Essential Calculus: Early Transcendentals - 2nd Edition - by James Stewart - ISBN 9781133112280
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Essential Calculus: Early Transcendenta...
2nd Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781133112280

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Chapter 2.2 - The Derivative As A FunctionChapter 2.3 - Basic Differentiation FormulasChapter 2.4 - The Product And Quotient RulesChapter 2.5 - The Chain RuleChapter 2.6 - Implicit DifferentiationChapter 2.7 - Related RatesChapter 2.8 - Linear Approximation And DifferentialsChapter 3 - Inverse Functions: Exponential, Logarithmic, And Inverse Trigonometric FunctionsChapter 3.1 - Exponential FunctionsChapter 3.2 - Inverse Functions And LogarithmsChapter 3.3 - Derivatives Of Logarithmic And Exponential FunctionsChapter 3.4 - Exponential Growth And DecayChapter 3.5 - Inverse Trigonometric FunctionsChapter 3.6 - Hyperbolic FunctionsChapter 3.7 - Indeterminate Forms And L'hospital's RuleChapter 4 - Applications Of DifferentiationChapter 4.1 - Maximum And Minimum ValuesChapter 4.2 - The Mean Value TheoremChapter 4.3 - Derivatives And The Shapes Of GraphsChapter 4.4 - Curve SketchingChapter 4.5 - Optimization ProblemChapter 4.6 - Newton's MethodChapter 4.7 - AntiderivativesChapter 5 - IntegralsChapter 5.1 - Areas And DistancesChapter 5.2 - The Definite IntegralChapter 5.3 - Evaluating Definite IntegralsChapter 5.4 - The Fundamental Theorem Of CalculusChapter 5.5 - The Substitution RuleChapter 6 - Techniques Of IntegrationChapter 6.1 - Integration By PartsChapter 6.2 - Trigonometric Integrals And SubstitutionChapter 6.3 - Partial FractionsChapter 6.4 - Integration With Tables And Computer Algebra SystemsChapter 6.5 - Approximate IntegrationChapter 6.6 - Improper IntegralsChapter 7 - Applications Of IntegrationChapter 7.1 - Areas Between CurvesChapter 7.2 - VolumesChapter 7.3 - Volumes By Cylindrical ShellsChapter 7.4 - Arc LengthChapter 7.5 - Area Of A Surface Of RevolutionChapter 7.6 - Applications To Physics And EngineeringChapter 7.7 - Differential EquationsChapter 8 - SeriesChapter 8.1 - SequencesChapter 8.2 - SeriesChapter 8.3 - The Integral And Comparison TestsChapter 8.4 - Other Convergence TestsChapter 8.5 - Power SeriesChapter 8.6 - Representing Functions As Power SeriesChapter 8.7 - Taylor And Maclaurin SeriesChapter 8.8 - Applications Of Taylor PolynomialsChapter 9 - Parametric Equations And Polar CoordinatesChapter 9.1 - Parametric CurvesChapter 9.2 - Calculus With Parametric CurvesChapter 9.3 - Polar CoordinatesChapter 9.4 - Areas And Lengths In Polar CoordinatesChapter 9.5 - Conic Sections In Polar CoordinatesChapter 10 - Vectors And The Geometry Of SpaceChapter 10.1 - Three-dimensional Coordinate SystemsChapter 10.2 - VectorsChapter 10.3 - The Dot ProductChapter 10.4 - The Cross ProductChapter 10.5 - Equations Of Lines And PlanesChapter 10.6 - Cylinders And Quadratic SurfacesChapter 10.7 - Vector Functions And Space CurvesChapter 10.8 - Arc Length And CurvatureChapter 10.9 - Motion In Space: Velocity And AccelerationChapter 11 - Partial DerivativesChapter 11.1 - Functions Of Several VariablesChapter 11.2 - Limits And ContinuityChapter 11.3 - Partial DerivativesChapter 11.4 - Tangent Planes And Linear ApproximationsChapter 11.5 - The Chain RuleChapter 11.6 - Directional Derivatives And The Gradient VectorChapter 11.7 - Maximum And Minimum ValuesChapter 11.8 - Lagrange MultipliersChapter 12 - Multiple IntegralsChapter 12.1 - Double Integrals Over RectanglesChapter 12.2 - Double Integrals Over General RegionsChapter 12.3 - Double Integrals In Polar CoordinatesChapter 12.4 - Applications Of Double IntegralsChapter 12.5 - Triple IntegralsChapter 12.6 - Triple Integrals In Cylindrical CoordinatesChapter 12.7 - Triple Integrals In Spherical CoordinatesChapter 12.8 - Change Of Variables In Multiple IntegralsChapter 13 - Vector CalculusChapter 13.1 - Vector FieldsChapter 13.2 - Line IntegralsChapter 13.3 - The Fundamental Theorem For Line IntegralsChapter 13.4 - Green's TheoremChapter 13.5 - Curl And DivergenceChapter 13.6 - Parametric Surfaces And Their AreasChapter 13.7 - Surface IntegralsChapter 13.8 - Stokes' TheoremChapter 13.9 - The Divergence TheoremChapter A - TrigonometryChapter B - Sigma NotationChapter C - The Logarithm Defined As An Integral

Book Details

1. FUNCTIONS AND LIMITS. Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity. 2. DERIVATIVES. Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials. 3. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS. Exponential Functions. Inverse Functions and Logarithms. Derivatives of Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton's Method. Antiderivatives. 5. INTEGRALS. Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. 6. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. 7. APPLICATIONS OF INTEGRATION. Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Differential Equations. 8. SERIES. Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials. 9. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. 10. VECTORS AND THE GEOMETRY OF SPACE. Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Vector Functions and Space Curves. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. 11. PARTIAL DERIVATIVES. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximations. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Lagrange Multipliers. 12. MULTIPLE INTEGRALS. Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Change of Variables in Multiple Integrals. 13. VECTOR CALCULUS. Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes' Theorem. The Divergence Theorem. Appendix A. Trigonometry. Appendix B. Proofs. Appendix C. Sigma Notation. Appendix D. The Logarithm Defined as an Integral

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