Calculus : Early Transcendentals

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This text is rigorous, fairly traditional and is appropriate for engineering and science calculus tracks. Hallmarks are accuracy, strong engineering and science applications, deep problem sets (in quantity, depth, and range), and spectacular more

Product details

  • Hardback | 1344 pages
  • 213.4 x 279.4 x 45.7mm | 2,812.31g
  • Pearson Education (US)
  • Pearson
  • Upper Saddle River, NJ, United States
  • English
  • 7th edition
  • 0131569899
  • 9780131569898

About C. Henry Edwards

C. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to being author or co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979). During the 1990s, he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based computer lab project for numerical analysis and differential equations students. David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 (under the direction of Prof. L. Bruce Treybig) while teaching at the University of New Orleans. Earlier he had worked in experimental biophysics at Tulane University and the Veteran's Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee's research team's primary focus was on the active transport of sodium ions by biological membranes. Penney's primary contribution here was the development of a mathematical model (using simultaneous ordinary differential equations) for the metabolic phenomena regulating such transport, with potential future applications in kidney physiology, management of hypertension, and treatment of congestive heart failure. He also designed and constructed servomechanisms for the accurate monitoring of ion transport, a phenomenon involving the measurement of potentials in microvolts at impedances of millions of megohms. Penney began teaching calculus at Tulane in 1957 and taught that course almost every term with enthusiasm and distinction until his retirement at the end of the last millennium. During his tenure at the University of Georgia, he received numerous University-wide teaching awards as well as directing several doctoral dissertations and seven undergraduate research projects. He is the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts more

Table of contents

TABLE OF CONTENTS About the AuthorsPreface 1 Functions, Graphs, and Models 1.1 Functions and Mathematical Modeling Investigation: Designing a Wading Pool 1.2 Graphs of Equations and Functions 1.3 Polynomials and Algebraic Functions 1.4 Transcendental Functions 1.5 Preview: What Is Calculus? REVIEW - Understanding: Concepts and Definitions Objectives: Methods and Techniques 2 Prelude to Calculus 2.1 Tangent Lines and Slope Predictors Investigation: Numerical Slope Investigations 2.2 The Limit Concept Investigation: Limits, Slopes, and Logarithms 2.3 More About Limits Investigation: Numerical Epsilon-Delta Limits 2.4 The Concept of Continuity REVIEW - Understanding: Concepts and Definitions Objectives: Methods and Techniques 3 The Derivative 3.1 The Derivative and Rates of Change 3.2 Basic Differentiation Rules 3.3 The Chain Rule 3.4 Derivatives of Algebraic Functions 3.5 Maxima and Minima of Functions on Closed Intervals Investigation: When Is Your Coffee Cup Stablest? 3.6 Applied Optimization Problems 3.7 Derivatives of Trigonometric Functions 3.8 Exponential and Logarithmic Functions Investigation: Discovering the Number e for Yourself 3.9 Implicit Differentiation and Related Rates Investigation: Constructing the Folium of Descartes 3.10 Successive Approximations and Newton's Method Investigation: How Deep Does a Floating Ball Sink? REVIEW - Understanding: Concepts, Definitions, and Formulas Objectives: Methods and Techniques 4 Additional Applications of the Derivative 4.1 Introduction 4.2 Increments, Differentials, and Linear Approximation 4.3 Increasing and Decreasing Functions and the Mean Value Theorem 4.4 The First Derivative Test and Applications Investigation: Constructing a Candy Box With Lid 4.5 Simple Curve Sketching 4.6 Higher Derivatives and Concavity 4.7 Curve Sketching and Asymptotes Investigation: Locating Special Points on Exotic Graphs 4.8 Indeterminate Forms and L'Hopital's Rule 4.9 More Indeterminate Forms REVIEW - Understanding: Concepts, Definitions, and Results Objectives: Methods and Techniques 5 The Integral 5.1 Introduction 5.2 Antiderivatives and Initial Value Problems 5.3 Elementary Area Computations 5.4 Riemann Sums and the Integral Investigation: Calculator/Computer Riemann Sums 5.5 Evaluation of Integrals 5.6 The Fundamental Theorem of Calculus 5.7 Integration by Substitution 5.8 Areas of Plane Regions 5.9 Numerical Integration Investigation: Trapezoidal and Simpson Approximations REVIEW - Understanding: Concepts, Definitions, and Results Objectives: Methods and Techniques 6 Applications of the Integral 6.1 Riemann Sum Approximations 6.2 Volumes by the Method of Cross Sections 6.3 Volumes by the Method of Cylindrical Shells Investigation: Design Your Own Ring! 6.4 Arc Length and Surface Area of Revolution 6.5 Force and Work 6.6 Centroids of Plane Regions and Curves 6.7 The Natural Logarithm as an Integral Investigation: Natural Functional Equations 6.8 Inverse Trigonometric Functions 6.9 Hyperbolic Functions REVIEW - Understanding: Concepts, Definitions, and Formulas Objectives: Methods and Techniques 7 Techniques of Integration 7.1 Introduction 7.2 Integral Tables and Simple Substitutions 7.3 Integration by Parts 7.4 Trigonometric Integrals 7.5 Rational Functions and Partial Fractions 7.6 Trigonometric Substitutions 7.7 Integrals Involving Quadratic Polynomials 7.8 Improper Integrals SUMMARY - Integration Strategies REVIEW - Understanding: Concepts and Techniques Objectives: Methods and Techniques 8 Differential Equations 8.1 Simple Equations and Models 8.2 Slope Fields and Euler's Method Investigation: Computer-Assisted Slope Fields and Euler's Method 8.3 Separable Equations and Applications 8.4 Linear Equations and Applications 8.5 Population Models Investigation: Predator-Prey Equations and Your Own Game Preserve 8.6 Linear Second-Order Equations 8.7 Mechanical Vibrations REVIEW - Understanding: Concepts, Definitions, and Methods Objectives: Methods and Techniques 9 Polar Coordinates and Parametric Curves 9.1 Analytic Geometry and the Conic Sections 9.2 Polar Coordinates 9.3 Area Computations in Polar Coordinates 9.4 Parametric Curves Investigation: Trochoids Galore 9.5 Integral Computations with Parametric Curves Investigation: Moon Orbits and Race Tracks 9.6 Conic Sections and Applications REVIEW - Understanding: Concepts, Definitions, and Formulas Objectives: Methods and Techniques 10 Infinite Series 10.1 Introduction 10.2 Infinite Sequences Investigation: Nested Radicals and Continued Fractions 10.3 Infinite Series and Convergence Investigation: Numerical Summation and Geometric Series 10.4 Taylor Series and Taylor Polynomials Investigation: Calculating Logarithms on a Deserted Island 10.5 The Integral Test Investigation: The Number p, Once and for All 10.6 Comparison Tests for Positive-Term Series 10.7 Alternating Series and Absolute Convergence 10.8 Power Series 10.9 Power Series Computations Investigation: Calculating Trigonometric Functions on a Deserted Island 10.10 Series Solutions of differential Equations REVIEW - Understanding: Concepts, and Results Objectives: Methods and Techniques 11 Vectors, Curves, and Surfaces in Space 11.1 Vectors in the Plane 11.2 Three-Dimensional Vectors 11.3 The Cross Product of Two Vectors 11.4 Lines and Planes in Space 11.5 Curves and Motion in Space Investigation: Does a Pitched Baseball Really Curve? 11.6 Curvature and Acceleration 11.7 Cylinders and Quadric Surfaces 11.8 Cylindrical and Spherical Coordinates REVIEW - Understanding: Concepts, Definitions, and Results Objectives: Methods and Techniques 12 Partial Differentiation 12.1 Introduction 12.2 Functions of Several Variables 12.3 Limits and Continuity 12.4 Partial Derivatives 12.5 Multivariable Optimization Problems 12.6 Increments and Linear Approximation 12.7 The Multivariable Chain Rule 12.8 Directional Derivatives and the Gradient Vector 12.9 Lagrange Multipliers and Constrained Optimization Investigation: Numerical Solution of Lagrange Multiplier Systems 12.10 Critical Points of Functions of Two Variables Investigation: Critical Point Investigations REVIEW - Understanding: Concepts, Definitions, and Results Objectives: Methods and Techniques 13 Multiple Integrals 13.1 Double Integrals Investigation: Midpoint Sums Approximating Double Integrals 13.2 Double Integrals over More General Regions 13.3 Area and Volume by Double Integration 13.4 Double Integrals in Polar Coordinates 13.5 Applications of Double Integrals Investigation: Optimal Design of Race Car Wheels 13.6 Triple Integrals Investigation: Archimedes' Floating Paraboloid 13.7 Integration in Cylindrical and Spherical Coordinates 13.8 Surface Area 13.9 Change of Variables in Multiple Integrals REVIEW - Understanding: Concepts, Definitions, and Results Objectives: Methods and Techniques 14 Vector Calculus 14.1 Vector Fields 14.2 Line Integrals 14.3 The Fundamental Theorem and Independence of Path 14.4 Green's Theorem 14.5 Surface Integrals Investigation: Surface Integrals and Rocket Nose Cones 14.6 The Divergence Theorem 14.7 Stokes' Theorem REVIEW - Understanding: Concepts, Definitions, and Results Objectives: Methods and Techniques AppendicesA: Real Numbers and InequalitiesB: The Coordinate Plane and Straight LinesC: Review of TrigonometryD: Proofs of the Limit LawsE: The Completeness of the Real Number SystemF: Existence of the IntegralG: Approximations and Riemann SumsH: L'Hopital's Rule and Cauchy's Mean Value TheoremI: Proof of Taylor's FormulaJ: Conic Sections as Sections of a ConeK: Proof of the Linear Approximation TheoremL: Units of Measurement and Conversion FactorsM: Formulas from Algebra, Geometry, and TrigonometryN: The Greek Alphabet Answers to Odd-Numbered ProblemsReferences for Further StudyIndexshow more

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