Single Variable Calculus: Early Transcendentals

Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher’s voice beyond the classroom. That voice–evident in the narrative, the figures, and the questions interspersed in the narrative–is a master teacher leading readers to deeper levels of understanding. The authors appeal to readers’ geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope.

Table of Contents:
Chapter 1: Functions 1.1 Review of Functions 1.2 Representing Functions 1.3 Inverse, Exponential, and Logarithm Functions 1.4 Trigonometric Functions and Their Inverses   Chapter 2: Limits 2.1 The Idea of Limits 2.2 Definitions of Limits 2.3 Techniques for Computing Limits 2.4 Infinite Limits 2.5 Limits at Infinity 2.6 Continuity 2.7 Precise Definitions of Limits   Chapter 3: Derivatives 3.1 Introducing the Derivative 3.2 Rules of Differentiation 3.3 The Product and Quotient Rules 3.4 Derivatives of Trigonometric Functions 3.5 Derivatives as Rates of Change 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Logarithmic and Exponential Functions 3.9 Derivatives of Inverse Trigonometric Functions 3.10 Related Rates   Chapter 4: Applications of the Derivative 4.1 Maxima and Minima 4.2 What Derivatives Tell Us 4.3 Graphing Functions 4.4 Optimization Problems 4.5 Linear Approximation and Differentials 4.6 Mean Value Theorem 4.7 L’Hôpital’s Rule 4.8 Antiderivatives   Chapter 5: Integration 5.1 Approximating Areas under Curves 5.2 Definite Integrals 5.3 Fundamental Theorem of Calculus 5.4 Working with Integrals 5.5 Substitution Rule   Chapter 6: Applications of Integration 6.1 Velocity and Net Change 6.2 Regions between Curves 6.3 Volume by Slicing 6.4 Volume by Shells 6.5 Length of Curves 6.6 Physical Applications 6.7 Logarithmic and exponential functions revisited 6.8 Exponential models   Chapter 7: Integration Techniques 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 7.4 Partial Fractions 7.5 Other Integration Strategies 7.6 Numerical Integration 7.7 Improper Integrals 7.8 Introduction to Differential Equations   Chapter 8: Sequences and Infinite Series 8.1 An Overview 8.2 Sequences 8.3 Infinite Series 8.4 The Divergence and Integral Tests 8.5 The Ratio and Comparison Tests 8.6 Alternating Series   Chapter 9: Power Series 9.1 Approximating Functions with Polynomials 9.2 Power Series 9.3 Taylor Series 9.4 Working with Taylor Series   Chapter 10: Parametric and Polar Curves 10.1 Parametric Equations 10.2 Polar Coordinates 10.3 Calculus in Polar Coordinates 10.4 Conic Sections