections Review Exercises Chapter 13 Vectors and the Geometry of Space Chapter Opener 13.1 Vectors in the Plane 13.2 Vectors in Three Dimensions 13.3 Dot Products 13.4 Cross Products 13.5 Lines and Planes in Space 13.6 Cylinders and Quadric Surfaces Review Exercises Chapter 14 Vector-Valued Functions Chapter Opener 14.1 Vector-Valued Functions 14.2 Calculus of Vector-Valued Functions 14.3 Motion in Space 14.4 Length of Curves 14.5 Curvature and Normal Vectors Review Exercises Chapter 15 Functions of Several Variables Chapter Opener 15.1 Graphs and Level Curves 15.2 Limits and Continuity 15.3 Partial Derivatives 15.4 The Chain Rule 15.5 Directional Derivatives and the Gradient 15.6 Tangent Planes and Linear Approximation 15.7 Maximum/Minimum Problems 15.8 Lagrange Multipliers Review Exercises Chapter 16 Multiple Integration Chapter Opener 16.1 Double Integrals over Rectangular Regions 16.2 Double Integrals over General Regions 16.3 Double Integrals in Polar Coordinates 16.4 Triple Integrals 16.5 Triple Integrals in Cylindrical and Spherical Coordinates 16.6 Integrals for Mass Calculations 16.7 Change of Variables in Multiple Integrals Review Exercises Chapter 17 Vector Calculus Chapter Opener 17.1 Vector Fields 17.2 Line Integrals 17.3 Conservative Vector Fields 17.4 Green's Theorem 17.5 Divergence and Curl 17.6 Surface Integrals 17.7 Stokes' Theorem 17.8 Divergence Theorem Review Exercises Chapter D2 Second-Order Differential Equations Chapter Opener D2.1 Basic Ideas D2.2 Linear Homogeneous Equations D2.3 Linear Nonhomogeneous Equations D2.4 Applications D2.5 Complex Forcing Functions Review Exercises Appendix A Proofs of Selected Theorems Appendix B Algebra Review Appendix C Complex Numbers Answers Index Index of Applications Table of Integrals