University calculus : early transcendentals

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Cover MyLab Math forUniversity Calculus, 4e in SI Units Tilte Page Copyright Page Contents Preface 1 Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms 2 Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 3 Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 4 Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hopital’s Rule 4.6 Applied Optimization 4.7 Newton’s Method 4.8 Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 5 Integrals 5.1 Area and 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 Method 5.6 Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 6 Applications of Definite Integrals 6.1 Volumes Using Cross‐Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 7 Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 8 Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions 8.5 Integral Tables and Computer Algebra Systems 8.6 Numerical Integration 8.7 Improper Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 9 Infinite Sequences and Series 9.1 Sequences 9.2 Infinite Series 9.3 The Integral Test 9.4 Comparison Tests 9.5 Absolute Convergence; The Ratio and Root Tests 9.6 Alternating Series and Conditional Convergence 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 Applications of Taylor Series Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 10 Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Graphing Polar Coordinate Equations 10.5 Areas and Lengths in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 11 Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Cylinders and Quadric Surfaces Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 12 Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents 12.2 Integrals of Vector Functions; Projectile Motion 12.3 Arc Length in Space 12.4 Curvature and Normal Vectors of a Curve 12.5 Tangential and Normal Components of Acceleration 12.6 Velocity and Acceleration in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 13 Partial Derivatives 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 13.3 Partial Derivatives 13.4 The Chain Rule 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes and Differentials 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multipliers Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 14 Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 14.4 Double Integrals in Polar Form 14.5 Triple Integrals in Rectangular Coordinates 14.6 Applications 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 15 Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions 15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 15.3 Path Independence, Conservative Fields, and Potential Functions 15.4 Green’s Theorem in the Plane 15.5 Surfaces and Area 15.6 Surface Integrals 15.7 Stokes’ Theorem 15.8 The Divergence Theorem and a Unified Theory Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 16 First-Order Differential Equations 16.1 Solutions, Slope Fields, and Euler’s Method 16.2 First-Order Linear Equations 16.3 Applications 16.4 Graphical Solutions of Autonomous Equations 16.5 Systems of Equations and Phase Planes Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 17 Second-Order Differential Equations 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power-Series Solutions Appendix A A.1 Real Numbers and the Real Line A.2 Mathematical Induction A.3 Lines and Circles A.4 Conic Sections A.5 Proofs of Limit Theorems A.6 Commonly Occurring Limits A.7 Theory of the Real Numbers A.8 Complex Numbers A.9 The Distributive Law for Vector Cross Products A.10 The Mixed Derivative Theorem and the Increment Theorem Appendix B B.1 Relative Rates of Growth B.2 Probability B.3 Conics in Polar Coordinates B.4 Taylor’s Formula for Two Variables B.5 Partial Derivatives with Constrained Variables Answers to Odd-Numbered Exercises Applications Index Subject Index Credits A Brief Table of Integrals