Calculus / / Stanley I. Grossman

• Autore: Grossman Stanley I.
• Pubblicazione: Orlando, Florida ; ; London, England : , : Academic Press, , 1984; ©1984
• Edizione: 3rd ed.
• Descrizione fisica: 1 online resource (1364 p.)
• Disciplina: 515
• Soggetto topico: Calculus
• Note generali: Includes index.
• Nota di contenuto: Front Cover; Calculus; Copyright Page; Dedication; Table ofContents; Preface; To the Instructor; CHAPTER 1.PRELIMINARIES; 1.1 Sets of Real Numbers; 1.2 Absolute Value and Inequalities; 1.3 The Cartesian Plane; 1.4 Lines; 1.5 Equations of a Straight Line; 1.6 Functions; 1.7 Operations with Functions; 1.8 Shifting the Graphs of Functions (Optional); Review Exercises for Chapter One; CHAPTER 2.LIMITS AND DERIVATIVES; 2.1 Introduction to the Derivative; 2.2 The Calculation of Limits; 2.3 The Limit Theorems; 2.4 Infinite Limits and Limits at Infinity; 2.5 Tangent Lines and Derivatives ; 2.6 The Derivative as a Rate of Change2.7 Continuity; 2.8 The Theory of Limits (Optional); Review Exercises for Chapter Two; CHAPTER 3.MORE ABOUT DERIVATIVES; 3.1 Some Differentiation Formulas; 3.2 The Product and Quotient Rules; 3.3 The Derivative of Composite Functions: The Chain Rule; 3.4 The Derivative of a Power Function; 3.5 The Derivatives of the Trigonometric Functions; 3.6 Implicit Differentiation; 3.7 Higher-Order Derivatives; 3.8 Approximation and Differentials; Review Exercises for Chapter Three; CHAPTER 4.APPLICATIONS OF THE DERIVATIVE; 4.1 Related Rates of Change ; 4.2 The Mean Value Theorem4.3 Elementary Curve Sketching I: Increasing and Decreasing Functions and the First Derivative Test; 4.4 Elementary Curve Sketching II: Concavity and the Second DerivativeTest; 4.5 The Theory of Maxima and Minima; 4.6 Maxima and Minima: Applications; 4.7 Some Applications in Economics (Optional); 4.8 Newton's Method for Solving Equations; Review Exercises for Chapter Four; CHAPTER 5.THE INTEGRAL; 5.1 Introduction; 5.2 Antiderivatives; 5.3 The Σ Notation; 5.4 Approximations to Area; 5.5 The Definite Integral; 5.6 The Fundamental Theorem of Calculus ; 5.7 Integration by Substitution5.8 The Area Between Two Curves; 5.9 Work, Power, and Energy (Optional); 5.10 Additional Integration Theory (Optional); Review Exercises for Chapter Five; CHAPTER 6.EXPONENTIALS AND LOGARITHMS; 6.1 Inverse Functions; 6.2 The Exponential and Logarithmic Functions I; 6.3 The Derivatives and Integrals of logax and ax; 6.4 The Exponential and Logarithmic Functions II; 6.5 Differentiation and Integration of More General Exponential and LogarithmicFunctions; 6.6 Differential Equations of Exponential Growth and Decay; 6.7 Applications in Economics (Optional) ; 6.8 A Model for Epidemics (Optional)Review Exercises for Chapter Six; CHAPTER 7.MORE ON TRIGONOMETRIC FUNCTIONS AND THE HYPERBOLIC FUNCTIONS; 7.1 Integration of Trigonometric Functions; 7.2 The Inverse Trigonometric Functions; 7.3 Periodic Motion (Optional); 7.4 The Hyperbolic Functions; 7.5 The Inverse Hyperbolic Functions (Optional); Review Exercises for Chapter Seven; CHAPTER 8.TECHNIQUES OF INTEGRATION; 8.1 Review of the Basic Formulas of Integration; 8.2 Integration by Parts; 8.3 Integrals of Certain Trigonometric Functions; 8.4 The Idea behind Integration by Substitution ; 8.5 Integrals Involving Va2 - x2, Va2 + x2, and Vx2 - a2: TrigonometricSubstitutions
• Sommario/riassunto: Calculus
• Titolo autorizzato: Calculus
• ISBN: 1-4832-6239-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910819046903321
• Lo trovi qui: Univ. Federico II