University Calculus: Early Transcendentals in SI Units

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This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.   For 3-semester or 4-quarter­ courses covering single­ variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics.   Clear, precise, concise University Calculus: Early Transcendentals helps students generalize and apply the key ideas of calculus through clear and precise explanations, thoughtfully chosen examples, meticulously crafted figures, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. In the 4th SI Edition, new co-authors Chris Heil (Georgia Institute of Technology) and Przemyslaw Bogacki (Old Dominion University) partner with author Joel Hass to preserve the text’s time-tested features while revisiting every word and figure with today’s students in mind.    Pearson MyLab Math is not included. Students, if Pearson MyLab Math is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. Pearson MyLab Math should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.   Reach every student by pairing this text with Pearson MyLab Math MyLab™ is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student.   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 Copyright Title Page Dedication Contents Chapter 1: ‘I’m thinking’ – Oh, but are you? Chapter 2: Renegade perception Chapter 3: The Pushbacker sting Chapter 4: ‘Covid’: The calculated catastrophe Chapter 5: There is no ‘virus’ Chapter 6: Sequence of deceit Chapter 7: War on your mind Chapter 8: ‘Reframing’ insanity Chapter 9: We must have it? So what is it? Chapter 10: Human 2.0 Chapter 11: Who controls the Cult? Chapter 12: Escaping Wetiko Postscript Appendix: Cowan-Kaufman-Morell Statement on Virus Isolation Bibliography Index Book Cover Diagnostic Tests A: Diagnostic Test: Algebra B: Diagnostic Test: Analytic Geometry C: Diagnostic Test: Functions D: Diagnostic Test: Trigonometry Chapter 1- Functions and Models 1.1: Four Ways to Represent a Function 1.2: Mathematical Models: A Catalog of Essential Functions 1.3: New Functions from Old Functions 1.4: Exponential Functions 1.5: Inverse Functions and Logarithms Review Principles of Problem Solving Chapter 2- Limits and Derivatives 2.1: The Tangent and Velocity Problems 2.2: The Limit of a Function 2.3: Calculating Limits Using the Limit Laws 2.4: The Precise Definition of a Limit 2.5: Continuity 2.6: Limits at Infinity; Horizontal Asymptotes 2.7: Derivatives and Rates of Change 2.8: The Derivative as a Function Review Problems Plus Chapter 3- Differentiation Rules 3.1: Derivatives of Polynomials and Exponential Functions 3.2: The Product and Quotient Rules 3.3: Derivatives of Trigonometric Functions 3.4: The Chain Rule 3.5: Implicit Differentiation 3.6: Derivatives of Logarithmic Functions 3.7: Rates of Change in the Natural and Social Sciences 3.8: Exponential Growth and Decay 3.9: Related Rates 3.10: Linear Approximations and Differentials 3.11: Hyperbolic Functions Review Problems Plus Chapter 4- Applications of Differentiation 4.1: Maximum and Minimum Values 4.2: The Mean Value Theorem 4.3: How Derivatives Affect the Shape of a Graph 4.4: Indeterminate Forms and L'Hospital's Rule 4.5: Summary of Curve Sketching 4.6: Graphing with Calculus and Calculators 4.7: Optimization Problems 4.8: Newton's Method 4.9: Antiderivatives Review Problems Plus Chapter 5- Integrals 5.1: Areas and Distances 5.2: The Definite Integral 5.3: The Fundamental Theorem of Calculus 5.4: Indefinite Integrals and the Net Change Theorem 5.5: The Substitution Rule Review Problems Plus Chapter 6- Applications of Integration 6.1: Areas between Curves 6.2: Volumes 6.3: Volumes by Cylindrical Shells 6.4: Work 6.5: Average Value of a Function Review Problems Plus Chapter 7- Techniques of Integration 7.1: Integration by Parts 7.2: Trigonometric Integrals 7.3: Trigonometric Substitution 7.4: Integration of Rational Functions by Partial Fractions 7.5: Strategy for Integration 7.6: Integration Using Tables and Computer Algebra Systems 7.7: Approximate Integration 7.8: Improper Integrals Review Problems Plus Chapter 8- Further Applications of Integration 8.1: Arc Length 8.2: Area of a Surface of Revolution 8.3: Applications to Physics and Engineering 8.4: Applications to Economics and Biology 8.5: Probability Review Problems Plus Chapter 9- Differential Equations 9.1: Modeling with Differential Equations 9.2: Direction Fields and Euler's Method 9.3: Separable Equations 9.4: Models for Population Growth 9.5: Linear Equations 9.6: Predator-Prey Systems Review Problems Plus Chapter 10- Parametric Equations and Polar Coordinates 10.1: Curves Defined by Parametric Equations 10.2: Calculus with Parametric Curves 10.3: Polar Coordinates 10.4: Areas and Lengths in Polar Coordinates 10.5: Conic Sections 10.6: Conic Sections in Polar Coordinates Review Problems Plus Chapter 11- Infinite sequences and Series 11.1: Sequences 11.2: Series 11.3: The Integral Test and Estimates of Sums 11.4: The Comparison Tests 11.5: Alternating Series 11.6: Absolute Convergence and the Ratio and Root Tests 11.7: Strategy for Testing Series 11.8: Power Series 11.9: Representations of Functions as Power Series 11.10: Taylor and Maclaurin Series 11.11: Applications of Taylor Polynomials Review Problems Plus Chapter 12- 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: Equations of Lines and Planes 12.6: Cylinders and Quadric Surfaces Review Problems Plus Chapter 13- Vector Functions 13.1: Vector Functions and Space Curves 13.2: Derivatives and Integrals of Vector Functions 13.3: Arc Length and Curvature 13.4: Motion in Space: Velocity and Acceleration Review Problems Plus Chapter 14- Partial Derivatives 14.1: Functions of Several Variables 14.2: Limits and Continuity 14.3: Partial Derivatives 14.4: Tangent Planes and Linear Approximations 14.5: The Chain Rule 14.6: Directional Derivatives and the Gradient Vector 14.7: Maximum and Minimum Values 14.8: Lagrange Multipliers Review Problems Plus Chapter 15- Multiple Integrals 15.1: Double Integrals over Rectangles 15.2: Double Integrals over General Regions 15.3: Double Integrals in Polar Coordinates 15.4: Applications of Double Integrals 15.5: Surface Area 15.6: Triple Integrals 15.7: Triple Integrals in Cylindrical Coordinates 15.8: Triple Integrals in Spherical Coordinates 15.9: Change of Variables in Multiple Integrals Review Problems Plus Chapter 16- Vector Calculus 16.1: Vector Fields 16.2: Line Integrals 16.3: The Fundamental Theorem for Line Integrals 16.4: Green's Theorem 16.5: Curl and Divergence 16.6: Parametric Surfaces and Their Areas 16.7: Surface Integrals 16.8: Stokes' Theorem 16.9: The Divergence Theorem Review Problems Plus Chapter 17- Second-Order Differential Equations 17.1: Second-Order Linear Equations 17.2: Nonhomogeneous Linear Equations 17.3: Applications of Second-Order Differential Equations 17.4: Series Solutions Review Appendixes A: Numbers, Inequalities, and Absolute Values B: Coordinate Geometry and Lines C: Graphs of Second-Degree Equations D: Trigonometry E: Sigma Notation G: The Logarithm Defined as an Integral H: Complex Numbers