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Calculus: Early Transcendentalsby Jon Rogawski
Synopses & ReviewsPublisher Comments:Organized to support an "early transcendentals" approach to the 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 informal--it has the perfect balance for instructors and their students. Also available in a late transcendentals version (0-7167-6911-5). About the AuthorAbout 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. Table of ContentsChapter 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'Hoˆpital'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 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 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 Chapter 12 VECTOR GEOMETRY 12.1 Vectors in the Plane 12.2 Vectors in Three Dimensions 12.3 Dot Product and the Angle Between Two Vectors 12.4 The Cross Product 12.5 Planes in Three-Space 12.6 Survey of Quadric Surfaces 12.7 Cylindrical and Spherical Coordinates Chapter 13 CALCULUS OF VECTOR-VALUED FUNCTIONS 13.1 Vector-Valued Functions 13.2 Calculus of Vector-Valued Functions 13.3 Arc Length and Speed 13.4 Curvature 13.5 Motion in Three-Space 13.6 Planetary Motion According to Kepler and Newton Chapter 14 DIFFERENTIATION IN SEVERAL VARIABLES 14.1 Functions in Two or More Variables 14.2 Limits and Continuity in Several Variables 14.3 Partial Derivatives 14.4 Linear Approximation,Differentiability, and Tangent Planes 14.5 The Gradient and Directional Derivatives 14.6 The Chain Rule 14.7 Optimization in Several Variables 14.8 Lagrange Multipliers: Optimizing with a Constraint Chapter 15 MULTIPLE INTEGRATION 15.1 Integrals in Several Variables 15.2 Double Integrals over More General Regions 15.3 Triple Integrals 15.4 Integration in Polar, Cylindrical, and Spherical Coordinates 15.5 Change of Variables Chapter 16 LINE AND SURFACE INTEGRALS 16.1 Vector Fields 16.2 Line Integrals 16.3 Conservative Vector Fields 16.4 Parametrized Surfaces and Surface Integrals 16.5 Integrals of Vector Fields Chapter 17 FUNDAMENTAL THEOREMS OF VECTOR ANALYSIS 17.1 Green's Theorem 17.2 Stokes' Theorem 17.3 Divergence Theorem APPENDICES A. The Language of Mathematics B. Properties of Real Numbers C. Mathematical Induction and the Binomial Theorem D. Additional Proofs of Theorems ANSWERS TO ODD-NUMBERED EXERCISES What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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