Calculus
Subtitle: Single and multivariable
Publisher: John wiley
Published: 2012
Place of publication: [s.l.]
Language: eng
Number of pages: 1248
ISBN-13: 9780470888612
Table of contents: title: Machine generated contents note: 1.A Library Of Functions; title: 1.1.Functions And Change; title: 1.2.Exponential Functions; title: 1.3.New Functions From Old; title: 1.4.Logarithmic Functions; title: 1.5.Trigonometric Functions; title: 1.6.Powers, Polynomials, And Rational Functions; title: 1.7.Introduction To Continuity; title: 1.8.Limits; title: Review Problems; title: Projects; title: 2.Key Concept: The Derivative; title: 2.1.How Do We Measure Speed?; title: 2.2.The Derivative At A Point; title: 2.3.The Derivative Function; title: 2.4.Interpretations Of The Derivative; title: 2.5.The Second Derivative; title: 2.6.Differentiability; title: Review Problems; title: Projects; title: 3.Short-cuts To Differentiation; title: 3.1.Powers And Polynomials; title: 3.2.The Exponential Function; title: 3.3.The Product And Quotient Rules; title: 3.4.The Chain Rule; title: 3.5.The Trigonometric Functions; title: 3.6.The Chain Rule And Inverse Functions; title: 3.7.Implicit Functions; title: 3.8.Hyperbolic Functions; title: 3.9.Linear Approximation And The Derivative; title: 3.10.Theorems About Differentiable Functions; title: Contents note continued: Review Problems; title: Projects; title: 4.Using The Derivative; title: 4.1.Using First And Second Derivatives; title: 4.2.Optimization; title: 4.3.Optimization And Modeling; title: 4.4.Families Of Functions And Modeling; title: 4.5.Applications To Marginality; title: 4.6.Rates And Related Rates; title: 4.7.L'hopital's Rule, Growth, And Dominance; title: 4.8.Parametric Equations; title: Review Problems; title: Project's; title: 5.Key Concept: The Definite Integral; title: 5.1.How Do We Measure Distance Traveled?; title: 5.2.The Definite Integral; title: 5.3.The Fundamental Theorem And Interpretations; title: 5.4.Theorems About Definite Integrals; title: Review Problems; title: Projects; title: 6.Constructing Antiderivatives; title: 6.1.Antiderivatives Graphically And Numerically; title: 6.2.Constructing Antiderivatives Analytically; title: 6.3.Differential Equations And Motion; title: 6.4.Second Fundamental Theorem Of Calculus; title: Review Problems; title: Projects; title: 7.Integration; title: 7.1.Integration By Substitution; title: 7.2.Integration By Parts; title: 7.3.Tables Of Integrals; title: Contents note continued: 7.4.Algebraic Identities And Trigonometric Substitutions; title: 7.5.Numerical Methods For Definite Integrals; title: 7.6.Improper Integrals; title: 7.7.Comparison Of Improper Integrals; title: Review Problems; title: Projects; title: 8.Using The Definite Integral; title: 8.1.Areas And Volumes; title: 8.2.Applications To Geometry; title: 8.3.Area And Arc Length In Polar Coordinates; title: 8.4.Density And Center Of Mass; title: 8.5.Applications To Physics; title: 8.6.Applications To Economics; title: 8.7.Distribution Functions; title: 8.8.Probability, Mean, And Median; title: Review Problems; title: Projects; title: 9.Sequences And Series; title: 9.1.Sequences; title: 9.2.Geometric Series; title: 9.3.Convergence Of Series; title: 9.4.Tests For Convergence; title: 9.5.Power Series And Interval Of Convergence; title: Review Problems; title: Projects; title: 10.Approximating Functions Using Series; title: 10.1.Taylor Polynomials; title: 10.2.Taylor Series; title: 10.3.Finding And Using Taylor Series; title: 10.4.The Error In Taylor Polynomial Approximations; title: 10.5.Fourier Series; title: Contents note continued: Review Problems; title: Projects; title: 11.Differential Equations; title: 11.1.What Is A Differential Equation?; title: 11.2.Slope Fields; title: 11.3.Euler's Method; title: 11.4.Separation Of Variables; title: 11.5.Growth And Decay; title: 11.6.Applications And Modeling; title: 11.7.The Logistic Model; title: 11.8.Systems Of Differential Equations; title: 11.9.Analyzing The Phase Plane; title: Review Problems; title: Projects; title: 12.Functions Of Several Variables; title: 12.1.Functions Of Two Variables; title: 12.2.Graphs And Surfaces; title: 12.3.Contour Diagrams; title: 12.4.Linear Functions; title: 12.5.Functions Of Three Variables; title: 12.6.Limits And Continuity; title: Review Problems; title: Projects; title: 13.A Fundamental Tool: Vectors; title: 13.1.Displacement Vectors; title: 13.2.Vectors In General; title: 13.3.The Dot Product; title: 13.4.The Cross Product; title: Review Problems; title: Projects; title: 14.Differentiating Functions Of Several Variables; title: 14.1.The Partial Derivative; title: 14.2.Computing Partial Derivatives Algebraically; title: 14.3.Local Linearity And The Differential; title: Contents note continued: 14.4.Gradients And Directional Derivatives In The Plane; title: 14.5.Gradients And Directional Derivatives In Space; title: 14.6.The Chain Rule; title: 14.7.Second-order Partial Derivatives; title: 14.8.Differentiability; title: Review Problems; title: Projects; title: 15.Optimization: Local and Global Extrema; title: 15.1.Critical Points: Local Extrema And Saddle Points; title: 15.2.Optimization; title: 15.3.Constrained Optimization: Lagrange Multipliers; title: Review Problems; title: Projects; title: 16.Integrating Functions Of Several Variables; title: 16.1.The Definite Integral Of A Function Of Two Variables; title: 16.2.Iterated Integrals; title: 16.3.Triple Integrals; title: 16.4.Double Integrals In Polar Coordinates; title: 16.5.Integrals In Cylindrical And Spherical Coordinates; title: 16.6.Applications Of Integration To Probability; title: Review Problems; title: Projects; title: 17.Parameterization And Vector Fields; title: 17.1.Parameterized Curves; title: 17.2.Motion, Velocity, And Acceleration; title: 17.3.Vector Fields; title: 17.4.The Flow Of A Vector Held; title: Contents note continued: Review Problems; title: Projects; title: 18.Line Integrals; title: 18.1.The Idea Of A Line Integral; title: 18.2.Computing Line Integrals Over Parameterized Curves; title: 18.3.Gradient Fields And Path-independent Fields; title: 18.4.Path-dependent Vector Fields And Green's Theorem; title: Review Problems; title: Projects; title: 19.Flux Integrals And Divergence; title: 19.1.The Idea Of A Flux Integral; title: 19.2.Flux Integrals For Graphs, Cylinders, And Spheres; title: 19.3.The Divergence Of A Vector Field; title: 19.4.The Divergence Theorem; title: Review Problems; title: Projects; title: 20.The Curl And Stokes' Theorem; title: 20.1.The Curl Of A Vector Field; title: 20.2.Stokes' Theorem; title: 20.3.The Three Fundamental Theorems; title: Review Problems; title: Projects; title: 21.Parameters, Coordinates, And Integrals; title: 21.1.Coordinates And Parameterized Surfaces; title: 21.2.Change Of Coordinates In A Multiple Integral; title: 21.3.Flux Integrals Over Parameterized Surfaces; title: Review Problems; title: Projects; title: APPENDIX; title: A.Roots, Accuracy, And Bounds; title: Contents note continued: B.Complex Numbers; title: C.Newton's Method; title: D.Vectors In The Plane; title: E.Determinants.