INDICE: Chapter 1 Basics Preview 1 Number Systems 2 Planar Coordinates and Graphing in the Plane 3 Lines and Their Slopes 4 Functions and Their Graphs 5 Combining Functions 6 Trigonometry Summary of Key Topics Review Exercises for Chapter 1 Genesis and Development Chapter 2 Limits Preview 1 The Concept of Limit 2 Limit Theorems 3 Continuity 4 Infinite Limits and Asymptotes 5 Limits ofSequences 6 Exponential and Logarithmic Functions Summary of Key Topics Review Exercises Genesis and Development Chapter 3 The Derivative Preview 1 Rates of Change and Tangent Lines 2 The Derivative 3 Rules for Differentiation 4 Differentiation of Some Basic Functions 5 The Chain Rule 6 Derivatives of Inverse Functions 7 Higher Derivatives 8 Implicit Differentiation 9 Differentials and Approximation of Functions 10 Other Transcendental Functions Summary of Key Topics Review Exercises Genesis and Development Chapter 4 Applications of the Derivative Preview 1 Related Rates 2 The Mean Value Theorem 3 Maxima and Minima of Functions 4 Applied Maximum-Minimum Problems 5 Concavity 6 Graphing Functions 7 LHopitals Rule 8 The Newton-Raphson Method 9 Antidifferentiation and Applications Summary of Key Topics Review Exercises Genesis and Development Chapter 5 The Integral Preview 1 Introduction to Integration--The Area Problem 2 TheRiemann Integral 3 Properties of the Integral 4 The Fundamental Theorem of Calculus 5 A Calculus Approach to the Logarithm and Exponential Functions 6 Integration by Substitution 7 More on the Calculation of Area 8 Numerical Techniques of Integration Summary of Key Topics Review Exercises Genesis and Development Chapter 6 Techniques of Integration Preview 1 Integration by Parts 2 Powersand Products of Trigonometric Functions 3 Trigonometric Substitution 4 Partial Fractions--Linear Factors 5 Partial Fractions--Irreducible Quadratic Factors6 Improper Integrals--Unbounded Integrands 7 Improper Integrals--Unbounded Intervals Summary of Key Topics Review Exercises Genesis and Development Chapter7 Applications of the Integral Preview 1 Volumes 2 Arc Length and Surface Area 3 The Average Value of a Function 4 Center of Mass 5 Work 6 First Order Differential Equations--Separable Equations 7 First Order Differential Equations--Linear Equations Summary of Key Topics Review Exercises Genesis and Development Chapter 8 Infinite Series Preview 1 Series 2 The Divergence Test and The Integral Test 3 The Comparison Tests 4 Alternating Series 5 The Ratio and Root Tests 6 Introduction to Power Series 7 Representing Functions by Power Series 8 Taylor Series Summary of Key Topics Review Exercises Genesis and Development Chapter 9 Vectors Preview 1 Vectors in the Plane 2 Vectors in Three-DimensionalSpace 3 The Dot Product and Applications 4 The Cross Product and Triple Product 5 Lines and Planes in Space Summary of Key Topics in Chapter 9 Review Exercises for Chapter 9 Genesis and Development Chapter 10 Curves in Space Preview 1 Vector-Valued Functions--Limits, Derivatives, and Continuity 2 Velocity and Acceleration 3 Tangent Vectors and Arc Length 4 Curvature 5 Applications of Vector-Valued Functions to Motion Summary of Key Topics in Chapter 10 Review Exercises for Chapter 10 Genesis and Development Chapter 11 Functions of Several Variables Preview 1 Functions of Several Variables 2 Cylinders and Quadric Surfaces 3 Limits and Continuity 4 Partial Derivatives 5 Differentiability and The Chain Rule 6 Gradients and Directional Derivatives 7 Tangent Planes 8 Maximum-Minimum Problems 9 Lagrange Multipliers Summary of Key Topics in Chapter 11 Review Exercises for Chapter 11 Genesis and Development Chapter 12 Multiple Integrals Preview 1 Double Integrals over Rectangular Regions 2 Integration overMore General Regions 3 Calculation of Volumes of Solids 4 Polar Coordinates 5Integrating in Polar Coordinates 6 Triple Integrals 7 Physical Applications 8Other Coordinate Systems Summary of Key Topics in Chapter 12 Review Exercisesfor Chapter 12 Genesis and Development Chapter 13 Vector Calculus Preview 1 Vector Fields 2 Line Integrals 3 Conservative Vector Fields and Path Independence 4 Divergence, Gradient, and Curl 5 Greens Theorem 6 Surface Integrals 7 Stokess Theorem 8 The Divergence Theorem Summary of Key Topics in Chapter 13 Review Exercises for Chapter 13 Genesis and Development
- ISBN: 978-0-470-45360-5
- Editorial: John Wiley & Sons
- Encuadernacion: Rústica
- Páginas: 1248
- Fecha Publicación: 12/10/2010
- Nº Volúmenes: 1
- Idioma: Inglés
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