Thomas' Calculus, 15th edition
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Overview
Thomas' Calculus goes beyond memorizing formulas and routine procedures to help you develop deeper understanding. It guides you to a level of mathematical proficiency, with additional support if needed through its clear and intuitive explanations, current applications and generalized concepts. Technology exercises in every section use the calculator or computer for solving problems, and Computer Explorations offer exercises requiring a computer algebra system like Maple or Mathematica. The 15th Edition adds exercises, revises figures and language for clarity, and updates many applications; new online chapters cover Complex Functions, Fourier Series and Wavelets.
Published by Pearson (December 29th 2022)  Copyright © 2023
ISBN13: 9780137616077
Subject: Calculus
Category: Calculus
Table of contents
 Functions
 1.1 Functions and Their Graphs
 1.2 Combining Functions; Shifting and Scaling Graphs
 1.3 Trigonometric Functions
 1.4 Graphing with Software
 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 OneSided Limits
 2.5 Continuity
 2.6 Limits Involving Infinity; Asymptotes of Graphs
 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 Related Rates
 3.10 Linearization and Differentials
 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 Applied Optimization
 4.6 Newton's Method
 4.7 Antiderivatives
 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
 Applications of Definite Integrals
 6.1 Volumes Using CrossSections
 6.2 Volumes Using Cylindrical Shells
 6.3 Arc Length
 6.4 Areas of Surfaces of Revolution
 6.5 Work and Fluid Forces
 6.6 Moments and Centers of Mass
 Transcendental Functions
 7.1 Inverse Functions and Their Derivatives
 7.2 Natural Logarithms
 7.3 Exponential Functions
 7.4 Exponential Change and Separable Differential Equations
 7.5 Indeterminate Forms and L'Hôpital's Rule
 7.6 Inverse Trigonometric Functions
 7.7 Hyperbolic Functions
 7.8 Relative Rates of Growth
 Techniques of Integration
 8.1 Using Basic Integration Formulas
 8.2 Integration by Parts
 8.3 Trigonometric Integrals
 8.4 Trigonometric Substitutions
 8.5 Integration of Rational Functions by Partial Fractions
 8.6 Integral Tables and Computer Algebra Systems
 8.7 Numerical Integration
 8.8 Improper Integrals
 8.9 Probability
 FirstOrder Differential Equations
 9.1 Solutions, Slope Fields, and Euler's Method
 9.2 FirstOrder Linear Equations
 9.3 Applications
 9.4 Graphical Solutions of Autonomous Equations
 9.5 Systems of Equations and Phase Planes
 Infinite Sequences and Series
 10.1 Sequences
 10.2 Infinite Series
 10.3 The Integral Test
 10.4 Comparison Tests
 10.5 Absolute Convergence; The Ratio and Root Tests
 10.6 Alternating Series and Conditional Convergence
 10.7 Power Series
 10.8 Taylor and Maclaurin Series
 10.9 Convergence of Taylor Series
 10.10 Applications of Taylor Series
 Parametric Equations and Polar Coordinates
 11.1 Parametrizations of Plane Curves
 11.2 Calculus with Parametric Curves
 11.3 Polar Coordinates
 11.4 Graphing Polar Coordinate Equations
 11.5 Areas and Lengths in Polar Coordinates
 11.6 Conic Sections
 11.7 Conics in Polar Coordinates
Appendix A
 A.1 Real Numbers and the Real Line
 A.2 Mathematical Induction
 A.3 Lines, Circles, and Parabolas
 A.4 Proofs of Limit Theorems
 A.5 Commonly Occurring Limits
 A.6 Theory of the Real Numbers
 A.7 The Distributive Law for Vector Cross Products
 A.8 The Mixed Derivative Theorem and the Increment Theorem
Appendix B (online)
 B.1 Determinants
 B.2 Extreme Values and Saddle Points for Functions of More than Two Variables
 B.3 The Method of Gradient Descent
Answers to OddNumbered Exercises
Applications Index
Subject Index
A Brief Table of Integrals
Credits
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