| Description |
xx, 1168 pages, 123 unnumbered pages : illustrations (some color), portraits ; 27 cm |
| Contents |
Machine derived contents note: Chapter 0 Before Calculus -- 0.1 Functions -- 0.2 New Functions from Old -- 0.4 Families of Functions -- 0.5 Inverse Functions; Inverse Trigonometric Functions -- 0.6 Exponential and Logarithmic Functions -- Chapter 1 Limits and Continuity -- 1.1 Limits (An Intuitive Approach) -- 1.2 Computing Limits -- 1.3 Limits at Infinity; End Behavior of a Function -- 1.4 Limits (Discussed More Rigorously) -- 1.5 Continuity -- 1.6 Continuity of Trigonometric, Exponential, and Inverse Functions -- Chapter 2 The Derivative -- 2.1 Tangent Lines and Rates of Change -- 2.2 The Derivative Function -- 2.3 Introduction to Techniques of Differentiation -- 2.4 The Product and Quotient Rules -- 2.5 Derivatives of Trigonometric Functions -- 2.6 The Chain Rule -- Chapter 3 Topics in Differentiation -- 3.1 Implicit Differentiation -- 3.2 Derivatives of Logarithmic Functions -- 3.3 Derivatives of Exponential and Inverse Trigonometric Functions -- 3.4 Related Rates -- 3.5 Local Linear Approximation; Differentials -- 3.6 L'Hp̥ital's Rule; Indeterminate Forms -- Chapter 4 The Derivative in Graphing and Applications -- 4.1 Analysis of Functions I: Increase, Decrease, and Concavity -- 4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials -- 4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents -- 4.4 Absolute Maxima and Minima -- 4.5 Applied Maximum and Minimum Problems -- 4.6 Rectilinear Motion -- 4.7 Newton's Method -- 4.8 Rolle's Theorem; Mean-Value Theorem -- Chapter 5 Integration -- 5.1 An Overview of the Area Problem -- 5.2 The Indefinite Integral -- 5.3 Integration by Substitution -- 5.4 The Definition of Area as a Limit; Sigma Notation -- 5.5 The Definite Integral -- 5.6 The Fundamental Theorem of Calculus -- 5.7 Rectilinear Motion Revisited Using Integration -- 5.8 Average Value of a Function and its Applications -- 5.9 Evaluating Definite Integrals by Substitution -- 5.10 Logarithmic and Other Functions Defined by Integrals -- Chapter 6 Applications of the Definite Integral in Geometry, Science, and Engineering -- 6.1 Area Between Two Curves -- 6.2 Volumes by Slicing; Disks and Washers -- 6.3 Volumes by Cylindrical Shells -- 6.4 Length of a Plane Curve -- 6.5 Area of a Surface of Revolution -- 6.6 Work -- 6.7 Moments, Centers of Gravity, and Centroids -- 6.8 Fluid Pressure and Force -- 6.9 Hyperbolic Functions and Hanging Cables -- Ch 7 Principles of Integral Evaluation -- 7.1 An Overview of Integration Methods -- 7.2 Integration by Parts -- 7.3 Integrating Trigonometric Functions -- 7.4 Trigonometric Substitutions -- 7.5 Integrating Rational Functions by Partial Fractions -- 7.6 Using Computer Algebra Systems and Tables of Integrals -- 7.7 Numerical Integration; Simpson's Rule -- 7.8 Improper Integrals -- Ch 8 Mathematical Modeling with Differential Equations -- 8.1 Modeling with Differential Equations -- 8,2 Separation of Variables -- 8.3 Slope Fields; Euler's Method -- 8.4 First-Order Differential Equations and Applications -- Ch 9 Infinite Series -- 9.1 Sequences -- 9.2 Monotone Sequences -- 9.3 Infinite Series -- 9.4 Convergence Tests -- 9.5 The Comparison, Ratio, and Root Tests -- 9.6 Alternating Series; Absolute and Conditional Convergence -- 9.7 Maclaurin and Taylor Polynomials -- 9.8 Maclaurin and Taylor Series; Power Series -- 9.9 Convergence of Taylor Series -- 9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series -- Ch 10 Parametric and Polar Curves; Conic Sections -- 10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves -- 10.2 Polar Coordinates -- 10.3 Tangent Lines, Arc Length, and Area for Polar Curves -- 10.4 Conic Sections -- 10.5 Rotation of Axes; Second-Degree Equations -- 10.6 Conic Sections in Polar Coordinates -- Ch 11 Three-Dimensional Space; Vectors -- 11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces -- 11.2 Vectors -- 11.3 Dot Product; Projections -- 11.4 Cross Product -- 11.5 Parametric Equations of Lines -- 11.6 Planes in 3-Space -- 11.7 Quadric Surfaces -- 11.8 Cylindrical and Spherical Coordinates -- Ch 12 Vector-Valued Functions -- 12.1 Introduction to Vector-Valued Functions -- 12.2 Calculus of Vector-Valued Functions -- 12.3 Change of Parameter; Arc Length -- 12.4 Unit Tangent, Normal, and Binormal Vectors -- 12.5 Curvature -- 12.6 Motion Along a Curve -- 12.7 Kepler's Laws of Planetary Motion -- Ch 13 Partial Derivatives -- 13.1 Functions of Two or More Variables -- 13.2 Limits and Continuity -- 13.3 Partial Derivatives -- 13.4 Differentiability, Differentials, and Local Linearity -- 13.5 The Chain Rule -- 13.6 Directional Derivatives and Gradients -- 13.7 Tangent Planes and Normal Vectors -- 13.8 Maxima and Minima of Functions of Two Variables -- 13.9 Lagrange Multipliers -- Ch 14 Multiple Integrals -- 14.1 Double Integrals -- 14.2 Double Integrals over Nonrectangular Regions -- 14.3 Double Integrals in Polar Coordinates -- 14.4 Surface Area; Parametric Surfaces} -- 14.5 Triple Integrals -- 14.6 Triple Integrals in Cylindrical and Spherical Coordinates -- 14.7 Change of Variable in Multiple Integrals; Jacobians -- 14.8 Centers of Gravity Using Multiple Integrals -- Ch 15 Topics in Vector Calculus -- 15.1 Vector Fields -- 15.2 Line Integrals -- 15.3 Independence of Path; Conservative Vector Fields -- 15.4 Green's Theorem -- 15.5 Surface Integrals -- 15.6 Applications of Surface Integrals; Flux -- 15.7 The Divergence Theorem -- 15.8 Stokes' Theorem -- Appendix [order of sections TBD] -- A Graphing Functions Using Calculators and Computer Algebra Systems -- B Trigonometry Review -- C Solving Polynomial Equations -- D Mathematical Models -- E Selected Proofs -- Web Appendices -- F Real Numbers, Intervals, and Inequalities -- G Absolute Value -- H Coordinate Planes, Lines, and Linear Functions -- I Distance, Circles, and Quadratic Functions -- J Second-Order Linear Homogeneous Differential Equations; The Vibrating String -- K The Discriminant -- Answers -- Photocredits -- Index |
| Summary |
Publisher's description: The ninth edition continues to provide engineers with an accessible resource for learning calculus. The book includes carefully worked examples and special problem types that help improve comprehension. New applied exercises demonstrate the usefulness of the mathematics. Additional summary tables with step-by-step details are also incorporated into the chapters to make the concepts easier to understand. The Quick Check and Focus on Concepts exercises have been updated as well. Engineers become engaged in the material because of the easy-to-read style and real-world examples |
| Notes |
Includes index |
| Subject |
Calculus -- Textbooks.
|
|
Calculus.
|
| Genre/Form |
Textbooks.
|
| Author |
Bivens, Irl.
|
|
Davis, Stephen, 1952-
|
| LC no. |
2010483174 |
| ISBN |
9780470183458 hardback |
|
0470183454 hardback |
|
