Single variable calculus : early transcendentals / James Stewart
- Author:
- Stewart, James, 1941-
- Published:
- Australia ; Belmont, CA : Brooks/Cole Cengage Learning, [2012]
- Copyright Date:
- ©2012
- Edition:
- 7th ed., Student ed.
- Physical Description:
- xxviii, 784, 123 pages : illustrations (some color) ; 26 cm
- Contents:
- Machine generated contents note: 1.Functions and Models -- 1.1.Four Ways to Represent a Function -- 1.2.Mathematical Models: A Catalog of Essential Functions -- 1.3.New Functions from Old Functions -- 1.4.Graphing Calculators and Computers -- 1.5.Exponential Functions -- 1.6.Inverse Functions and Logarithms -- Review -- Principles of Problem Solving -- 2.Limits and Derivatives -- 2.1.The Tangent and Velocity Problems -- 2.2.The Limit of a Function -- 2.3.Calculating Limits Using the Limit Laws -- 2.4.The Precise Definition of a Limit -- 2.5.Continuity -- 2.6.Limits at Infinity; Horizontal Asymptotes -- 2.7.Derivatives and Rates of Change -- Writing Project Early Methods for Finding Tangents -- 2.8.The Derivative as a Function -- Review -- Problems Plus -- 3.Differentiation Rules -- 3.1.Derivatives of Polynomials and Exponential Functions -- Applied Project Building a Better Roller Coaster -- 3.2.The Product and Quotient Rules -- 3.3.Derivatives of Trigonometric Functions -- 3.4.The Chain Rule -- Applied Project Where Should a Pilot Start Descent? -- 3.5.Implicit Differentiation -- Laboratory Project Families of Implicit Curves -- 3.6.Derivatives of Logarithmic Functions -- 3.7.Rates of Change in the Natural and Social Sciences -- 3.8.Exponential Growth and Decay -- 3.9.Related Rates -- 3.10.Linear Approximations and Differentials -- Laboratory Project Taylor Polynomials -- 3.11.Hyperbolic Functions -- Review -- Problems Plus -- 4.Applications of Differentiation -- 4.1.Maximum and Minimum Values -- Applied Project The Calculus of Rainbows -- 4.2.The Mean Value Theorem -- 4.3.How Derivatives Affect the Shape of a Graph -- 4.4.Indeterminate Forms and l'Hospital's Rule -- Writing Project The Origins of l'Hospital's Rule -- 4.5.Summary of Curve Sketching -- 4.6.Graphing with Calculus and Calculators -- 4.7.Optimization Problems -- Applied Project The Shape of a Can -- 4.8.Newton's Method -- 4.9.Antiderivatives -- Review -- Problems Plus -- 5.Integrals -- 5.1.Areas and Distances -- 5.2.The Definite Integral -- Discovery Project Area Functions -- 5.3.The Fundamental Theorem of Calculus -- 5.4.Indefinite Integrals and the Net Change Theorem -- Writing Project Newton, Leibniz, and the Invention of Calculus -- 5.5.The Substitution Rule -- Review -- Problems Plus -- 6.Applications of Integration -- 6.1.Areas Between Curves -- Applied Project The Gini Index -- 6.2.Volumes -- 6.3.Volumes by Cylindrical Shells -- 6.4.Work -- 6.5.Average Value of a Function -- Applied Project Calculus and Baseball -- Applied Project Where to Sit at the Movies -- Review -- Problems Plus -- 7.Techniques of Integration -- 7.1.Integration by Parts -- 7.2.Trigonometric Integrals -- 7.3.Trigonometric Substitution -- 7.4.Integration of Rational Functions by Partial Fractions -- 7.5.Strategy for Integration -- 7.6.Integration Using Tables and Computer Algebra Systems -- Discovery Project Patterns in Integrals -- 7.7.Approximate Integration -- 7.8.Improper Integrals -- Review -- Problems Plus -- 8.Further Applications of Integration -- 8.1.Arc Length -- Discovery Project Arc Length Contest -- 8.2.Area of a Surface of Revolution -- Discovery Project Rotating on a Slant -- 8.3.Applications to Physics and Engineering -- Discovery Project Complementary Coffee Cups -- 8.4.Applications to Economics and Biology -- 8.5.Probability -- Review -- Problems Plus -- 9.Differential Equations -- 9.1.Modeling with Differential Equations -- 9.2.Direction Fields and Euler's Method -- 9.3.Separable Equations -- Applied Project How Fast Does a Tank Drain? -- Applied Project Which Is Faster, Going Up or Coming Down? -- 9.4.Models for Population Growth -- 9.5.Linear Equations -- 9.6.Predator-Prey Systems -- Review -- Problems Plus -- 10.Parametric Equations and Polar Coordinates -- 10.1.Curves Defined by Parametric Equations -- Laboratory ProjectRunning Circles around Circles -- 10.2.Calculus with Parametric Curves -- Laboratory Project Bezier Curves -- 10.3.Polar Coordinates -- Laboratory Project Families of Polar Curves -- 10.4.Areas and Lengths in Polar Coordinates -- 10.5.Conic Sections -- 10.6.Conic Sections in Polar Coordinates -- Review -- Problems Plus -- 11.Infinite Sequences and Series -- 11.1.Sequences -- Laboratory Project Logistic Sequences -- 11.2.Series -- 11.3.The Integral Test and Estimates of Sums -- 11.4.The Comparison Tests -- 11.5.Alternating Series -- 11.6.Absolute Convergence and the Ratio and Root Tests -- 11.7.Strategy for Testing Series -- 11.8.Power Series -- 11.9.Representations of Functions as Power Series -- 11.10.Taylor and Maclaurin Series -- Laboratory Project An Elusive Limit -- Writing Project How Newton Discovered the Binomial Series -- 11.11.Applications of Taylor Polynomials -- Applied Project Radiation from the Stars -- Review -- Problems Plus -- Appendixes -- A.Numbers, Inequalities, and Absolute Values -- B.Coordinate Geometry and Lines -- C.Graphs of Second-Degree Equations -- D.Trigonometry -- E.Sigma Notation -- F.Proofs of Theorems -- G.The Logarithm Defined as an Integral -- H.Complex Numbers -- I.Answers to Odd-Numbered Exercises.
- Subject(s):
- ISBN:
- 9780538498678
0538498676 - Note:
- Includes index.
- Source of Acquisition:
- Purchased with funds from the J. Harvey Fahnestock Endowment for Scientific, Engineering and Rare Books; 2013
- Endowment Note:
- J. Harvey Fahnestock Endowment for Scientific, Engineering and Rare Books
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