Calculus: Early Transcendentals (7th Edition)
A comprehensive textbook covering the fundamentals and advanced topics of calculus, including functions, limits, derivatives, integrals, differential equations, and vector calculus, with an emphasis on conceptual understanding through the 'Rule of Four'.
Course Overview
Content Summary
A comprehensive textbook covering the fundamentals and advanced topics of calculus, including functions, limits, derivatives, integrals, differential equations, and vector calculus, with an emphasis on conceptual understanding through the 'Rule of Four'.
Master the art of calculus with the world's most widely used textbook for early transcendentals.
Author: James Stewart
Acknowledgments: The author acknowledges the help of many reviewers including Amy Austin, Anthony J. Bevelacqua, and others from institutions such as Texas A&M University and University of Florida. Funding and production support provided by Brooks/Cole, Cengage Learning.
Learning Objectives
- Define and represent functions using four methods and determine their domain, range, and symmetry.
- Classify and apply a catalog of essential functions (linear, polynomial, trigonometric, exponential, and logarithmic) to model real-world phenomena.
- Execute vertical/horizontal transformations and function compositions.
- Calculate limits using algebraic laws, direct substitution, and the Squeeze Theorem.
- Define continuity and identify types of discontinuities using limits.
- Apply the Intermediate Value Theorem to locate roots of equations.
- Apply the Power, Product, Quotient, and Chain Rules to differentiate algebraic, trigonometric, exponential, logarithmic, and inverse functions.
- Execute implicit differentiation and logarithmic differentiation to solve complex structural equations and power-based functions (x^x).
- Model and solve real-world rate-of-change problems involving simple harmonic motion, electric current, isothermal compressibility, and Newton’s Law of Cooling.
- Identify and calculate absolute and local extrema using the Closed Interval Method and Fermat’s Theorem.