Calculus: Single and Multivariable
by Deborah Hughes-Hallett, Andrew M. Gleason, William G. McCallum
8th Edition
Publisher: Wiley
Book Details
| Print ISBN | 9781119696551 |
| eText ISBN | 9781119694298 |
| Publisher | Wiley |
| Publishing Year | 2020 |
| Edition | 8th Edition |
| Language | English |
| Pages | 1216 |
Mastering higher-level mathematics requires more than memorizing formulas; it demands a deep, intuitive grasp of how mathematical concepts operate in the real world. Calculus: Single and Multivariable 8th Edition addresses this educational challenge directly by transforming abstract theory into practical, visual problem-solving tools. Created by the Calculus Consortium based at Harvard University, this landmark textbook continues to lead the field in promoting active learning and critical thinking. In an era where data-driven fields like machine learning, quantitative finance, and bioengineering are expanding rapidly, a robust understanding of calculus has never been more vital. This edition equips students with the analytical agility needed to navigate these complex disciplines.
The authors structure their curriculum around the celebrated Rule of Four, which examines mathematical problems from graphical, numerical, symbolic, and verbal perspectives. This multi-faceted approach ensures that students with diverse learning styles can find an entry point into complex topics. By balancing rigorous theory with practical applications, the text covers everything from basic functions and limits to vector calculus and multivariable integration. Rather than treating calculus as a series of isolated procedures, the authors emphasize the underlying connections between derivatives, integrals, and real-world change. This cohesive framework helps students build a solid conceptual foundation that supports advanced study in science, technology, engineering, and mathematics.
Designed specifically to support active learning and flipped classroom environments, Calculus: Single and Multivariable 8th Edition engages students across multiple majors with current, highly relevant examples. This edition introduces interactive graphing questions and dynamic visualizations powered by GeoGebra, allowing learners to manipulate figures and explore mathematical relationships in real time. Instructors and students alike will find that the Calculus: Single and Multivariable 8th Edition PDF provides a seamless digital learning experience, making complex multi-part questions highly accessible. Whether you are an engineering major, an economics student, or a future researcher, this text delivers the essential skills needed to master the language of change.
Table of Contents
Chapter 1: Foundation For Calculus: Functions and Limits
- • Functions and Change
- • Exponential Functions
- • New Functions From Old
- • Logarithmic Functions
- • Trigonometric Functions
- • Powers, Polynomials, and Rational Functions
- • Introduction To Limits and Continuity
- • Extending The Idea of A Limit
- • Further Limit Calculations Using Algebra
- • Preview of The Formal Definition of A Limit
Chapter 2: Key Concept: The Derivative
- • How Do We Measure Speed?
- • The Derivative At A Point
- • The Derivative Function
- • Interpretations of The Derivative
- • The Second Derivative
- • Differentiability
Chapter 3: Short-Cuts To Differentiation
- • Powers and Polynomials
- • The Exponential Function
- • The Product and Quotient Rules
- • The Chain Rule
- • The Trigonometric Functions
- • The Chain Rule and Inverse Functions
- • Implicit Functions
- • Hyperbolic Functions
- • Linear Approximation and The Derivative
- • Theorems About Differentiable Functions
Chapter 4: Using The Derivative
- • Using First and Second Derivatives
- • Optimization
- • Optimization and Modeling
- • Families of Functions and Modeling
- • Applications To Marginality
- • Rates and Related Rates
- • L'hopital's Rule, Growth, and Dominance
- • Parametric Equations
Chapter 5: Key Concept: The Definite Integral
- • How Do We Measure Distance Traveled?
- • The Definite Integral
- • The Fundamental Theorem and Interpretations
- • Theorems About Definite Integrals
Chapter 6: Constructing Antiderivatives
- • Antiderivatives Analytically
- • Antiderivatives Graphically and Numerically
- • The Equations of Motion
- • The Second Fundamental Theorem of Calculus
Chapter 7: Integration Techniques and Applications
- • Integration by Substitution
- • Integration by Parts
- • Tables of Integrals
- • Algebraic Identities and Trigonometric Substitutions
- • Numerical Methods for Definite Integrals
- • Improper Integrals
- • Comparison of Improper Integrals
Chapter 8: Using the Definite Integral
- • Areas and Volumes
- • Applications to Geometry
- • Applications to Physics
- • Applications to Economics
- • Applications to Biology
Chapter 9: Sequences and Series
- • Geometric Series
- • Convergence of Series
- • Tests for Convergence
- • Power Series
- • Taylor Series
- • Applications of Taylor Series
Chapter 10: Multivariable Functions
- • Functions of Two or More Variables
- • Graphs and Contour Diagrams
- • Linear Functions
- • Limits and Continuity
Chapter 11: Derivatives for Multivariable Functions
- • Partial Derivatives
- • The Tangent Approximation
- • The Gradient Vector
- • Directional Derivatives
- • Local and Global Extrema
- • Constrained Optimization
Chapter 12: Integrals for Multivariable Functions
- • Double Integrals
- • Double Integrals in Polar Coordinates
- • Triple Integrals
- • Triple Integrals in Cylindrical and Spherical Coordinates
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▶Research Sources (10)
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