Thomas' Calculus: Early Transcendentals (Thirteenth Edition in SI Units)

Description

This text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors). Thomas’ Calculus: Early Transcendentals, Thirteenth Edition, introduces readers to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded—always with the goal of developing technical competence while furthering readers’ appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today's learners.   Cover Thomas’ Calculus: Early Transcendentals Copyright Contents Preface Chapter 1: Functions Functions and Their Graphs Combining Functions; Shifting and Scaling Graphs Trigonometric Functions Graphing with Software Exponential Functions Inverse Functions and Logarithms Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 2: Limits and Continuity Rates of Change and Tangents to Curves Limit of a Function and Limit Laws The Precise Definition of a Limit One-Sided Limits Continuity Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 3: Derivatives Tangents and the Derivative at a Point The Derivative as a Function Differentiation Rules The Derivative as a Rate of Change Derivatives of Trigonometric Functions The Chain Rule Implicit Differentiation Derivatives of Inverse Functions and Logarithms Inverse Trigonometric Functions Related Rates Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 4: Applications of Derivatives Extreme Values of Functions The Mean Value Theorem Monotonic Functions and the First Derivative Test Concavity and Curve Sketching Indeterminate Forms and L’Hôpital’s Rule Applied Optimization Newton’s Method Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 5: Integrals Area and Estimating with Finite Sums Sigma Notation and Limits of Finite Sums The Definite Integral The Fundamental Theorem of Calculus Indefinite Integrals and the Substitution Method Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 6: Applications of Definite Integrals Volumes Using Cross-Sections Volumes Using Cylindrical Shells Arc Length Areas of Surfaces of Revolution Work and Fluid Forces Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 7: Integrals and Transcendental Functions The Logarithm Defined as an Integral Exponential Change and Separable Differential Equations Hyperbolic Functions Relative Rates of Growth Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 8: Techniques of Integration Using Basic Integration Formulas Integration by Parts Trigonometric Integrals Trigonometric Substitutions Integration of Rational Functions by Partial Fractions Integral Tables and Computer Algebra Systems Numerical Integration Improper Integrals Probability Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 9: First-Order Differential Equations Solutions, Slope Fields, and Euler’s Method First-Order Linear Equations Applications Graphical Solutions of Autonomous Equations Systems of Equations and Phase Planes Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 10: Infinite Sequences and Series Sequences Infinite Series The Integral Test Comparison Tests Absolute Convergence; The Ratio and Root Tests Alternating Series and Conditional Convergence Power Series Taylor and Maclaurin Series Convergence of Taylor Series The Binomial Series and Applications of Taylor Series Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 11: Parametric Equations and Polar Coordinates Parametrizations of Plane Curves Calculus with Parametric Curves Polar Coordinates Graphing Polar Coordinate Equations Areas and Lengths in Polar Coordinates Conic Sections Conics in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 12: Vectors and the Geometry of Space Three-Dimensional Coordinate Systems Vectors The Dot Product The Cross Product Lines and Planes in Space Cylinders and Quadric Surfaces Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 13: Vector-Valued Functions and Motion in Space Curves in Space and Their Tangents Integrals of Vector Functions; Projectile Motion Arc Length in Space Curvature and Normal Vectors of a Curve Tangential and Normal Components of Acceleration Velocity and Acceleration in Polar Coordinates Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 14: Partial Derivatives Functions of Several Variables Limits and Continuity in Higher Dimensions Partial Derivatives The Chain Rule Directional Derivatives and Gradient Vectors Tangent Planes and Differentials Extreme Values and Saddle Points Lagrange Multipliers Taylor’s Formula for Two Variables Partial Derivatives with Constrained Variables Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 15: Multiple Integrals Double and Iterated Integrals over Rectangles Double Integrals over General Regions Area by Double Integration Double Integrals in Polar Form Triple Integrals in Rectangular Coordinates Moments and Centers of Mass Triple Integrals in Cylindrical and Spherical Coordinates Substitutions in Multiple Integrals Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 16: Integrals and Vector Fields Line Integrals Vector Fields and Line Integrals: Work, Circulation, and Flux Path Independence, Conservative Fields, and Potential Functions Green’s Theorem in the Plane Surfaces and Area Surface Integrals Stokes’ Theorem The Divergence Theorem and a Unified Theory Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises Chapter 17: Second-Order Differential Equations Second-Order Linear Equations Nonhomogeneous Linear Equations Applications Euler Equations Power Series Solutions Appendices Real Numbers and the Real Line Mathematical Induction Lines, Circles, and Parabolas Proofs of Limit Theorems Commonly Occurring Limits Theory of the Real Numbers Complex Numbers The Distributive Law for Vector Cross Products The Mixed Derivative Theorem and the Increment Theorem Answers to Odd-Numbered Exercises Index Credits A Brief Table of Integrals Basic Formulas and Rules