[eBook] [PDF] for Calculus, Single and Multivariable, 7th Edition By Deborah Hughes-Hallett

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Cover Page Title Page Dedication Copyright Preface Acknowledgments Chapter 1: Foundation for Calculus: Functions and Limits 1.1 Functions and change 1.2 Exponential functions 1.3 New function... s from old 1.4 Logarithmic functions 1.5 Trigonometric functions 1.6 Powers, Polynomials, and Rational functions 1.7 Introduction to limits and continuity 1.8 Extending the idea of a limit 1.9 Further limit calculations using Algebra 1.10 Optional preview of the formal definition of a limit Chapter 2: Key Concept: The Derivative 2.1 How do we measure speed? 2.2 The Derivative at a point 2.3 The Derivative function 2.4 Interpretations of the derivative 2.5 The second derivative 2.6 Differentiability Chapter 3: Short-Cuts to Differentiation 3.1 Powers and Polynomials 3.2 The Exponential Function 3.3 The Product and Quotient Rules 3.4 The Chain Rule 3.5 The Trigonometric functions 3.6 The chain rule and inverse functions 3.7 Implicit functions 3.8 Hyperbolic functions 3.9 Linear approximation and the derivative 3.10 Theorems about differentiable functions Chapter 4 Using the Derivative 4.1 Using first and second derivatives 4.2 Optimization 4.3 Optimization and Modeling 4.4 Families of functions and Modeling 4.5 Applications to marginality 4.6 Rates and related rates 4.7 L'Hopital's rule, growth, and dominance 4.8 Parametric Equations Chapter 5: Key Concept: The Definite Integral 5.1 How do we measure distance traveled? 5.2 The definite integral 5.3 The fundamental theorem and interpretations 5.4 Theorems about definite integrals Chapter 6: Constructing Antiderivatives 6.1 Antiderivatives graphically and numerically 6.2 Constructing antiderivatives analytically 6.3 Differential equations and motion 6.4 Second fundamental theorem of calculus Chapter 7: Integration 7.1 Integration by substitution 7.2 Integration by parts 7.3 Tables of integrals 7.4 Algebraic identities and trigonometric substitutions 7.5 Numerical methods for definite integrals 7.6 Improper integrals 7.7 Comparison of improper integrals Chapter 8: Using the Definite Integral 8.1 Areas and volumes 8.2 Applications to geometry 8.3 Area and ARC length in polar coordinates 8.4 Density and center of mass 8.5 Applications to physics 8.6 Applications to economics 8.7 Distribution Functions 8.8 Probability, mean, and median Chapter 9: Sequences and Series 9.1 Sequences 9.2 Geometric series 9.3 Convergence of series 9.4 Tests for convergence 9.5 Power series and interval of convergence Chapter 10: Approximating Functions using Series 10.1 Taylor polynomials 10.2 Taylor series 10.3 Finding and using taylor series 10.4 The error in taylor polynomial approximations 10.5 Fourier Series Chapter 11: Differential Equations 11.1 What is a differential equation? 11.2 Slope fields 11.3 Euler's method 11.4 Separation of variables 11.5 Growth and decay 11.6 Applications and modeling 11.7 The Logistic model 11.8 Systems of differential equations 11.9 Analyzing the phase plane 11.10 Second-order differential equations: Oscillations 11.11 Linear second-order differential equations Chapter 12: Functions of Several Variables 12.1 Functions of two variables 12.2 Graphs and surfaces 12.3 Contour diagrams 12.4 Linear functions 12.5 Functions of three variables 12.6 Limits and continuity Chapter 13: A Fundamental Tool: Vectors 13.1 Displacement vectors 13.2 Vectors in general 13.3 The Dot product 13.4 The Cross product Chapter 14: Differentiating Functions of Several Variables 14.1 The Partial derivative 14.2 Computing partial derivatives algebraically 14.3 Local linearity and the differential 14.4 Gradients and directional derivatives in the plane 14.5 Gradients and directional derivatives in space 14.6 The Chain Rule 14.7 Second-order partial derivatives 14.8 Differentiability Chapter 15: Optimization: Local and Global Extrema 15.1 Critical Points: Local extrema and saddle points 15.2 Optimization 15.3 Constrained optimization: Lagrange multipliers Chapter 16: Integrating Functions of Several Variables 16.1 The Definite integral of a function of two variables 16.2 Iterated integrals 16.3 Triple integrals 16.4 Double integrals in polar coordinates 16.5 Integrals in cylindrical and spherical coordinates 16.6 Applications of integration to probability Chapter 17: Parameterization and Vector Fields 17.1 Parameterized curves 17.2 Motion, velocity, and acceleration 17.3 Vector fields 17.4 The Flow of a vector field Chapter 18: Line Integrals 18.1 The Idea of a line integral 18.2 Computing line integrals over parameterized curves 18.3 Gradient fields and path-independent fields 18.4 Path-dependent vector fields and green's theorem Chapter 19: Flux Integrals and Divergence 19.1 The Idea of a flux integral 19.2 Flux integrals for graphs, cylinders, and spheres 19.3 The Divergence of a vector field 19.4 The Divergence theorem Chapter 20: The Curl and Stokes' Theorem 20.1 The Curl of a vector field 20.2 Stokes' theorem 20.3 The Three fundamental theorems Chapter 21: Parameters, Coordinates, and Integrals 21.1 Coordinates and parameterized surfaces 21.2 Change of coordinates in a multiple integral 21.3 Flux integrals over parameterized surfaces Appendices A Roots, Accuracy, and Bounds B Complex Numbers C Newton's Method D Vectors in the Plane Ready Reference Index EULA [Show More]

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