9781429210751

Organized to support an "early transcendentals" approach to the single variable course, this version of Rogawski's highly anticipated text presents calculus with solid mathematical precision but with an everyday sensibility that puts the main concepts in clear terms. It is rigorous without being inaccessible and clear without being too informalit has the perfect balance for instructors and their students.

About Jon Rogawski
Jon Rogawski received his undergraduate degree (and simultaneously a master's degree in mathematics) at Yale, and a Ph.D. in mathematics from Princeton University, where he studied under Robert Langlands. Prior to joining the Department of Mathematics at UCLA, where he is currently Full Professor, he held teaching positions at Yale and the University of Chicago, and research positions at the Institute for Advanced Study and University of Bonn.

Jon's areas of interest are number theory, automorphic forms, and harmonic analysis on semisimple groups. He has published numerous research articles in leading mathematical journals, including a research monograph entitled "Automorphic Representations of Unitary Groups in Three Variables" (Princeton University Press). He is the recipient of a Sloan Fellowship and an editor of The Pacific Journal of Mathematics.

Jon and his wife Julie, a physician in family practice, have four children. They run a busy household and, whenever possible, enjoy family vacations in the mountains of California. Jon is a passionate classical music lover and plays the violin and classical guitar.

Chapter 1 PRECALCULUS REVIEW
1.1 Real Numbers, Functions, Equations, and Graphs
1.2 Linear and Quadratic Functions
1.3 The Basic Classes of Functions
1.4 Trigonometric Functions
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
1.7 Technology: Calculators and Computers

Chapter 2 LIMITS
2.1 Limits, Rates of Change, and Tangent Lines
2.2 Limits: A Numerical and Graphical Approach
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Evaluating Limits Algebraically
2.6 Trigonometric Limits
2.7 Intermediate Value Theorem
2.8 The Formal Definition of a Limit

Chapter 3 DIFFERENTIATION
3.1 Definition of the Derivative
3.2 The Derivative as a Function
3.3 Product and Quotient Rules
3.4 Rates of Change
3.5 Higher Derivatives
3.6 Derivatives of Trigonometric Functions
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Derivatives of Inverse Functions
3.10 Derivatives of Logarithmic Functions
3.11 Related Rates

Chapter 4 APPLICATIONS OF THE DERIVATIVE
4.1 Linear Approximation and Applications
4.2 Extreme Values
4.3 The Mean Value Theorem and Monotonicity
4.4 The Shape of a Graph
4.5 Graph Sketching and Asymptotes
4.6 Applied Optimization
4.7 L'HoË†pital's Rule
4.8 Newton's Method
4.9 Antiderivatives

Chapter 5 THE INTEGRAL
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus, Part I
5.4 The Fundamental Theorem of Calculus, Part II
5.5 Net or Total Change as the Integral of a Rate
5.6 Substitution Method
5.7 Integrals of Exponential and Logarithmic Functions
5.8 Exponential Growth and Decay

Chapter 6 APPLICATIONS OF THE INTEGRAL
6.1 Area Between Two Curves
6.2 Setting Up Integrals: Volumes, Density, Average Value
6.3 Volumes of Revolution
6.4 The Method of Cylindrical Shells
6.5 Work and Energy

Chapter 7 TECHNIQUES OF INTEGRATION
7.1 Numerical Integration
7.2 Integration by Parts
7.3 Trigonometric Integrals
7.4 Trigonometric Substitution
7.5 Integrals of Hyperbolic and Inverse Hyperbolic
Functions
7.6 The Method of Partial Fractions
7.7 Improper Integrals

Chapter 8 FURTHER APPLICATIONSOF THE INTEGRAL AND TAYLOR POLYNOMIALS
8.1 Arc Length and Surface Area
8.2 Fluid Pressure and Force
8.3 Center of Mass
8.4 Taylor Polynomials

Chapter 9 INTRODUCTION TO DIFFERENTIAL EQUATIONS
9.1 Separable Equations
9.2 Models Involving y'= k(y-b)
9.3 Graphical and Numerical Methods
9.4 The Logistic Equation
9.5 First-order Linear Equations

Chapter 10 INFINITE SERIES
10.1 Sequences
10.2 Summing an Infinite Series
10.3 Convergence of Series with Positive Terms
10.4 Absolute and Conditional Convergence
10.5 The Ratio and Root Tests
10.6 Power Series
10.7 Taylor Series

Chapter 11 PARAMETRIC EQUATIONS, mPOLAR COORDINATES, AND CONIC SECTIONS
11.1 Parametric Equations
11.2 Arc Length and Speed
11.3 Polar Coordinates
11.4 Area and Arc Length in Polar Coordinates
11.5 Conic Sections

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Single Variable Calculus: Early Transcendentals

Single Variable Calculus: Early Transcendentals

1429210753

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