Thomas' Calculus

Name: Thomas' Calculus
Price: 94.99 USD
Availability: InStock
ISBN: 9780137615582

by Joel R. Hass, Christopher E. Heil, Maurice D. Weir, Przemyslaw Bogacki

15th Edition

Publisher: Pearson

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Mathematics

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Book Details

Print ISBN	9780137615582
eText ISBN	9780137616237
Publisher	Pearson
Publishing Year	2023
Edition	15th Edition
Language	English
Pages	1000

Mastering the complexities of higher mathematics requires far more than the simple memorization of formulas and mechanical procedures. Thomas' Calculus 15th Edition establishes a rigorous yet highly accessible framework that encourages students to develop a profound, intuitive understanding of mathematical concepts. By balancing precise theoretical foundations with vibrant, real-world applications, this textbook ensures that learners do not just solve equations but truly comprehend the underlying structures of calculus. In an era where data science, advanced engineering, and technological innovation demand exceptional quantitative skills, this updated volume serves as an indispensable foundation for academic and professional success, helping students bridge the gap between abstract theory and practical application in their future careers.

The authors present a cohesive mathematical narrative that spans single-variable and multivariable calculus, guiding students through limits, derivatives, integration, and infinite series. Throughout Thomas' Calculus 15th Edition, the pedagogical approach emphasizes clarity and mathematical precision, utilizing beautifully revised figures and modernized language to eliminate ambiguity. The text integrates specialized computer explorations and technology exercises, prompting students to leverage advanced tools like Maple or Mathematica to solve complex problems. This thoughtful blend of classical theory and modern computational practice provides a comprehensive perspective, preparing students to apply mathematical reasoning to diverse scientific disciplines, physical systems, and complex engineering challenges.

Specifically designed for college and university students, this edition introduces several key enhancements, including updated application exercises and brand-new online chapters covering complex functions, Fourier series, and wavelets. Instructors worldwide adopt this textbook for its unparalleled academic accuracy and structured problem-solving strategies that build student confidence. For students seeking a flexible and portable learning solution, the Thomas' Calculus 15th Edition PDF offers seamless digital access to these comprehensive resources. This digital format enables interactive learning, allowing aspiring mathematicians, engineers, and scientists to master challenging concepts at their own pace while maintaining the rigorous standards of the traditional print edition.

Chapter 1: Functions
- • Functions and Their Graphs
- • Combining Functions; Shifting and Scaling Graphs
- • Trigonometric Functions
- • Graphing with Software
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
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
- • Related Rates
- • Linearization and Differentials
Chapter 4: Applications of Derivatives
- • Extreme Values of Functions
- • The Mean Value Theorem
- • Monotonic Functions and the First Derivative Test
- • Concavity and Curve Sketching
- • Applied Optimization
- • Newton's Method
- • Antiderivatives
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
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
Chapter 7: Transcendental Functions
- • Inverse Functions and Their Derivatives
- • Natural Logarithms
- • Exponential Functions
- • Indeterminate Forms and L'Hôpital's Rule
- • Inverse Trigonometric Functions
- • Hyperbolic Functions
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
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
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
- • Applications of Taylor Series
Chapter 11: Parametric Equations and Polar Coordinates
- • Parametric Equations
- • Calculus with Parametric Curves
- • Polar Coordinates
- • Graphing in Polar Coordinates
- • Areas and Lengths in Polar Coordinates
- • Conic Sections
- • Conics in Polar Coordinates
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
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
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
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
- • Applications
- • Triple Integrals in Cylindrical and Spherical Coordinates
- • Substitutions in Multiple Integrals

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Table of Contents

Chapter 1: Functions
- • Functions and Their Graphs
- • Combining Functions; Shifting and Scaling Graphs
- • Trigonometric Functions
- • Graphing with Software
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
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
- • Related Rates
- • Linearization and Differentials
Chapter 4: Applications of Derivatives
- • Extreme Values of Functions
- • The Mean Value Theorem
- • Monotonic Functions and the First Derivative Test
- • Concavity and Curve Sketching
- • Applied Optimization
- • Newton's Method
- • Antiderivatives
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
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
Chapter 7: Transcendental Functions
- • Inverse Functions and Their Derivatives
- • Natural Logarithms
- • Exponential Functions
- • Indeterminate Forms and L'Hôpital's Rule
- • Inverse Trigonometric Functions
- • Hyperbolic Functions
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
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
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
- • Applications of Taylor Series
Chapter 11: Parametric Equations and Polar Coordinates
- • Parametric Equations
- • Calculus with Parametric Curves
- • Polar Coordinates
- • Graphing in Polar Coordinates
- • Areas and Lengths in Polar Coordinates
- • Conic Sections
- • Conics in Polar Coordinates
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
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
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
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
- • Applications
- • Triple Integrals in Cylindrical and Spherical Coordinates
- • Substitutions in Multiple Integrals