| Description |
xx, 1186 pages, 131 unnumbered page : illustrations (some color) ; 29 cm |
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regular print |
| Series |
Always learning |
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Always learning.
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| Contents |
Contents note continued: 12.2.Vectors in Three Dimensions -- 12.3.Dot Products -- 12.4.Cross Products -- 12.5.Lines and Curves in Space -- 12.6.Calculus of Vector-Valued Functions -- 12.7.Motion in Space -- 12.8.Length of Curves -- 12.9.Curvature and Normal Vectors -- Review Exercises -- 13.Functions of Several Variables -- 13.1.Planes and Surfaces -- 13.2.Graphs and Level Curves -- 13.3.Limits and Continuity -- 13.4.Partial Derivatives -- 13.5.The Chain Rule -- 13.6.Directional Derivatives and the Gradient -- 13.7.Tangent Planes and Linear Approximation -- 13.8.Maximum/Minimum Problems -- 13.9.Lagrange Multipliers -- Review Exercises -- 14.Multiple Integration -- 14.1.Double Integrals over Rectangular Regions -- 14.2.Double Integrals over General Regions -- 14.3.Double Integrals in Polar Coordinates -- 14.4.Triple Integrals -- 14.5.Triple Integrals in Cylindrical and Spherical Coordinates -- 14.6.Integrals for Mass Calculations -- |
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Contents note continued: 14.7.Change of Variables in Multiple Integrals -- Review Exercises -- 15.Vector Calculus -- 15.1.Vector Fields -- 15.2.Line Integrals -- 15.3.Conservative Vector Fields -- 15.4.Green's Theorem -- 15.5.Divergence and Curl -- 15.6.Surface Integrals -- 15.7.Stokes' Theorem -- 15.8.Divergence Theorem -- Review Exercises |
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Contents note continued: 4.4.Optimization Problems -- 4.5.Linear Approximation and Differentials -- 4.6.Mean Value Theorem -- 4.7.L'Hopital's Rule -- 4.8.Newton's Method -- 4.9.Antiderivatives -- Review Exercises -- 5.Integration -- 5.1.Approximating Areas under Curves -- 5.2.Definite Integrals -- 5.3.Fundamental Theorem of Calculus -- 5.4.Working with Integrals -- 5.5.Substitution Rule -- Review Exercises -- 6.Applications of Integration -- 6.1.Velocity and Net Change -- 6.2.Regions Between Curves -- 6.3.Volume by Slicing -- 6.4.Volume by Shells -- 6.5.Length of Curves -- 6.6.Surface Area -- 6.7.Physical Applications -- 6.8.Logarithmic and Exponential Functions Revisited -- 6.9.Exponential Models -- 6.10.Hyperbolic Functions -- Review Exercises -- 7.Integration Techniques -- 7.1.Basic Approaches -- 7.2.Integration by Parts -- 7.3.Trigonometric Integrals -- 7.4.Trigonometric Substitutions -- 7.5.Partial Fractions -- 7.6.Other Integration Strategies -- 7.7.Numerical Integration -- |
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Contents note continued: 7.8.Improper Integrals -- Review Exercises -- 8.Differential Equations -- 8.1.Basic Ideas -- 8.2.Direction Fields and Euler's Method -- 8.3.Separable Differential Equations -- 8.4.Special First-Order Differential Equations -- 8.5.Modeling with Differential Equations -- Review Exercises -- 9.Sequences and Infinite Series -- 9.1.An Overview -- 9.2.Sequences -- 9.3.Infinite Series -- 9.4.The Divergence and Integral Tests -- 9.5.The Ratio, Root, and Comparison Tests -- 9.6.Alternating Series -- Review Exercises -- 10.Power Series -- 10.1.Approximating Functions with Polynomials -- 10.2.Properties of Power Series -- 10.3.Taylor Series -- 10.4.Working with Taylor Series -- Review Exercises -- 11.Parametric and Polar Curves -- 11.1.Parametric Equations -- 11.2.Polar Coordinates -- 11.3.Calculus in Polar Coordinates -- 11.4.Conic Sections -- Review Exercises -- 12.Vectors and Vector-Valued Functions -- 12.1.Vectors in the Plane -- |
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Machine generated contents note: 1.Functions -- 1.1.Review of Functions -- 1.2.Representing Functions -- 1.3.Inverse, Exponential, and Logarithmic Functions -- 1.4.Trigonometric Functions and Their Inverses -- Review Exercises -- 2.Limits -- 2.1.The Idea of Limits -- 2.2.Definitions of Limits -- 2.3.Techniques for Computing Limits -- 2.4.Infinite Limits -- 2.5.Limits at Infinity -- 2.6.Continuity -- 2.7.Precise Definitions of Limits -- Review Exercises -- 3.Derivatives -- 3.1.Introducing the Derivative -- 3.2.Rules of Differentiation -- 3.3.The Product and Quotient Rules -- 3.4.Derivatives of Trigonometric Functions -- 3.5.Derivatives as Rates of Change -- 3.6.The Chain Rule -- 3.7.Implicit Differentiation -- 3.8.Derivatives of Logarithmic and Exponential Functions -- 3.9.Derivatives of Inverse Trigonometric Functions -- 3.10.Related Rates -- Review Exercises -- 4.Applications of the Derivative -- 4.1.Maxima and Minima -- 4.2.What Derivatives Tell Us -- 4.3.Graphing Functions -- |
| Notes |
Includes index |
| Subject |
Calculus -- Textbooks.
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Transcendental functions -- Textbooks.
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| Genre/Form |
Textbooks.
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| Author |
Briggs, William L.
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| LC no. |
2011044521 |
| ISBN |
0321785371 |
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9780321785374 |
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