Joel Hass received his PhD from the University of California - Berkeley. He is currently a professor of mathematics at the University of California - Davis. He has coauthored widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass's current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil's current areas of research include redundant representations, operator theory, and applied harmonic analysis. In his spare time, Heil pursues his hobby of astronomy.The late Maurice D. Weir of the the Naval Postgraduate School in Monterey, California was Professor Emeritus as a member of the Department of Applied Mathematics. He held a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. Weir was awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He co-authored eight books, including University Calculus and Thomas' Calculus.Przemyslaw Bogacki is an Associate Professor of Mathematics and Statistics and a University Professor at Old Dominion University. He received his PhD in 1990 from Southern Methodist University. He is also the author of a text on linear algebra, which appeared in 2019. He is actively involved in applications of technology in collegiate mathematics. His areas of research include computer aided geometric design and numerical solution of initial value problems for ordinary differential equations.

• 1. Functions 1.1 Functions and Their Graphs1.2 Combining Functions; Shifting and Scaling Graphs1.3 Trigonometric Functions1.4 Graphing with SoftwareQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects2. Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves2.2 Limit of a Function and Limit Laws2.3 The Precise Definition of a Limit2.4 One-Sided Limits2.5 Limits Involving Infinity; Asymptotes of Graphs2.6 ContinuityQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects3. Derivatives 3.1 Tangent Lines and the Derivative at a Point3.2 The Derivative as a Function3.3 Differentiation Rules3.4 The Derivative as a Rate of Change3.5 Derivatives of Trigonometric Functions3.6 The Chain Rule3.7 Implicit Differentiation3.8 Related Rates3.9 Linearization and DifferentialsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects4. Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals4.2 The Mean Value Theorem4.3 Monotonic Functions and the First Derivative Test4.4 Concavity and Curve Sketching4.5 Applied Optimization4.6 Newton's Method4.7 AntiderivativesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects5. Integrals 5.1 Area and Estimating with Finite Sums5.2 Sigma Notation and Limits of Finite Sums5.3 The Definite Integral5.4 The Fundamental Theorem of Calculus5.5 Indefinite Integrals and the Substitution Method5.6 Definite Integral Substitutions and the Area Between CurvesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects6. Applications of Definite Integrals 6.1 Volumes Using Cross-Sections6.2 Volumes Using Cylindrical Shells6.3 Arc Length6.4 Areas of Surfaces of Revolution6.5 Work and Fluid Forces6.6 Moments and Centers of MassQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects7. Transcendental Functions 7.1 Inverse Functions and Their Derivatives7.2 Natural Logarithms7.3 Exponential Functions7.4 Exponential Change and Separable Differential Equations7.5 Indeterminate Forms and L'Hôpital's Rule7.6 Inverse Trigonometric Functions7.7 Hyperbolic Functions7.8 Relative Rates of GrowthQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced Exercises8. Techniques of Integration 8.1 Using Basic Integration Formulas8.2 Integration by Parts8.3 Trigonometric Integrals8.4 Trigonometric Substitutions8.5 Integration of Rational Functions by Partial Fractions8.6 Integral Tables and Computer Algebra Systems8.7 Numerical Integration8.8 Improper IntegralsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects9. Infinite Sequences and Series 9.1 Sequences9.2 Infinite Series9.3 The Integral Test9.4 Comparison Tests9.5 Absolute Convergence; The Ratio and Root Tests9.6 Alternating Series and Conditional Convergence9.7 Power Series9.8 Taylor and Maclaurin Series9.9 Convergence of Taylor Series9.10 Applications of Taylor SeriesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects10. Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves10.2 Calculus with Parametric Curves10.3 Polar Coordinates10.4 Graphing Polar Coordinate Equations10.5 Areas and Lengths in Polar Coordinates10.6 Conic Sections10.7 Conics in Polar CoordinatesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects11. Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems11.2 Vectors11.3 The Dot Product11.4 The Cross Product11.5 Lines and Planes in Space11.6 Cylinders and Quadric SurfacesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects12. Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents12.2 Integrals of Vector Functions; Projectile Motion12.3 Arc Length in Space12.4 Curvature and Normal Vectors of a Curve12.5 Tangential and Normal Components of Acceleration12.6 Velocity and Acceleration in Polar CoordinatesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects13. Partial Derivatives 13.1 Functions of Several Variables13.2 Limits and Continuity in Higher Dimensions13.3 Partial Derivatives13.4 The Chain Rule13.5 Directional Derivatives and Gradient Vectors13.6 Tangent Planes and Differentials13.7 Extreme Values and Saddle Points13.8 Lagrange Multipliers13.9 Taylor’s Formula for Two Variables13.10 Partial Derivatives with Constrained VariablesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects14. Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles14.2 Double Integrals over General Regions14.3 Area by Double Integration14.4 Double Integrals in Polar Form14.5 Triple Integrals in Rectangular Coordinates14.6 Applications14.7 Triple Integrals in Cylindrical and Spherical Coordinates14.8 Substitutions in Multiple IntegralsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects15. Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux15.3 Path Independence, Conservative Fields, and Potential Functions15.4 Green’s Theorem in the Plane15.5 Surfaces and Area15.6 Surface Integrals15.7 Stokes’ Theorem15.8 The Divergence Theorem and a Unified TheoryQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects16. First-Order Differential Equations 16.1 Solutions, Slope Fields, and Euler’s Method16.2 First-Order Linear Equations16.3 Applications16.4 Graphical Solutions of Autonomous Equations16.5 Systems of Equations and Phase PlanesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects17. Second-Order Differential Equations (online) 17.1 Second-Order Linear Equations17.2 Nonhomogeneous Linear Equations17.3 Applications17.4 Euler Equations17.5 Power-Series Solutions18. Complex Functions (online) 18.1 Complex Numbers18.2 Functions of a Complex Variable18.3 Derivatives18.4 The Cauchy-Riemann Equations18.5 Complex Power Series18.6 Some Complex Functions18.7 Conformal MapsQuestions to Guide Your ReviewAdditional and Advanced Exercises19. Fourier Series and Wavelets (online) 19.1 Periodic Functions19.2 Summing Sines and Cosines19.3 Vectors and Approximation in Three and More Dimensions19.4 Approximation of Functions19.5 Advanced Topic: The Haar System and WaveletsQuestions to Guide Your ReviewAdditional and Advanced ExercisesAppendix A A.1 Real Numbers and the Real LineA.2 Mathematical InductionA.3 Lines, Circles, and ParabolasA.4 Proofs of Limit TheoremsA.5 Commonly Occurring LimitsA.6 Theory of the Real NumbersA.7 ProbabilityA.8 The Distributive Law for Vector Cross ProductsA.9 The Mixed Derivative Theorem and the Increment TheoremAppendix B (online) B.1 DeterminantsB.2 Extreme Values and Saddle Points for Functions of More than Two VariablesB.3 The Method of Gradient DescentAnswers to Odd-Numbered Exercises Applications Index Subject Index Credits A Brief Table of Integrals

Joel Hass received his PhD from the University of California - Berkeley. He is currently a professor of mathematics at the University of California - Davis. He has coauthored widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass's current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil's current areas of research include redundant representations, operator theory, and applied harmonic analysis. In his spare time, Heil pursues his hobby of astronomy.The late Maurice D. Weir of the the Naval Postgraduate School in Monterey, California was Professor Emeritus as a member of the Department of Applied Mathematics. He held a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. Weir was awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He co-authored eight books, including University Calculus and Thomas' Calculus.Przemyslaw Bogacki is an Associate Professor of Mathematics and Statistics and a University Professor at Old Dominion University. He received his PhD in 1990 from Southern Methodist University. He is also the author of a text on linear algebra, which appeared in 2019. He is actively involved in applications of technology in collegiate mathematics. His areas of research include computer aided geometric design and numerical solution of initial value problems for ordinary differential equations.

• 1. Functions 1.1 Functions and Their Graphs1.2 Combining Functions; Shifting and Scaling Graphs1.3 Trigonometric Functions1.4 Graphing with SoftwareQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects2. Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves2.2 Limit of a Function and Limit Laws2.3 The Precise Definition of a Limit2.4 One-Sided Limits2.5 Limits Involving Infinity; Asymptotes of Graphs2.6 ContinuityQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects3. Derivatives 3.1 Tangent Lines and the Derivative at a Point3.2 The Derivative as a Function3.3 Differentiation Rules3.4 The Derivative as a Rate of Change3.5 Derivatives of Trigonometric Functions3.6 The Chain Rule3.7 Implicit Differentiation3.8 Related Rates3.9 Linearization and DifferentialsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects4. Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals4.2 The Mean Value Theorem4.3 Monotonic Functions and the First Derivative Test4.4 Concavity and Curve Sketching4.5 Applied Optimization4.6 Newton's Method4.7 AntiderivativesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects5. Integrals 5.1 Area and Estimating with Finite Sums5.2 Sigma Notation and Limits of Finite Sums5.3 The Definite Integral5.4 The Fundamental Theorem of Calculus5.5 Indefinite Integrals and the Substitution Method5.6 Definite Integral Substitutions and the Area Between CurvesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects6. Applications of Definite Integrals 6.1 Volumes Using Cross-Sections6.2 Volumes Using Cylindrical Shells6.3 Arc Length6.4 Areas of Surfaces of Revolution6.5 Work and Fluid Forces6.6 Moments and Centers of MassQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects7. Transcendental Functions 7.1 Inverse Functions and Their Derivatives7.2 Natural Logarithms7.3 Exponential Functions7.4 Exponential Change and Separable Differential Equations7.5 Indeterminate Forms and L'Hôpital's Rule7.6 Inverse Trigonometric Functions7.7 Hyperbolic Functions7.8 Relative Rates of GrowthQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced Exercises8. Techniques of Integration 8.1 Using Basic Integration Formulas8.2 Integration by Parts8.3 Trigonometric Integrals8.4 Trigonometric Substitutions8.5 Integration of Rational Functions by Partial Fractions8.6 Integral Tables and Computer Algebra Systems8.7 Numerical Integration8.8 Improper IntegralsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects9. Infinite Sequences and Series 9.1 Sequences9.2 Infinite Series9.3 The Integral Test9.4 Comparison Tests9.5 Absolute Convergence; The Ratio and Root Tests9.6 Alternating Series and Conditional Convergence9.7 Power Series9.8 Taylor and Maclaurin Series9.9 Convergence of Taylor Series9.10 Applications of Taylor SeriesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects10. Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves10.2 Calculus with Parametric Curves10.3 Polar Coordinates10.4 Graphing Polar Coordinate Equations10.5 Areas and Lengths in Polar Coordinates10.6 Conic Sections10.7 Conics in Polar CoordinatesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects11. Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems11.2 Vectors11.3 The Dot Product11.4 The Cross Product11.5 Lines and Planes in Space11.6 Cylinders and Quadric SurfacesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects12. Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents12.2 Integrals of Vector Functions; Projectile Motion12.3 Arc Length in Space12.4 Curvature and Normal Vectors of a Curve12.5 Tangential and Normal Components of Acceleration12.6 Velocity and Acceleration in Polar CoordinatesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects13. Partial Derivatives 13.1 Functions of Several Variables13.2 Limits and Continuity in Higher Dimensions13.3 Partial Derivatives13.4 The Chain Rule13.5 Directional Derivatives and Gradient Vectors13.6 Tangent Planes and Differentials13.7 Extreme Values and Saddle Points13.8 Lagrange Multipliers13.9 Taylor’s Formula for Two Variables13.10 Partial Derivatives with Constrained VariablesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects14. Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles14.2 Double Integrals over General Regions14.3 Area by Double Integration14.4 Double Integrals in Polar Form14.5 Triple Integrals in Rectangular Coordinates14.6 Applications14.7 Triple Integrals in Cylindrical and Spherical Coordinates14.8 Substitutions in Multiple IntegralsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects15. Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux15.3 Path Independence, Conservative Fields, and Potential Functions15.4 Green’s Theorem in the Plane15.5 Surfaces and Area15.6 Surface Integrals15.7 Stokes’ Theorem15.8 The Divergence Theorem and a Unified TheoryQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects16. First-Order Differential Equations 16.1 Solutions, Slope Fields, and Euler’s Method16.2 First-Order Linear Equations16.3 Applications16.4 Graphical Solutions of Autonomous Equations16.5 Systems of Equations and Phase PlanesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects17. Second-Order Differential Equations (online) 17.1 Second-Order Linear Equations17.2 Nonhomogeneous Linear Equations17.3 Applications17.4 Euler Equations17.5 Power-Series Solutions18. Complex Functions (online) 18.1 Complex Numbers18.2 Functions of a Complex Variable18.3 Derivatives18.4 The Cauchy-Riemann Equations18.5 Complex Power Series18.6 Some Complex Functions18.7 Conformal MapsQuestions to Guide Your ReviewAdditional and Advanced Exercises19. Fourier Series and Wavelets (online) 19.1 Periodic Functions19.2 Summing Sines and Cosines19.3 Vectors and Approximation in Three and More Dimensions19.4 Approximation of Functions19.5 Advanced Topic: The Haar System and WaveletsQuestions to Guide Your ReviewAdditional and Advanced ExercisesAppendix A A.1 Real Numbers and the Real LineA.2 Mathematical InductionA.3 Lines, Circles, and ParabolasA.4 Proofs of Limit TheoremsA.5 Commonly Occurring LimitsA.6 Theory of the Real NumbersA.7 ProbabilityA.8 The Distributive Law for Vector Cross ProductsA.9 The Mixed Derivative Theorem and the Increment TheoremAppendix B (online) B.1 DeterminantsB.2 Extreme Values and Saddle Points for Functions of More than Two VariablesB.3 The Method of Gradient DescentAnswers to Odd-Numbered Exercises Applications Index Subject Index Credits A Brief Table of Integrals

Joel Hass received his PhD from the University of California - Berkeley. He is currently a professor of mathematics at the University of California - Davis. He has coauthored widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass's current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking.Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey articles. He serves on the editorial boards of Applied and Computational Harmonic Analysis and The Journal of Fourier Analysis and Its Applications. Heil's current areas of research include redundant representations, operator theory, and applied harmonic analysis. In his spare time, Heil pursues his hobby of astronomy.The late Maurice D. Weir of the the Naval Postgraduate School in Monterey, California was Professor Emeritus as a member of the Department of Applied Mathematics. He held a DA and MS from Carnegie-Mellon University and received his BS at Whitman College. Weir was awarded the Outstanding Civilian Service Medal, the Superior Civilian Service Award, and the Schieffelin Award for Excellence in Teaching. He co-authored eight books, including University Calculus and Thomas' Calculus.Przemyslaw Bogacki is an Associate Professor of Mathematics and Statistics and a University Professor at Old Dominion University. He received his PhD in 1990 from Southern Methodist University. He is also the author of a text on linear algebra, which appeared in 2019. He is actively involved in applications of technology in collegiate mathematics. His areas of research include computer aided geometric design and numerical solution of initial value problems for ordinary differential equations.

• 1. Functions 1.1 Functions and Their Graphs1.2 Combining Functions; Shifting and Scaling Graphs1.3 Trigonometric Functions1.4 Graphing with SoftwareQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects2. Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves2.2 Limit of a Function and Limit Laws2.3 The Precise Definition of a Limit2.4 One-Sided Limits2.5 Limits Involving Infinity; Asymptotes of Graphs2.6 ContinuityQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects3. Derivatives 3.1 Tangent Lines and the Derivative at a Point3.2 The Derivative as a Function3.3 Differentiation Rules3.4 The Derivative as a Rate of Change3.5 Derivatives of Trigonometric Functions3.6 The Chain Rule3.7 Implicit Differentiation3.8 Related Rates3.9 Linearization and DifferentialsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects4. Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals4.2 The Mean Value Theorem4.3 Monotonic Functions and the First Derivative Test4.4 Concavity and Curve Sketching4.5 Applied Optimization4.6 Newton's Method4.7 AntiderivativesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects5. Integrals 5.1 Area and Estimating with Finite Sums5.2 Sigma Notation and Limits of Finite Sums5.3 The Definite Integral5.4 The Fundamental Theorem of Calculus5.5 Indefinite Integrals and the Substitution Method5.6 Definite Integral Substitutions and the Area Between CurvesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects6. Applications of Definite Integrals 6.1 Volumes Using Cross-Sections6.2 Volumes Using Cylindrical Shells6.3 Arc Length6.4 Areas of Surfaces of Revolution6.5 Work and Fluid Forces6.6 Moments and Centers of MassQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects7. Transcendental Functions 7.1 Inverse Functions and Their Derivatives7.2 Natural Logarithms7.3 Exponential Functions7.4 Exponential Change and Separable Differential Equations7.5 Indeterminate Forms and L'Hôpital's Rule7.6 Inverse Trigonometric Functions7.7 Hyperbolic Functions7.8 Relative Rates of GrowthQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced Exercises8. Techniques of Integration 8.1 Using Basic Integration Formulas8.2 Integration by Parts8.3 Trigonometric Integrals8.4 Trigonometric Substitutions8.5 Integration of Rational Functions by Partial Fractions8.6 Integral Tables and Computer Algebra Systems8.7 Numerical Integration8.8 Improper IntegralsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects9. Infinite Sequences and Series 9.1 Sequences9.2 Infinite Series9.3 The Integral Test9.4 Comparison Tests9.5 Absolute Convergence; The Ratio and Root Tests9.6 Alternating Series and Conditional Convergence9.7 Power Series9.8 Taylor and Maclaurin Series9.9 Convergence of Taylor Series9.10 Applications of Taylor SeriesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects10. Parametric Equations and Polar Coordinates 10.1 Parametrizations of Plane Curves10.2 Calculus with Parametric Curves10.3 Polar Coordinates10.4 Graphing Polar Coordinate Equations10.5 Areas and Lengths in Polar Coordinates10.6 Conic Sections10.7 Conics in Polar CoordinatesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects11. Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems11.2 Vectors11.3 The Dot Product11.4 The Cross Product11.5 Lines and Planes in Space11.6 Cylinders and Quadric SurfacesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects12. Vector-Valued Functions and Motion in Space 12.1 Curves in Space and Their Tangents12.2 Integrals of Vector Functions; Projectile Motion12.3 Arc Length in Space12.4 Curvature and Normal Vectors of a Curve12.5 Tangential and Normal Components of Acceleration12.6 Velocity and Acceleration in Polar CoordinatesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects13. Partial Derivatives 13.1 Functions of Several Variables13.2 Limits and Continuity in Higher Dimensions13.3 Partial Derivatives13.4 The Chain Rule13.5 Directional Derivatives and Gradient Vectors13.6 Tangent Planes and Differentials13.7 Extreme Values and Saddle Points13.8 Lagrange Multipliers13.9 Taylor’s Formula for Two Variables13.10 Partial Derivatives with Constrained VariablesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects14. Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles14.2 Double Integrals over General Regions14.3 Area by Double Integration14.4 Double Integrals in Polar Form14.5 Triple Integrals in Rectangular Coordinates14.6 Applications14.7 Triple Integrals in Cylindrical and Spherical Coordinates14.8 Substitutions in Multiple IntegralsQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects15. Integrals and Vector Fields 15.1 Line Integrals of Scalar Functions15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux15.3 Path Independence, Conservative Fields, and Potential Functions15.4 Green’s Theorem in the Plane15.5 Surfaces and Area15.6 Surface Integrals15.7 Stokes’ Theorem15.8 The Divergence Theorem and a Unified TheoryQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects16. First-Order Differential Equations 16.1 Solutions, Slope Fields, and Euler’s Method16.2 First-Order Linear Equations16.3 Applications16.4 Graphical Solutions of Autonomous Equations16.5 Systems of Equations and Phase PlanesQuestions to Guide Your ReviewPractice ExercisesAdditional and Advanced ExercisesTechnology Application Projects17. Second-Order Differential Equations (online) 17.1 Second-Order Linear Equations17.2 Nonhomogeneous Linear Equations17.3 Applications17.4 Euler Equations17.5 Power-Series Solutions18. Complex Functions (online) 18.1 Complex Numbers18.2 Functions of a Complex Variable18.3 Derivatives18.4 The Cauchy-Riemann Equations18.5 Complex Power Series18.6 Some Complex Functions18.7 Conformal MapsQuestions to Guide Your ReviewAdditional and Advanced Exercises19. Fourier Series and Wavelets (online) 19.1 Periodic Functions19.2 Summing Sines and Cosines19.3 Vectors and Approximation in Three and More Dimensions19.4 Approximation of Functions19.5 Advanced Topic: The Haar System and WaveletsQuestions to Guide Your ReviewAdditional and Advanced ExercisesAppendix A A.1 Real Numbers and the Real LineA.2 Mathematical InductionA.3 Lines, Circles, and ParabolasA.4 Proofs of Limit TheoremsA.5 Commonly Occurring LimitsA.6 Theory of the Real NumbersA.7 ProbabilityA.8 The Distributive Law for Vector Cross ProductsA.9 The Mixed Derivative Theorem and the Increment TheoremAppendix B (online) B.1 DeterminantsB.2 Extreme Values and Saddle Points for Functions of More than Two VariablesB.3 The Method of Gradient DescentAnswers to Odd-Numbered Exercises Applications Index Subject Index Credits A Brief Table of Integrals